Ch5 Regression Forecasting Causal Test Bank Docx

Forecasting and Predictive Analytics with Forecast X, 7e (Keating)

Chapter 5 Explanatory Models 1. Forecasting with Multiple Regression Causal Models

1) A regression of retail sales on disposable income and two interest rates, the prime rate and the short-term savings rate, is likely to have the problem of

A) seasonality.

B) heteroscedasticity.

C) multicollinearity.

D) serial correlation.

E) None of the options are correct.

2) Perfect multicollinearity is the

A) presence of a perfect linear association among independent variables in the sample.

B) presence of zero linear association among independent variables in the sample.

C) presence of significant covariation between adjacent residuals.

D) absence of significant covariation between adjacent residuals.

E) None of the options are correct.

3) Dummy variables

A) are used to measure the presence or absence of a certain attribute.

B) can be used to model the effects of seasonality in the data.

C) take on the value of either zero or one.

D) are indicator random variables.

E) All of the options are correct.

4) Personnel Test

The personnel department of a large manufacturing firm selected a random sample of 23 workers. The workers were interviewed and given several tests. On the basis of the test results, the following variables were investigated: X2 = manual dexterity score, X3 = mental aptitude score, and X4 = personnel assessment score.

Subsequently, the workers were observed in order to determine the average number of units of work completed (Y) in a given time period for each worker. Regression analysis yielded these results:

Adjusted

−212

1.90X2

2.00X3

0.25X4

0.75.

(0.50)

(0.060)

(0.20)

Note: The numbers shown in parentheses below the coefficients are the standard errors of the coefficients.

The quantities in parentheses are the standard errors of the regression coefficients. The standard error of the regression is 25, and the standard deviation of the dependent variable is 50.

Which variables are making a significant contribution to the prediction of units of work completed at the 0.01 significance level (two tailed)?

A) All three variables

B) Manual dexterity and personnel assessment

C) Manual dexterity and mental aptitude

D) Personnel assessment

E) None of the variables are statistically significant.

5) Personnel Test

Subsequently, the workers were observed in order to determine the average number of units of work completed (Y) in a given time period for each worker. Regression analysis yielded these results:

Adjusted

−212

1.90X2

2.00X3

0.25X4

0.75.

(0.50)

(0.060)

(0.20)

Note: The numbers shown in parentheses below the coefficients are the standard errors of the coefficients.

The quantities in parentheses are the standard errors of the regression coefficients. The standard error of the regression is 25, and the standard deviation of the dependent variable is 50.

Which of the following statements is the correct interpretation of the mental aptitude regression coefficient?

A) If we increase mental aptitude by one unit, holding the predictor variables constant, units of work completed will increase by an average of 2.0.

B) If we increase units of work completed by one unit, holding the other predictor variables constant, the mental aptitude score will increase by an average of 2.0.

C) If we increase mental aptitude by one unit, holding the other predictor variables constant, units of work completed will increase by an average of 0.6.

D) If we increase mental aptitude by one unit, holding the other predictor variables constant, units of work completed will decrease by an average of 0.6.

E) If we increase mental aptitude by one unit, units of work completed will increase by an average of 2.0 even if the other predictor variables change.

6) Personnel Test

Subsequently, the workers were observed in order to determine the average number of units of work completed (Y) in a given time period for each worker. Regression analysis yielded these results:

Adjusted

−212

1.90X2

2.00X3

0.25X4

0.75.

(0.50)

(0.060)

(0.20)

Note: The numbers shown in parentheses below the coefficients are the standard errors of the coefficients.

The quantities in parentheses are the standard errors of the regression coefficients. The standard error of the regression is 25, and the standard deviation of the dependent variable is 50.

What percent of the variation of units of work completed can be explained by this model?

A) 50

B) 25

C) 90

D) 60

E) 75

7) Personnel Test

Subsequently, the workers were observed in order to determine the average number of units of work completed (Y) in a given time period for each worker. Regression analysis yielded these results:

−212

1.90X2

2.00X3

0.25X4

0.75.

(0.50)

(0.060)

(0.20)

Note: The numbers shown in parentheses below the coefficients are the standard errors of the coefficients.

The quantities in parentheses are the standard errors of the regression coefficients. The standard error of the regression is 25, and the standard deviation of the dependent variable is 50.

What is the correct estimate for the number of units of work completed by a worker with a manual dexterity score of 100, a mental aptitude score of 80 and a personnel assessment score of 10? Use the regression estimated, as given, to make this calculation.

A) 140.5

B) 154.3

C) 105.5

D) 138.0

E) 150.0

8) Personnel Test

Subsequently, the workers were observed in order to determine the average number of units of work completed (Y) in a given time period for each worker. Regression analysis yielded these results:

−212

1.90X2

2.00X3

0.25X4

0.75.

(0.50)

(0.060)

(0.20)

Note: The numbers shown in parentheses below the coefficients are the standard errors of the coefficients.

The quantities in parentheses are the standard errors of the regression coefficients. The standard error of the regression is 25, and the standard deviation of the dependent variable is 50.

What is the table t value to test whether a regression coefficient is statistically significant at the 0.05 level (one tailed) for this problem?

A) 1.729

B) 2.093

C) 1.725

D) 2.086

E) 1.328

9) Graphically, a linear least squares multiple regression model with two independent variables looks like a

A) line.

B) plane.

C) hyperplane.

D) rectangle.

E) quadrilateral.

10) A multiple regression model using 200 data points (with three independent variables) has how many degrees of freedom for testing the statistical significance of individual slope coefficients?

A) 199

B) 198

C) 197

D) 196

11) Using the significance levels reported by ForecastXTM, at what level can we reject a one-sided null relating to a slope coefficient's statistical significance such that we are 95% confident?

A) 0.12

B) 0.11

C) 0.1

D) 0.09

E) None of the options are correct.

12) The value of the F-statistic applied to multiple regression can be rewritten in terms of the estimated

A) R-squared.

B) Durbin-Watson statistic.

C) standard error of the Y-intercept.

D) correlation between independent variables.

E) None of the options are correct.

13) What action may reduce multicollinearity when two independent variables have a common trend?

A) Squaring one of the variables

B) Subtracting one from the other

C) First-differencing the data

D) Dividing one by the other

E) All of the options are correct.

14) If autocorrelation is caused by an omitted variable, which technique is not likely to reduce any bias due to the omitted variable?

A) Respecify the model.

B) Apply Cochrane-Orcutt.

C) Add another independent variable.

D) Add a squared value of an independent variable.

E) None of the options are correct.

15) Which of the following is not recommended in selecting the correct set of independent variables for multiple regression?

A) R-squared

B) Adjusted R-squared

C) Akaike Information Criterion

D) Bayesian Information Criterion

E) None of the options are correct.

16) How are the AIC and BIC model selection criteria used in the model selection process for multiple regression?

A) AIC is minimized whereas BIC is maximized.

B) AIC is maximized whereas BIC is minimized.

C) Both AIC and BIC are maximized.

D) Both AIC and BIC are minimized.

E) None of the options are correct.

17) Which of the following is not correct about near multicollinearity?

A) It arises when we have two or more independent variables which essentially measure the same effect on the dependent variable.

B) It arises when we have two or more independent variables which are highly correlated.

C) It is often indicated by a large value of the calculated F statistic for the multiple regression model accompanied by relatively small values of the calculated t-statistics for individual parameters.

D) It is often indicated by coefficient signs that seem to violate business and economic logic accompanied by relatively small values of the calculated t-statistics for individual parameters.

E) It is often indicated by coefficient signs that seem to violate business and economic logic accompanied by relatively large values of the calculated t-statistics for individual parameters.

18) Estimated Demand Function

The following is an estimated demand function:

875

6XA

15Y

−

(125)

(2)

(−1.2)

Where Q is quantity sold, XA is advertising expenditure (in thousands of dollars), Y is income (in thousands of dollars), and P is the good's price. The standard errors for each estimate are in parentheses. The equation has been estimated from 10 years of quarterly data. The R2 was 0.92; the F-statistic was 57; the Standard Error of the Estimate (SEE) is 25.

According to the common 95 percent level of significance (estimated) for the regression above,

A) all variables are probably significant.

B) only price is significant.

C) no variable is significant.

D) both income and price are significant.

19) Estimated Demand Function

The following is an estimated demand function:

875

6XA

15Y

−

(125)

(2)

(−1.2)

Suppose the values of the explanatory variables next period are: Advertising = $100,000; Income = $10,000; and Price = $100. Using the above fitted regression, what is the predicted value of sales?

A) 2125

B) 1625

C) 1125

D) 1870

E) Unable to determine from the information given.

20) Estimated Demand Function

The following is an estimated demand function:

875

6XA

15Y

−

(125)

(2)

(−1.2)

Where Q is quantity sold, XA is advertising expenditure (in thousands of dollars), Y is income (in thousands of dollars), and P is the good's price. The standard errors for each estimate are in parentheses. The equation has been estimated from 10 years of quarterly data. The adjusted R2 was 0.92; the F-statistic was 57; the Standard Error of the Estimate (SEE) is 25. Suppose the values of the explanatory variables next period are: Advertising = $100,000; Income = $10,000; and Price = $100.

For the above regression, an estimated 95 percent confidence interval around the sales prediction would be

A) 1125 to 1225.

B) 1025 to 1125.

C) 1425 to 1850.

D) 1760 to 1920.

E) 1075 to 1175.

21) Which of the following "goodness-of-fit" measures should not be used in the context of multiple regression?

A) The F statistic

B) The Durbin-Watson statistic

C) The Simple Coefficient of Determination

D) The AIC and BIC criteria

E) None of the options are correct.

22) The F-statistic in the multiple regression model

A) is used to test for the presence of serial correlation.

B) tests for the presence of first-order autocorrelation.

C) tests for the overall significance of the estimated multiple regression.

D) is used to test for data non-linearity.

E) All of the options are correct.

23) The F-statistic in the multiple regression model

A) tests a joint hypothesis that all of the coefficients are equal to zero at the same time.

B) is used to measure a regression "goodness of fit."

C) tests the significance of the R-squared statistic.

D) tests a common null for all regression slope coefficients.

E) All of the options are correct.

24) A potential diagnosis and/or cure for the multicollinearity problem does not include

A) dropping all but one of the highly correlated independent variables from the model.

B) valuing variables in nominal, not real, terms.

C) testing for a high degree of correlation among the independent variables.

D) comparing signs and sizes of estimated coefficients with what is expected on the basis of economic theory.

E) All of the options are correct.

25) Forecasters who base model selection criteria on the maximization of R2 should

A) be wary that extremely high values of R2 may indicate a definitional relationship rather than causal as required by the multiple regression models.

B) be aware that the simple R-squared measure is suspect when autocorrelation is present.

C) be aware that R-squared can be made arbitrarily large by adding additional explanatory variables to the model.

D) instead use the adjusted R-squared measure.

E) All of the options are correct.

26) Multicollinearity in a regression model occurs when

A) the Durbin-Watson statistic and the R-squared are correlated.

B) there is some correlation among the residuals and the values of the explanatory variables.

C) there is no correlation between the forecast error in one period and the error in the next period.

D) a nonlinear specification is used.

E) None of the options are correct.

27) Which statement is not correct?

A) R-squared is a measure of the degree of variability in the dependent variable about its sample mean explained by the regression line.

B) The adjusted R-squared measure should be used in the case of more than one independent variable.

C) The null hypothesis that R2 = 0 can be tested using the F-statistic.

D) Forecasters should always select independent variables on the basis of R2.

E) All of the options are correct.

28) When autocorrelation is present, which of the following is true?

A) Regression coefficient estimates are biased.

B) The t and F distributions are no longer applicable.

C) The D-W statistic is close to minus one.

D) Spurious regression

E) None of the options are correct.

29) The F-test in multiple regression

A) is used to test for the presence of autocorrelation.

B) tests for the presence of first-order autocorrelation.

C) tests the significance of the Durbin-Watson statistic.

D) tests a null involving all regression slope coefficients simultaneously.

E) is used to test the significance of individual coefficients.

30) The Durbin-Watson statistic

A) is used to test the null hypothesis of first-order autocorrelation.

B) has a t distribution with N − (K + 1) degrees of freedom.

C) is the squared value of the F-statistic.

D) is used to test the null of no multicollinearity.

E) None of the options are correct.

31) Which of the following statements are true?

A) Autocorrelation arises when there is a perfect linear association between the dependent and independent variables.

B) Autocorrelation implies the error terms have differing variances.

C) Autocorrelation causes the estimated regression standard error to be biased.

D) Autocorrelation can be tested using the F-statistic.

32) The inclusion of seasonal dummy variables to a multiple regression model may help eliminate

A) autocorrelation if the data are characterized by seasonal fluctuations.

B) perfect multicollinearity.

C) near multicollinearity.

D) bias in OLS slope estimates caused by autocorrelation.

E) All of the options are correct.

33) Consider the following group: R-squared, Adjusted R-squared, Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC). Which one doesn't belong with the rest of the others?

A) R-squared

B) Adjusted R-squared

C) Akaike Information Criterion (AIC)

D) Bayesian Information Criterion (BIC)

34) Model A has an AIC number of 300 whereas model B has an AIC number of 400 (both models have the same dependent variable). This suggests that which model is more correctly specified?

A) Model A

B) Model B

C) Can't tell without knowing sample size.

D) Not enough information is provided.

35) Which of the following is not correct? Seasonality in a time series data set containing quarterly observations can be handled by

A) using four dummy variables, one for each season.

B) using three dummy variables to represent any three of the quarters.

C) using Winter's smoothing.

D) deseasonalizing the data and then applying nonseasonal methods.

36) A company has computed a seasonal index for its quarterly sales. Which of the following statements about the index is not correct?

A) The sum of the four quarterly index numbers should be 4.

B) An index of 0.75 for the first quarter indicates that sales were 25 percent lower than the average quarterly sales.

C) An index of 1.1 for the second quarter indicates that sales were 10 percent above the average quarterly sales.

D) The index for any quarter must be between zero and 2.

E) The average index for each of the four quarters should be 1.

37) How would you model the effect of rain on attendance to a soccer game?

A) Create a dummy variable to represent rain and a second dummy variable to represent no rain.

B) Introduce a variable measuring the inches of rain for a given day.

C) Create a single rain dummy variable.

D) Omit rain days from the data set.

E) All of the options are correct.

38) Which of the following is probably not a potential cause of data seasonality?

A) Weather

B) Cultural Traditions

C) Religious Traditions

D) Government Behavior

E) All of the options could be a potential cause of data seasonality.

39) Quarterly seasonal dummy variables take on values

A) 1 to 4.

B) 1 to 3.

C) 0 to 3.

D) 0 to 4.

E) None of the options are correct.

40) Including male and female dummy variables in the same regression to represent sex will likely result in

A) near multicollinearity.

B) perfect multicollinearity.

C) serial correlation.

D) heteroscedasticity.

E) All of the options are correct.

41) In using quarterly time series data, which quarter can serve as the base period for interpretation of dummy variables?

A) Quarter one

B) Quarter two

C) Quarter three

D) Quarter four

E) Any of the above.

42) In a regression of sales on income and seasonal dummy variables for a quarterly time series, a negative sign of the quarter 3 dummy variable means

A) sales for quarter three are negative.

B) sales for quarter three are below average.

C) sales for quarter three are below that of the base quarter.

D) sales for quarter three are above average.

E) None of the options are correct.

43) Adding a lagged value of the dependent variable to a regression model may

A) increase serial correlation.

B) induce heteroscedasticity.

C) help model the speed of adjustment in the dependent variable.

D) induce data nonlinearity.

E) None of the options are correct.

44) Which of the following is not useful advice in using multiple regression to generate forecasts?

A) One should always prefer quantitative models to subjective expertise.

B) Keep the model simple.

C) Use the AIC and BIC measures to help in selecting the appropriate set of independent variables.

D) Focus on model accuracy rather than model fit.

E) All of the options are correct.

45) Large and complicated forecasting models

A) are expensive to maintain.

B) are hard to explain to upper-level management.

C) tend to be distrusted by management.

D) tend to put too much emphasis on quantitative aspects of forecasting.

E) All of the options are correct.

46) Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		1,834,180.23		5		366,836.05
Error		494,506.47		34		14,544.31		120.60
Total		2,328,686.70		39

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
DCS	Dependent	3,266.66	288.10	11.34
DCSP	Yes	-0.10	0.01	-7.18
PR	Yes	-21.17	13.77	-1.54
Q2	Yes	292.88	54.02	5.42
Q3	Yes	149.07	54.11	2.76
Q4	Yes	-60.25	54.22	-1.11

Series Description	P-value	F-test	Elasticity	Overall F-test
DCS	0.00	128.56		25.22
DCSP	0.00	51.50	-0.76
PR	0.13	2.36	-0.11
Q2	0.00	29.39	0.04
Q3	0.01	7.59	0.02
Q4	0.27	1.23	-0.01

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	492.41		Durbin Watson	1.62
BIC	494.10		Mean	1,802.86
Mean Absolute Percentage Error (MAPE)	5.30	%	Standard Deviation	244.36
R-Square	78.76	%	Max	2,272.60
Adjusted R-Square	75.64	%	Min	1,421.30
Root Mean Square Error	111.19		Range	851.30

Does the regression pass the "first quick check (i.e., economic realism)?"

A) No, because the sign of one of the regression coefficients is incorrect.

B) Yes, because the signs of all the regression coefficients are correct.

C) No, because the price variable does not make economic sense to include in the regression.

D) Yes, because the SEE passes its statistical test.

47) Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		1,834,180.23		5		366,836.05
Error		494,506.47		34		14,544.31		120.60
Total		2,328,686.70		39

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
DCS	Dependent	3,266.66	288.10	11.34
DCSP	Yes	-0.10	0.01	-7.18
PR	Yes	-21.17	13.77	-1.54
Q2	Yes	292.88	54.02	5.42
Q3	Yes	149.07	54.11	2.76
Q4	Yes	-60.25	54.22	-1.11

Series Description	P-value	F-test	Elasticity	Overall F-test
DCS	0.00	128.56		25.22
DCSP	0.00	51.50	-0.76
PR	0.13	2.36	-0.11
Q2	0.00	29.39	0.04
Q3	0.01	7.59	0.02
Q4	0.27	1.23	-0.01

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	492.41		Durbin Watson	1.62
BIC	494.10		Mean	1,802.86
Mean Absolute Percentage Error (MAPE)	5.30	%	Standard Deviation	244.36
R-Square	78.76	%	Max	2,272.60
Adjusted R-Square	75.64	%	Min	1,421.30
Root Mean Square Error	111.19		Range	851.30

For the domestic car sales regression, which variable coefficients pass the "second quick check (i.e., statistical significance)?"

A) All of the coefficients pass.

B) None of the coefficients pass.

C) Those that pass are DCSP, Q2, and Q3.

D) Those that pass are DCSP, PR, and Q4.

E) Those that pass are Q2, Q3, and Q4.

48) Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		1,834,180.23		5		366,836.05
Error		494,506.47		34		14,544.31		120.60
Total		2,328,686.70		39

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
DCS	Dependent	3,266.66	288.10	11.34
DCSP	Yes	-0.10	0.01	-7.18
PR	Yes	-21.17	13.77	-1.54
Q2	Yes	292.88	54.02	5.42
Q3	Yes	149.07	54.11	2.76
Q4	Yes	-60.25	54.22	-1.11

Series Description	P-value	F-test	Elasticity	Overall F-test
DCS	0.00	128.56		25.22
DCSP	0.00	51.50	-0.76
PR	0.13	2.36	-0.11
Q2	0.00	29.39	0.04
Q3	0.01	7.59	0.02
Q4	0.27	1.23	-0.01

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	492.41		Durbin Watson	1.62
BIC	494.10		Mean	1,802.86
Mean Absolute Percentage Error (MAPE)	5.30	%	Standard Deviation	244.36
R-Square	78.76	%	Max	2,272.60
Adjusted R-Square	75.64	%	Min	1,421.30
Root Mean Square Error	111.19		Range	851.30

For the domestic car sales regression above, the "third quick check" shows what (i.e., accuracy)?

A) It shows that more than three-quarters of the variation in DCS is explained.

B) It shows that almost no serial correlation exists.

C) It shows that a great deal of seasonality exists in the data.

D) It shows that a small trend exists in the data.

49) Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		1,834,180.23		5		366,836.05
Error		494,506.47		34		14,544.31		120.60
Total		2,328,686.70		39

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
DCS	Dependent	3,266.66	288.10	11.34
DCSP	Yes	-0.10	0.01	-7.18
PR	Yes	-21.17	13.77	-1.54
Q2	Yes	292.88	54.02	5.42
Q3	Yes	149.07	54.11	2.76
Q4	Yes	-60.25	54.22	-1.11

Series Description	P-value	F-test	Elasticity	Overall F-test
DCS	0.00	128.56		25.22
DCSP	0.00	51.50	-0.76
PR	0.13	2.36	-0.11
Q2	0.00	29.39	0.04
Q3	0.01	7.59	0.02
Q4	0.27	1.23	-0.01

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	492.41		Durbin Watson	1.62
BIC	494.10		Mean	1,802.86
Mean Absolute Percentage Error (MAPE)	5.30	%	Standard Deviation	244.36
R-Square	78.76	%	Max	2,272.60
Adjusted R-Square	75.64	%	Min	1,421.30
Root Mean Square Error	111.19		Range	851.30

In the domestic car sales regression above, what evidence do you have of any pattern in the error terms?

A) The SEE indicates a high probability of a pattern in the error terms.

B) The AIC and BIC both indicate a pattern in the error terms.

C) There are no error terms in this regression and so there can be no pattern.

D) The Durbin Watson statistic indicates little pattern in the error terms.

50) Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		1,834,180.23		5		366,836.05
Error		494,506.47		34		14,544.31		120.60
Total		2,328,686.70		39

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
DCS	Dependent	3,266.66	288.10	11.34
DCSP	Yes	-0.10	0.01	-7.18
PR	Yes	-21.17	13.77	-1.54
Q2	Yes	292.88	54.02	5.42
Q3	Yes	149.07	54.11	2.76
Q4	Yes	-60.25	54.22	-1.11

Series Description	P-value	F-test	Elasticity	Overall F-test
DCS	0.00	128.56		25.22
DCSP	0.00	51.50	-0.76
PR	0.13	2.36	-0.11
Q2	0.00	29.39	0.04
Q3	0.01	7.59	0.02
Q4	0.27	1.23	-0.01

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	492.41		Durbin Watson	1.62
BIC	494.10		Mean	1,802.86
Mean Absolute Percentage Error (MAPE)	5.30	%	Standard Deviation	244.36
R-Square	78.76	%	Max	2,272.60
Adjusted R-Square	75.64	%	Min	1,421.30
Root Mean Square Error	111.19		Range	851.30

For the domestic car sales regression above, assume that:

DCSP = $10,000

PR = 10 percent

and that it is the first quarter of the year.

What will DCS be predicted to be by the regression model?

A) 6,545.45

B) 1,858.62

C) 3,466.16

D) 2,054.96

51) Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		1,834,180.23		5		366,836.05
Error		494,506.47		34		14,544.31		120.60
Total		2,328,686.70		39

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
DCS	Dependent	3,266.66	288.10	11.34
DCSP	Yes	-0.10	0.01	-7.18
PR	Yes	-21.17	13.77	-1.54
Q2	Yes	292.88	54.02	5.42
Q3	Yes	149.07	54.11	2.76
Q4	Yes	-60.25	54.22	-1.11

Series Description	P-value	F-test	Elasticity	Overall F-test
DCS	0.00	128.56		25.22
DCSP	0.00	51.50	-0.76
PR	0.13	2.36	-0.11
Q2	0.00	29.39	0.04
Q3	0.01	7.59	0.02
Q4	0.27	1.23	-0.01

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	492.41		Durbin Watson	1.62
BIC	494.10		Mean	1,802.86
Mean Absolute Percentage Error (MAPE)	5.30	%	Standard Deviation	244.36
R-Square	78.76	%	Max	2,272.60
Adjusted R-Square	75.64	%	Min	1,421.30
Root Mean Square Error	111.19		Range	851.30

For the domestic car sales regression above, assume that:

DCSP = $10,000

PR = 10 percent

and that it is the first quarter of the year.

What will be the approximate 95% confidence interval for the DCS prediction?

A) 2296 to 1814

B) 1649 to 2039

C) 2964 to 4126

D) 4620 to 7156

52) Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		1,834,180.23		5		366,836.05
Error		494,506.47		34		14,544.31		120.60
Total		2,328,686.70		39

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
DCS	Dependent	3,266.66	288.10	11.34
DCSP	Yes	-0.10	0.01	-7.18
PR	Yes	-21.17	13.77	-1.54
Q2	Yes	292.88	54.02	5.42
Q3	Yes	149.07	54.11	2.76
Q4	Yes	-60.25	54.22	-1.11

Series Description	P-value	F-test	Elasticity	Overall F-test
DCS	0.00	128.56		25.22
DCSP	0.00	51.50	-0.76
PR	0.13	2.36	-0.11
Q2	0.00	29.39	0.04
Q3	0.01	7.59	0.02
Q4	0.27	1.23	-0.01

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	492.41		Durbin Watson	1.62
BIC	494.10		Mean	1,802.86
Mean Absolute Percentage Error (MAPE)	5.30	%	Standard Deviation	244.36
R-Square	78.76	%	Max	2,272.60
Adjusted R-Square	75.64	%	Min	1,421.30
Root Mean Square Error	111.19		Range	851.30

In the domestic car sales function, there is evidence of seasonality. How does the regression model show this evidence?

A) With the Durbin Watson statistic

B) With the t-statistics on the dummy variables

C) With the SEE

D) With the F-statistic

E) With the R-Square

53) Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		1,834,180.23		5		366,836.05
Error		494,506.47		34		14,544.31		120.60
Total		2,328,686.70		39

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
DCS	Dependent	3,266.66	288.10	11.34
DCSP	Yes	-0.10	0.01	-7.18
PR	Yes	-21.17	13.77	-1.54
Q2	Yes	292.88	54.02	5.42
Q3	Yes	149.07	54.11	2.76
Q4	Yes	-60.25	54.22	-1.11

Series Description	P-value	F-test	Elasticity	Overall F-test
DCS	0.00	128.56		25.22
DCSP	0.00	51.50	-0.76
PR	0.13	2.36	-0.11
Q2	0.00	29.39	0.04
Q3	0.01	7.59	0.02
Q4	0.27	1.23	-0.01

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	492.41		Durbin Watson	1.62
BIC	494.10		Mean	1,802.86
Mean Absolute Percentage Error (MAPE)	5.30	%	Standard Deviation	244.36
R-Square	78.76	%	Max	2,272.60
Adjusted R-Square	75.64	%	Min	1,421.30
Root Mean Square Error	111.19		Range	851.30

For the domestic car sales regression, the multiple coefficient of determination shows that

A) 120.60 is the error associated with the independent variable.

B) 288.10 will be the error associated with DCS.

C) 3,266.66 will be the most likely value of DCS.

D) 75.64% of the variation in DCS is explained by variation in the independent variables.

54) Domestic Car Sales

Consider the following multiple regression model of domestic car sales (DCS) where:

DCS = domestic car sales

DCSP = domestic car sales price (in dollars)

PR = prime rate as a percent (i.e., 10% would be entered as 10)

Q2 = quarter 2 dummy variable

Q3 = quarter 3 dummy variable

Q4 = quarter 4 dummy variable

Multiple Regression — Result Formula

DCS = 3,266.66 + ((DCSP) × −0.098297) + ((PR) × −21.17) + ((Q2) × 292.88) + ((Q3) × 149.07) + ((Q4) × −60.25)

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		1,834,180.23		5		366,836.05
Error		494,506.47		34		14,544.31		120.60
Total		2,328,686.70		39

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
DCS	Dependent	3,266.66	288.10	11.34
DCSP	Yes	-0.10	0.01	-7.18
PR	Yes	-21.17	13.77	-1.54
Q2	Yes	292.88	54.02	5.42
Q3	Yes	149.07	54.11	2.76
Q4	Yes	-60.25	54.22	-1.11

Series Description	P-value	F-test	Elasticity	Overall F-test
DCS	0.00	128.56		25.22
DCSP	0.00	51.50	-0.76
PR	0.13	2.36	-0.11
Q2	0.00	29.39	0.04
Q3	0.01	7.59	0.02
Q4	0.27	1.23	-0.01

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	492.41		Durbin Watson	1.62
BIC	494.10		Mean	1,802.86
Mean Absolute Percentage Error (MAPE)	5.30	%	Standard Deviation	244.36
R-Square	78.76	%	Max	2,272.60
Adjusted R-Square	75.64	%	Min	1,421.30
Root Mean Square Error	111.19		Range	851.30

The domestic car sales model

A) could be used to forecast DCS at some future date.

B) was estimated using a least squares model.

C) is a linear model.

D) All of the options are correct.

E) None of the options are correct.

55) The AIC can be of help in model selection when choosing among

A) coefficients in a multiple regression.

B) appropriate lag structures.

C) different orders of a polynomial regression.

D) All of the options are correct.

56) The Akaike rule of thumb is

A) if the AIC is between 0 to 2 from the "best" model, there is substantial support for both models.

B) if the AIC is between 4 and 7 from the "best" model, there is substantial support for both models.

C) if the AIC is negative, neither model can be optimal.

D) if the AIC is less than 10, there is substantial support for neither model.

57) Use the Akaike criterion

A) in observational studies when there are large numbers of variables.

B) in exploratory studies when you have no a priori hypotheses.

C) in experimental studies when you are testing few effects.

D) to select the correct degrees of freedom to use in evaluating summary statistics.

58) ForecastX Regressions

Exhibit #1

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
SALES	Dependent	-51.24	54.32	-0.94
PRICE	Yes	30.92	10.32	3.00

Series Description	P-value	F-test	Elasticity	Overall F-test
SALES	0.36	0.89		8.98
PRICE	0.01	8.98	1.46

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		SALES		PRICE
SALES		Dependent		1.00		0.63
PRICE		Yes		0.63		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	130.02		Durbin Watson(1)	0.34
BIC	130.80		Mean	111.19
Mean Absolute Percentage Error (MAPE)	10.67	%	Standard Deviation	17.49
R-Square	39.07	%	Ljung-Box	39.71
Adjusted R-Square	34.72	%
Root Mean Square Error	13.22

Exhibit #2

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
SALES	Dependent	123.47	19.40	6.36
PRICE	Yes	-24.84	4.95	-5.02
INCOME	Yes	0.03	0.00	13.55

Series Description	P-value	F-test	Elasticity	Overall F-test
SALES	0.00	40.51		154.86
PRICE	0.00	25.17	-1.17
INCOME	0.00	183.62	1.06

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		SALES		PRICE		INCOME
SALES		Dependent		1.00		0.63		0.94
PRICE		Yes		0.63		1.00		0.83
INCOME		Yes		0.94		0.83		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	86.56		Durbin Watson(1)	1.67
BIC	87.34		Mean	111.19
Mean Absolute Percentage Error (MAPE)	2.22	%	Standard Deviation	17.49
R-Square	95.97	%	Ljung-Box	15.22
Adjusted R-Square	95.35	%
Root Mean Square Error	3.40

Consider the two regressions presented above in answering the following questions.

In the simple regression above,

A) the first quick check fails.

B) the second quick check fails.

C) there does not appear to be first order serial correlation.

D) the independent variable is Sales.

59) ForecastX Regressions

Exhibit #1

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
SALES	Dependent	-51.24	54.32	-0.94
PRICE	Yes	30.92	10.32	3.00

Series Description	P-value	F-test	Elasticity	Overall F-test
SALES	0.36	0.89		8.98
PRICE	0.01	8.98	1.46

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		SALES		PRICE
SALES		Dependent		1.00		0.63
PRICE		Yes		0.63		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	130.02		Durbin Watson(1)	0.34
BIC	130.80		Mean	111.19
Mean Absolute Percentage Error (MAPE)	10.67	%	Standard Deviation	17.49
R-Square	39.07	%	Ljung-Box	39.71
Adjusted R-Square	34.72	%
Root Mean Square Error	13.22

Exhibit #2

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
SALES	Dependent	123.47	19.40	6.36
PRICE	Yes	-24.84	4.95	-5.02
INCOME	Yes	0.03	0.00	13.55

Series Description	P-value	F-test	Elasticity	Overall F-test
SALES	0.00	40.51		154.86
PRICE	0.00	25.17	-1.17
INCOME	0.00	183.62	1.06

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		SALES		PRICE		INCOME
SALES		Dependent		1.00		0.63		0.94
PRICE		Yes		0.63		1.00		0.83
INCOME		Yes		0.94		0.83		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	86.56		Durbin Watson(1)	1.67
BIC	87.34		Mean	111.19
Mean Absolute Percentage Error (MAPE)	2.22	%	Standard Deviation	17.49
R-Square	95.97	%	Ljung-Box	15.22
Adjusted R-Square	95.35	%
Root Mean Square Error	3.40

Consider the two regressions shown above.

A) The simple regression is probably overfit.

B) The simple regression is probably underfit.

C) The multiple regression has only one significant independent variable.

D) The multiple regression probably suffers from rampant multicollinearity.

60) ForecastX Regressions

Exhibit #1

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
SALES	Dependent	-51.24	54.32	-0.94
PRICE	Yes	30.92	10.32	3.00

Series Description	P-value	F-test	Elasticity	Overall F-test
SALES	0.36	0.89		8.98
PRICE	0.01	8.98	1.46

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		SALES		PRICE
SALES		Dependent		1.00		0.63
PRICE		Yes		0.63		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	130.02		Durbin Watson(1)	0.34
BIC	130.80		Mean	111.19
Mean Absolute Percentage Error (MAPE)	10.67	%	Standard Deviation	17.49
R-Square	39.07	%	Ljung-Box	39.71
Adjusted R-Square	34.72	%
Root Mean Square Error	13.22

Exhibit #2

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
SALES	Dependent	123.47	19.40	6.36
PRICE	Yes	-24.84	4.95	-5.02
INCOME	Yes	0.03	0.00	13.55

Series Description	P-value	F-test	Elasticity	Overall F-test
SALES	0.00	40.51		154.86
PRICE	0.00	25.17	-1.17
INCOME	0.00	183.62	1.06

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		SALES		PRICE		INCOME
SALES		Dependent		1.00		0.63		0.94
PRICE		Yes		0.63		1.00		0.83
INCOME		Yes		0.94		0.83		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	86.56		Durbin Watson(1)	1.67
BIC	87.34		Mean	111.19
Mean Absolute Percentage Error (MAPE)	2.22	%	Standard Deviation	17.49
R-Square	95.97	%	Ljung-Box	15.22
Adjusted R-Square	95.35	%
Root Mean Square Error	3.40

Consider the two regressions shown above. For the multiple regression above, the Akaike Information Criterion indicates

A) that the multiple regression is less optimal than the simple regression.

B) that approximately 86% of the variation in sales is explained.

C) that the addition of an income variable resulted in a more optimal model.

D) that the researcher should give substantial consideration to both the simple and multiple regression.

61) ForecastX Regressions

Exhibit #1

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
SALES	Dependent	-51.24	54.32	-0.94
PRICE	Yes	30.92	10.32	3.00

Series Description	P-value	F-test	Elasticity	Overall F-test
SALES	0.36	0.89		8.98
PRICE	0.01	8.98	1.46

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		SALES		PRICE
SALES		Dependent		1.00		0.63
PRICE		Yes		0.63		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	130.02		Durbin Watson(1)	0.34
BIC	130.80		Mean	111.19
Mean Absolute Percentage Error (MAPE)	10.67	%	Standard Deviation	17.49
R-Square	39.07	%	Ljung-Box	39.71
Adjusted R-Square	34.72	%
Root Mean Square Error	13.22

Exhibit #2

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
SALES	Dependent	123.47	19.40	6.36
PRICE	Yes	-24.84	4.95	-5.02
INCOME	Yes	0.03	0.00	13.55

Series Description	P-value	F-test	Elasticity	Overall F-test
SALES	0.00	40.51		154.86
PRICE	0.00	25.17	-1.17
INCOME	0.00	183.62	1.06

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		SALES		PRICE		INCOME
SALES		Dependent		1.00		0.63		0.94
PRICE		Yes		0.63		1.00		0.83
INCOME		Yes		0.94		0.83		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	86.56		Durbin Watson(1)	1.67
BIC	87.34		Mean	111.19
Mean Absolute Percentage Error (MAPE)	2.22	%	Standard Deviation	17.49
R-Square	95.97	%	Ljung-Box	15.22
Adjusted R-Square	95.35	%
Root Mean Square Error	3.40

Consider the two regressions shown above.

A) The simple regression probably suffers from specification error.

B) The multiple regression probably suffers from specification error.

C) The simple regression probably suffers from multicollinearity.

D) The multiple regression probably suffers from autocorrelation.

62) Bottled Water

Shown above is the demand for bottled water in thousands of Gallons for 110 consecutive weeks. From weeks 75 through 84, there was a severe flood in the area. Shown below are two regression results using this data. The "Week" variable is an index of weeks from 1 through 109. The "Intervention" variable is a dummy variable equaling one during the intervention and zero otherwise.

Regression #1

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		33,763.50		1		33,763.50
Error		6,697.97		108		62.02		7.88
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.55	0.02	23.33
Demand	Dependent	94.28	1.51	62.35

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.25
Demand	0.00		544.41

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand
Week		Yes		1.00		0.91
Demand		Dependent		0.91		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	766.17		Durbin Watson	0.60
BIC	768.87		Mean	124.90
Mean Absolute Percentage Error (MAPE)	4.00	%	Standard Deviation	19.27
R-Square	83.45	%	Max	167.08
Adjusted R-Square	83.29	%	Min	89.55
Mean Square Error	60.89		Range	77.54
Root Mean Square Error	7.80

Method Statistics	Value
Method Selected	Multiple Regression

Regression #2

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		38,993.33		2		19,496.66
Error		1.468.14		107		13.72		3.70
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.50	0.01	43.50
Demand	Dependent	95.00	0.71	133.39
Intervention	Yes	24.70	1.27	19.52

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.22
Demand	0.00		1,420.94
Intervention	0.00	0.22

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand		Intervention
Week		Yes		1.00		0.91		0.24
Demand		Dependent		0.91		1.00		0.57
Intervention		Yes		0.24		0.57		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	599.21		Durbin Watson	1.84
BIC	601.91		Mean	124.90
Mean Absolute Percentage Error (MAPE)	2.47	%	Standard Deviation	19.27
R-Square	96.37	%	Max	167.08
Adjusted R-Square	96.30	%	Min	89.55
Mean Square Error	13.35		Range	77.54
Root Mean Square Error	3.65

Method Statistics	Value
Method Selected	Multiple Regression

Consider the two regressions shown above. Which of the following statements is true?

A) All independent variables are significant at the 99% level in both regressions.

B) The coefficient on the "Week" index has an incorrect sign in both regressions.

C) Neither regression seems to suffer from serial correlation.

D) Both regressions explain more than 90% of the variation in "Demand."

E) None of the options are correct.

63) Bottled Water

Regression #1

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		33,763.50		1		33,763.50
Error		6,697.97		108		62.02		7.88
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.55	0.02	23.33
Demand	Dependent	94.28	1.51	62.35

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.25
Demand	0.00		544.41

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand
Week		Yes		1.00		0.91
Demand		Dependent		0.91		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	766.17		Durbin Watson	0.60
BIC	768.87		Mean	124.90
Mean Absolute Percentage Error (MAPE)	4.00	%	Standard Deviation	19.27
R-Square	83.45	%	Max	167.08
Adjusted R-Square	83.29	%	Min	89.55
Mean Square Error	60.89		Range	77.54
Root Mean Square Error	7.80

Method Statistics	Value
Method Selected	Multiple Regression

Regression #2

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		38,993.33		2		19,496.66
Error		1.468.14		107		13.72		3.70
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.50	0.01	43.50
Demand	Dependent	95.00	0.71	133.39
Intervention	Yes	24.70	1.27	19.52

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.22
Demand	0.00		1,420.94
Intervention	0.00	0.22

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand		Intervention
Week		Yes		1.00		0.91		0.24
Demand		Dependent		0.91		1.00		0.57
Intervention		Yes		0.24		0.57		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	599.21		Durbin Watson	1.84
BIC	601.91		Mean	124.90
Mean Absolute Percentage Error (MAPE)	2.47	%	Standard Deviation	19.27
R-Square	96.37	%	Max	167.08
Adjusted R-Square	96.30	%	Min	89.55
Mean Square Error	13.35		Range	77.54
Root Mean Square Error	3.65

Method Statistics	Value
Method Selected	Multiple Regression

Examine the Akaike Information Criterion for both Regression #1 and Regression #2 above.

A) Both AIC measures are statistically significant at the 95% level.

B) Neither AIC measure is significant at the 95% level.

C) Only the Regression #2 AIC is significant at the 95% level.

D) Both AIC measures are significant at the 99% level.

E) None of the options are correct.

64) Bottled Water

Regression #1

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		33,763.50		1		33,763.50
Error		6,697.97		108		62.02		7.88
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.55	0.02	23.33
Demand	Dependent	94.28	1.51	62.35

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.25
Demand	0.00		544.41

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand
Week		Yes		1.00		0.91
Demand		Dependent		0.91		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	766.17		Durbin Watson	0.60
BIC	768.87		Mean	124.90
Mean Absolute Percentage Error (MAPE)	4.00	%	Standard Deviation	19.27
R-Square	83.45	%	Max	167.08
Adjusted R-Square	83.29	%	Min	89.55
Mean Square Error	60.89		Range	77.54
Root Mean Square Error	7.80

Method Statistics	Value
Method Selected	Multiple Regression

Regression #2

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		38,993.33		2		19,496.66
Error		1.468.14		107		13.72		3.70
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.50	0.01	43.50
Demand	Dependent	95.00	0.71	133.39
Intervention	Yes	24.70	1.27	19.52

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.22
Demand	0.00		1,420.94
Intervention	0.00	0.22

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand		Intervention
Week		Yes		1.00		0.91		0.24
Demand		Dependent		0.91		1.00		0.57
Intervention		Yes		0.24		0.57		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	599.21		Durbin Watson	1.84
BIC	601.91		Mean	124.90
Mean Absolute Percentage Error (MAPE)	2.47	%	Standard Deviation	19.27
R-Square	96.37	%	Max	167.08
Adjusted R-Square	96.30	%	Min	89.55
Mean Square Error	13.35		Range	77.54
Root Mean Square Error	3.65

Method Statistics	Value
Method Selected	Multiple Regression

Consider the two regressions immediately above. The "Intervention" variable in Regression #2 represents the flood period by taking on a value of "1" when there is a flood during that week and a value of zero otherwise. How would you interpret the coefficient of the "Intervention" variable in Regression #2?

A) For each week in which flood occurred, 24.70 more bottled water is demanded than in the first week in the time series.

B) For each week in which flood occurred, 24.70 more bottled water is demanded than in the week immediately preceding the beginning of the flood.

C) For each week in which flood occurred, 24.70 more bottled water is demanded than in the average week in the time series.

D) For each week in which flood occurred, 24.70 more bottled water is demanded than in the average nonflood week in the time series.

65) Bottled Water

Regression #1

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		33,763.50		1		33,763.50
Error		6,697.97		108		62.02		7.88
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.55	0.02	23.33
Demand	Dependent	94.28	1.51	62.35

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.25
Demand	0.00		544.41

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand
Week		Yes		1.00		0.91
Demand		Dependent		0.91		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	766.17		Durbin Watson	0.60
BIC	768.87		Mean	124.90
Mean Absolute Percentage Error (MAPE)	4.00	%	Standard Deviation	19.27
R-Square	83.45	%	Max	167.08
Adjusted R-Square	83.29	%	Min	89.55
Mean Square Error	60.89		Range	77.54
Root Mean Square Error	7.80

Method Statistics	Value
Method Selected	Multiple Regression

Regression #2

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		38,993.33		2		19,496.66
Error		1.468.14		107		13.72		3.70
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.50	0.01	43.50
Demand	Dependent	95.00	0.71	133.39
Intervention	Yes	24.70	1.27	19.52

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.22
Demand	0.00		1,420.94
Intervention	0.00	0.22

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand		Intervention
Week		Yes		1.00		0.91		0.24
Demand		Dependent		0.91		1.00		0.57
Intervention		Yes		0.24		0.57		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	599.21		Durbin Watson	1.84
BIC	601.91		Mean	124.90
Mean Absolute Percentage Error (MAPE)	2.47	%	Standard Deviation	19.27
R-Square	96.37	%	Max	167.08
Adjusted R-Square	96.30	%	Min	89.55
Mean Square Error	13.35		Range	77.54
Root Mean Square Error	3.65

Method Statistics	Value
Method Selected	Multiple Regression

Consider Regression #2 immediately above. You should use the rule of thumb taught in class to answer this question. In order to create the approximate 95% confidence interval for an estimate of demand,

A) 19.27 must be added to and subtracted from the point estimate.

B) two times 19.27 must be added to and subtracted from the point estimate.

C) 3.70 must be added to and subtracted from the point estimate.

D) two times 3.70 must be added to and subtracted from the point estimate.

E) None of the options are correct statements of how to construct the approximate 95% confidence interval.

66) Bottled Water

Regression #1

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		33,763.50		1		33,763.50
Error		6,697.97		108		62.02		7.88
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.55	0.02	23.33
Demand	Dependent	94.28	1.51	62.35

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.25
Demand	0.00		544.41

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand
Week		Yes		1.00		0.91
Demand		Dependent		0.91		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	766.17		Durbin Watson	0.60
BIC	768.87		Mean	124.90
Mean Absolute Percentage Error (MAPE)	4.00	%	Standard Deviation	19.27
R-Square	83.45	%	Max	167.08
Adjusted R-Square	83.29	%	Min	89.55
Mean Square Error	60.89		Range	77.54
Root Mean Square Error	7.80

Method Statistics	Value
Method Selected	Multiple Regression

Regression #2

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		38,993.33		2		19,496.66
Error		1.468.14		107		13.72		3.70
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.50	0.01	43.50
Demand	Dependent	95.00	0.71	133.39
Intervention	Yes	24.70	1.27	19.52

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.22
Demand	0.00		1,420.94
Intervention	0.00	0.22

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand		Intervention
Week		Yes		1.00		0.91		0.24
Demand		Dependent		0.91		1.00		0.57
Intervention		Yes		0.24		0.57		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	599.21		Durbin Watson	1.84
BIC	601.91		Mean	124.90
Mean Absolute Percentage Error (MAPE)	2.47	%	Standard Deviation	19.27
R-Square	96.37	%	Max	167.08
Adjusted R-Square	96.30	%	Min	89.55
Mean Square Error	13.35		Range	77.54
Root Mean Square Error	3.65

Method Statistics	Value
Method Selected	Multiple Regression

Consider the two regression models immediately above. When comparing these two regressions with respect to accuracy,

A) it is correct to choose the model that minimizes RMSE but maximizes MAPE.

B) it is incorrect to use either RMSE or MAPE; only MAPE can be used across different regression models.

C) it is correct to choose the model that minimizes both RMSE and MAPE.

D) only the F Statistic should be compared across two different regressions.

E) None of the options statements concerning accuracy are correct.

67) Bottled Water

Regression #1

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		33,763.50		1		33,763.50
Error		6,697.97		108		62.02		7.88
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.55	0.02	23.33
Demand	Dependent	94.28	1.51	62.35

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.25
Demand	0.00		544.41

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand
Week		Yes		1.00		0.91
Demand		Dependent		0.91		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	766.17		Durbin Watson	0.60
BIC	768.87		Mean	124.90
Mean Absolute Percentage Error (MAPE)	4.00	%	Standard Deviation	19.27
R-Square	83.45	%	Max	167.08
Adjusted R-Square	83.29	%	Min	89.55
Mean Square Error	60.89		Range	77.54
Root Mean Square Error	7.80

Method Statistics	Value
Method Selected	Multiple Regression

Regression #2

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		38,993.33		2		19,496.66
Error		1.468.14		107		13.72		3.70
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.50	0.01	43.50
Demand	Dependent	95.00	0.71	133.39
Intervention	Yes	24.70	1.27	19.52

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.22
Demand	0.00		1,420.94
Intervention	0.00	0.22

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand		Intervention
Week		Yes		1.00		0.91		0.24
Demand		Dependent		0.91		1.00		0.57
Intervention		Yes		0.24		0.57		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	599.21		Durbin Watson	1.84
BIC	601.91		Mean	124.90
Mean Absolute Percentage Error (MAPE)	2.47	%	Standard Deviation	19.27
R-Square	96.37	%	Max	167.08
Adjusted R-Square	96.30	%	Min	89.55
Mean Square Error	13.35		Range	77.54
Root Mean Square Error	3.65

Method Statistics	Value
Method Selected	Multiple Regression

Consider the two regressions immediately above. In using the Akaike Information Criterion and the Bayesian Information Criterion, "closeness" counts (as in the game of horseshoes). Using the rule of thumb we learned in class regarding the interpretation of the information criteria, we could correctly say

A) both models have "substantial support" because the AIC and BIC are so close in value to one another.

B) only Regression #1 has "substantial support" because of the differences in the values of the AIC and BIC.

C) only Regression #2 has "substantial support" because of the differences in the values of the AIC and BIC.

D) neither regression has "substantial support" since both regressions have AIC and BIC values substantially above 100.

68) Bottled Water

Regression #1

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		33,763.50		1		33,763.50
Error		6,697.97		108		62.02		7.88
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.55	0.02	23.33
Demand	Dependent	94.28	1.51	62.35

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.25
Demand	0.00		544.41

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand
Week		Yes		1.00		0.91
Demand		Dependent		0.91		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	766.17		Durbin Watson	0.60
BIC	768.87		Mean	124.90
Mean Absolute Percentage Error (MAPE)	4.00	%	Standard Deviation	19.27
R-Square	83.45	%	Max	167.08
Adjusted R-Square	83.29	%	Min	89.55
Mean Square Error	60.89		Range	77.54
Root Mean Square Error	7.80

Method Statistics	Value
Method Selected	Multiple Regression

Regression #2

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		38,993.33		2		19,496.66
Error		1.468.14		107		13.72		3.70
Total		40,461.47		109

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Week	Yes	0.50	0.01	43.50
Demand	Dependent	95.00	0.71	133.39
Intervention	Yes	24.70	1.27	19.52

Series Description	P-value	Elasticity	Overall F-test
Week	0.00	0.22
Demand	0.00		1,420.94
Intervention	0.00	0.22

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Week		Demand		Intervention
Week		Yes		1.00		0.91		0.24
Demand		Dependent		0.91		1.00		0.57
Intervention		Yes		0.24		0.57		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	599.21		Durbin Watson	1.84
BIC	601.91		Mean	124.90
Mean Absolute Percentage Error (MAPE)	2.47	%	Standard Deviation	19.27
R-Square	96.37	%	Max	167.08
Adjusted R-Square	96.30	%	Min	89.55
Mean Square Error	13.35		Range	77.54
Root Mean Square Error	3.65

Method Statistics	Value
Method Selected	Multiple Regression

The Akaike Information Criterion (AIC) may be used

A) to determine the correct set of independent variables in a regression.

B) to determine the correct "form" of a regression.

C) to determine the best lag structure in a regression.

D) All of the options are correct.

E) None of the options are correct.

69) Television Add Yields

Television add yields are sometimes measured in millions of retained impressions. The following two regressions model the effectiveness of adds for 21 consumer products. The data is from The Wall Street Journal, March 1, 1984.

The variables collected for each of the 21 products are:

SPENDING: TV advertising budget, ($ millions) MILIMP: Millions of retained impressions,

MILIMP Sqrd: Millions of retained impressions squared.

A scatterplot of the data used appears below:

Regression #1

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		7,723.28		1		7,723.28
Error		10,494.11		19		552.32		23.50
Total		18,217.39		20

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Spending	Yes	0.36	0.10	3.74
Milimp	Dependent	22.16	7.09	3.13

Series Description	P-value	F-test	Elasticity	Overall F-test
Spending	0.00	13.98	0.45
Milimp	0.01	9.77		13.98

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Spending		Milimp
Spending		Yes		1.00		0.65
Milimp		Dependent		0.65		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	192.09		Durbin Watson(4)	1.50
BIC	193.13		Mean	40.47
Mean Absolute Percentage Error (MAPE)	82.67	%	Standard Deviation	30.18
R-Square	42.40	%	Max	99.60
Adjusted R-Square	39.36	%	Min	4.40
Mean Square Error	499.72		Range	95.20
Root Mean Square Error	22.35		Root Mean Square	29.45
Theil	0.43		Ljung-Box	10.45

Regression #2

Audit Trail – ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		17,236.77		2		8,618.38
Error		980.62		18		54.48		7.38
Total		18,217.39		20

Audit Trail – Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Spending	Yes	0.03	0.04	0.74
Milimp	Dependent	16.33	2.27	7.19
Milimp Sqrd	Yes	0.01	0.00	13.21

Series Description	P-value	F-test	Elasticity	Overall F-test
Spending	0.47	0.55	0.04
Milimp	0.00	51.74		158.20
Milimp Sqrd	0.00	174.63	0.56

Audit Trail – Correlation Coefficient Table
Series Description	Included in Model		Spending		Milimp		Milimp Sqrd
Spending		Yes		1.00		0.65		0.64
Milimp		Dependent		0.65		1.00		0.97
Milimp Sqrd		Yes		0.64		0.97		1.00

Accuracy Measures	Value		Forecast Statistics	Value
AIC	142.31		Durbin Watson(4)	1.42
BIC	143.36		Mean	40.47
Mean Absolute Percentage Error (MAPE)	35.54	%	Standard Deviation	30.18
R-Square	94.62	%	Max	99.60
Adjusted R-Square	94.02	%	Min	4.40
Mean Square Error	46.70		Range	95.20
Root Mean Square Error	6.83		Root Mean Square	29.45
Theil	0.12		Ljung-Box	7.15

Regression #1 above

A) has a better Akaike score than Regression #2.

B) has a better Coefficient of Variation score than Regression #2.

C) suffers from a serious multicollinearity problem.

D) has a serious serial correlation problem.

E) None of the options are correct.

70) Television Add Yields

The variables collected for each of the 21 products are:

SPENDING: TV advertising budget, ($ millions) MILIMP: Millions of retained impressions,

MILIMP Sqrd: Millions of retained impressions squared.

A scatterplot of the data used appears below:

Regression #1

Audit Trail – ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		7,723.28		1		7,723.28
Error		10,494.11		19		552.32		23.50
Total		18,217.39		20

Audit Trail – Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Spending	Yes	0.36	0.10	3.74
Milimp	Dependent	22.16	7.09	3.13

Series Description	P-value	F-test	Elasticity	Overall F-test
Spending	0.00	13.98	0.45
Milimp	0.01	9.77		13.98

Audit Trail – Correlation Coefficient Table
Series Description	Included in Model		Spending		Milimp
Spending		Yes		1.00		0.65
Milimp		Dependent		0.65		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	192.09		Durbin Watson(4)	1.50
BIC	193.13		Mean	40.47
Mean Absolute Percentage Error (MAPE)	82.67	%	Standard Deviation	30.18
R-Square	42.40	%	Max	99.60
Adjusted R-Square	39.36	%	Min	4.40
Mean Square Error	499.72		Range	95.20
Root Mean Square Error	22.35		Root Mean Square	29.45
Theil	0.43		Ljung-Box	10.45

Regression #2

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		17,236.77		2		8,61838
Error		980.62		18		54.48		7.38
Total		18,217.39		20

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Spending	Yes	0.03	0.04	0.74
Milimp	Dependent	16.33	2.27	7.19
Milimp Sqrd	Yes	0.01	0.00	13.21

Series Description	P-value	F-test	Elasticity	Overall F-test
Spending	0.47	0.55	0.04
Milimp	0.00	51.74		158.20
Milimp Sqrd	0.00	174.63	0.56

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Spending		Milimp		Milimp Sqrd
Spending		Yes		1.00		0.65		0.64
Milimp		Dependent		0.65		1.00		0.97
Milimp Sqrd		Yes		0.64		0.97		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	142.31		Durbin Watson(4)	1.42
BIC	143.36		Mean	40.47
Mean Absolute Percentage Error (MAPE)	35.54	%	Standard Deviation	30.18
R-Square	94.62	%	Max	99.60
Adjusted R-Square	94.02	%	Min	4.40
Mean Square Error	46.70		Range	95.20
Root Mean Square Error	6.83		Root Mean Square	29.45
Theil	0.12		Ljung-Box	7.15

Regression #2 above for TV Add Yields

A) may suffer from autocorrelation.

B) is superior to Regression #1 in terms of Akaike score.

C) is inferior to Regression #1 in terms of the Adjusted Coefficient of Determination score.

D) has P-values that are lower than acceptable.

E) None of the options are correct.

71) Television Add Yields

The variables collected for each of the 21 products are:

SPENDING: TV advertising budget, ($ millions) MILIMP: Millions of retained impressions,

MILIMP Sqrd: Millions of retained impressions squared.

A scatterplot of the data used appears below:

Regression #1

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		7,723.28		1		7,723.28
Error		10,494.11		19		552.32		23.50
Total		18,217.39		20

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Spending	Yes	0.36	0.10	3.74
Milimp	Dependent	22.16	7.09	3.13

Series Description	P-value	F-test	Elasticity	Overall F-test
Spending	0.00	13.98	0.45
Milimp	0.01	9.77		13.98

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Spending		Milimp
Spending		Yes		1.00		0.65
Milimp		Dependent		0.65		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	192.09		Durbin Watson(4)	1.50
BIC	193.13		Mean	40.47
Mean Absolute Percentage Error (MAPE)	82.67	%	Standard Deviation	30.18
R-Square	42.40	%	Max	99.60
Adjusted R-Square	39.36	%	Min	4.40
Mean Square Error	499.72		Range	95.20
Root Mean Square Error	22.35		Root Mean Square	29.45
Theil	0.43		Ljung-Box	10.45

Regression #2

Audit Trail — ANOVA Table (Multiple Regression Selected)
Source of variation	SS		df		MS		SEE
Regression		17236.77		2		8,61838
Error		980.62		18		54.48		7.38
Total		18,217.39		20

Audit Trail — Coefficient Table (Multiple Regression Selected)

Series Description	Included in Model	Coefficient	Standard Error	T-test
Spending	Yes	0.03	0.04	0.74
Milimp	Dependent	16.33	2.27	7.19
Milimp Sqrd	Yes	0.01	0.00	13.21

Series Description	P-value	F-test	Elasticity	Overall F-test
Spending	0.47	0.55	0.04
Milimp	0.00	51.74		158.20
Milimp Sqrd	0.00	174.63	0.56

Audit Trail — Correlation Coefficient Table
Series Description	Included in Model		Spending		Milimp		Milimp Sqrd
Spending		Yes		1.00		0.65		0.64
Milimp		Dependent		0.65		1.00		0.97
Milimp Sqrd		Yes		0.64		0.97		1.00

Audit Trail - Statistics
Accuracy Measures	Value		Forecast Statistics	Value
AIC	142.21		Durbin Watson(4)	1.42
BIC	143.36		Mean	40.47
Mean Absolute Percentage Error (MAPE)	35.54	%	Standard Deviation	30.18
R-Square	94.62	%	Max	99.60
Adjusted R-Square	94.02	%	Min	4.40
Mean Square Error	46.70		Range	95.20
Root Mean Square Error	6.83		Root Mean Square	29.45
Theil	0.12		Ljung-Box	7.15

For the TV Add Yield regressions above,

A) the standard error of the estimate is better for Regression #1.

B) the standard error of the estimate is better for Regression #2.

C) a forecast confidence interval will be wider for Regression #2.

D) only Regression #1 has acceptable t-statistics.

E) None of the options are correct.

72) The internal auditor of a bank has developed a multiple regression model which has been used for a number of years to forecast the amount of interest income from commercial loans. During the current year, the auditor applies the model and discovers that the adjusted R2 value has decreased dramatically, but otherwise the model seems to be working okay. Which of the following conclusions are justified by the change?

A) Changing to a cross-sectional regression analysis should cause the adjusted R2 to increase.

B) Regression analysis is no longer an appropriate technique to estimate interest income.

C) Some new factors, not included in the model, are causing interest income to change.

D) A linear regression analysis would increase the model's reliability.

73) Lackland

Lackland Ski Resort uses multiple regression to forecast ski lift revenues for the next week based on the forecasted number of days with temperatures above 10 degrees and predicted number of inches of snow. The following function has been developed:

Sales = 10,902 + 255 (number days predicted above 10 degrees) + 300 (number of inches of snow predicted)

Other information generated from the analysis include

Adjusted R2 = 0.6789

Standard Error of the Estimate (SEE) = 1,879

F-statistic = 6.279 with a significance of 0.049

Which variable(s) in this function is (are) the dependent variable(s)?

A) Predicted number of days above 10 degrees

B) Predicted number of inches of snow

C) Sales

D) Predicted number of days above 10 degrees and predicted number of inches of snow

74) Lackland Ski Resort uses multiple regression to forecast ski lift revenues for the next week based on the forecasted number of days with temperatures above 10 degrees and predicted number of inches of snow. The following function has been developed:

Sales = 10,902 + 255 (number days predicted above 10 degrees) + 300 (number of inches of snow predicted)

Other information generated from the analysis include

Adjusted R2 = 0.6789

Standard Error of the Estimate (SEE) = 1,879

F-statistic = 6.279 with a significance of 0.049

Assume that the management predicts the number of days above 10 degrees for the next week to be 6 and the number of inches of snow to be 12. Calculate the predicted amount of revenue for the next week.

A) $10,902

B) $11,362

C) $16,032

D) $20,547

75) Lackland Ski Resort uses multiple regression to forecast ski lift revenues for the next week based on the forecasted number of days with temperatures above 10 degrees and predicted number of inches of snow. The following function has been developed:

Sales = 10,902 + 255 (number days predicted above 10 degrees) + 300 (number of inches of snow predicted)

Other information generated from the analysis include

Adjusted R2 = 0.6789

Standard Error of the Estimate (SEE) = 1,879

F-statistic = 6.279 with a significance of 0.049

Which of the following represents an accurate interpretation of the results of Lackland's regression analysis?

A) 6.729% of the variation in revenue is explained by the predicted number of days above 10 degrees and the number of inches of snow.

B) The relationships are not significant.

C) The predicted number of days above 10 degrees is a more significant variable than the number of inches of snow.

D) 67.89% of the variation in revenue is explained by the predicted number of days above 10 degrees and the number of inches of snow.

76) Lackland Ski Resort uses multiple regression to forecast ski lift revenues for the next week based on the forecasted number of days with temperatures above 10 degrees and predicted number of inches of snow. The following function has been developed:

Sales = 10,902 + 255 (number days predicted above 10 degrees) + 300 (number of inches of snow predicted)

Other information generated from the analysis include

Adjusted R2 = 0.6789

Standard Error of the Estimate (SEE) = 1,879

F-statistic = 6.279 with a significance of 0.049

Assume that Lackland's model predicts revenue for a week to be $13,400. Calculate the 95% confidence interval for the amount of revenue for the week. You should use the "rule of thumb" we discussed in class.

A) $13,400 ± 6,279

B) $13,400 ± 3,758

C) $13,400 ± 6,786

D) $13,400 ± 8,564

77) The Akaike Information Criterion (AIC)

A) can be quite useful in formulating simple regressions.

B) will always be a number between zero and four.

C) can help in selecting the correct independent variables.

D) tests for statistical significance of each variable independently.

78) The Bayesian Information Criterion (BIC)

A) provides much the same information as the Akaike.

B) is used to test the significance of the independent variables in a regression.

C) is used with exponential smoothing models to test for significance.

D) can only be used with time series decomposition models.

79) In a multiple regression analysis involving two independent variables, if b1 is computed to be + 2.0, it means that

A) the relationship between X1 and Y is significant.

B) the estimated average of Y increases by 2 units for each increase of 1 unit of X1, holding X2 constant.

C) the estimated average of Y increases by 2 units for each increase of 1 unit of X1, without regard to X2.

D) the estimated average of Y is 2 when X1 equals zero.

80) In a multiple regression analysis, the value of the coefficient of multiple determination

A) has to fall between -1 and +1.

B) has to fall between 0 and +1.

C) has to fall between -1 and 0.

D) can fall between any pair of real numbers.

81) A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. The builder randomly selected 50 families and ran a multiple regression. The regression statistics are below:

Regression Statistics


R Square		0.748
Adjusted R Square		0.726
Standard Error		5.195
Observations		50

ANOVA Table
	df	SS		MS		F	Sig. F
Regression			3605.7736		901.4434			0.0001
Error			1214.2264		29.9892
Total	49		4820.0000

	Coefficient		Std. Error		T-test		P-Value
Intercept		−1.6335		5.8078		−0.281		0.7798
Income		0.4485		0.1137		3.9545		0.0003
Size		4.2615		0.8062		5.286		0.0001
School		−0.6517		0.4319		−1.509		0.1383

Dependent variable is House.

Referring to the Real Estate Builder regression results, what fraction of the variability in house size is explained by variations in income, size of family, and education?

A) 27.0%

B) 33.4%

C) 72.6%

D) 86.5%

82) A real estate builder wishes to determine how house size (House) is influenced by family income (Income), family size (Size), and education of the head of household (School). House size is measured in hundreds of square feet, income is measured in thousands of dollars, and education is measured in years. The builder randomly selected 50 families and ran a multiple regression. The regression statistics are below:

Regression Statistics


R Square		0.748
Adjusted R Square		0.726
Standard Error		5.195
Observations		50

ANOVA Table
	df	SS		MS		F	Sig. F
Regression			3605.7736		901.4434			0.0001
Error			1214.2264		29.9892
Total	49		4820.0000

	Coefficient		Std. Error		T-test		P-Value
Intercept		−1.6335		5.8078		−0.281		0.7798
Income		0.4485		0.1137		3.9545		0.0003
Size		4.2615		0.8062		5.286		0.0001
School		−0.6517		0.4319		−1.509		0.1383

Dependent variable is House.

Referring to the Real Estate Builder regression results, which of the independent variables in the model are statistically significant at the 98% level?

A) Income, Size, School

B) Income, Size

C) Size, School

D) Income, School

83) Regression Statistics


R Square		0.748
Adjusted R Square		0.726
Standard Error		5.195
Observations		50

ANOVA Table
	df	SS		MS		F	Sig. F
Regression			3605.7736		901.4434			0.0001
Error			1214.2264		29.9892
Total	49		4820.0000

	Coefficient		Std. Error		T-test		P-Value
Intercept		−1.6335		5.8078		−0.281		0.7798
Income		0.4485		0.1137		3.9545		0.0003
Size		4.2615		0.8062		5.286		0.0001
School		−0.6517		0.4319		−1.509		0.1383

Dependent variable is House.

Referring to the Real Estate Builder regression results, when the builder used a simple linear regression model with house size (House) as the dependent variable and education (School) as the independent variable, she obtained an Adjusted R Squared value of 23.0%. What additional percentage of the total variation in house size has been explained by including family size and income in the multiple regression?

A) 2.8%

B) 49.6%

C) 72.6%

D) 74.8%

84) Regression Statistics


R Square		0.748
Adjusted R Square		0.726
Standard Error		5.195
Observations		50

ANOVA Table
	df	SS		MS		F	Sig. F
Regression			3605.7736		901.4434			0.0001
Error			1214.2264		29.9892
Total	49		4820.0000

	Coefficient		Std. Error		T-test		P-Value
Intercept		−1.6335		5.8078		−0.281		0.7798
Income		0.4485		0.1137		3.9545		0.0003
Size		4.2615		0.8062		5.286		0.0001
School		−0.6517		0.4319		−1.509		0.1383

Dependent variable is House.

Referring to the Real Estate Builder regression results, which of the following values for the level of significance is the smallest for which all explanatory variables are significant individually?

A) 99%

B) 97.5%

C) 95%

D) 85%

85) Regression Statistics


R Square		0.748
Adjusted R Square		0.726
Standard Error		5.195
Observations		50

ANOVA Table
	df	SS		MS		F	Sig. F
Regression			3605.7736		901.4434			0.0001
Error			1214.2264		29.9892
Total	49		4820.0000

	Coefficient		Std. Error		T-test		P-Value
Intercept		−1.6335		5.8078		−0.281		0.7798
Income		0.4485		0.1137		3.9545		0.0003
Size		4.2615		0.8062		5.286		0.0001
School		−0.6517		0.4319		−1.509		0.1383

Dependent variable is House.

Referring to the Real Estate Builder regression results, which of the following values for the level of significance is the greatest for which at least two explanatory variables are significant individually?

A) 99%

B) 97.5%

C) 95%

D) 85%

86) Regression Statistics


R Square		0.748
Adjusted R Square		0.726
Standard Error		5.195
Observations		50

ANOVA Table
	df	SS		MS		F	Sig. F
Regression			3605.7736		901.4434			0.0001
Error			1214.2264		29.9892
Total	49		4820.0000

	Coefficient		Std. Error		T-test		P-Value
Intercept		−1.6335		5.8078		−0.281		0.7798
Income		0.4485		0.1137		3.9545		0.0003
Size		4.2615		0.8062		5.286		0.0001
School		−0.6517		0.4319		−1.509		0.1383

Dependent variable is House.

Referring to the Real Estate Builder regression results, which of the following values for the level of significance is the smallest for which the regression model as a whole is significant?

A) 90%

B) 92%

C) 99%

D) 95%

87) Regression Statistics


R Square		0.748
Adjusted R Square		0.726
Standard Error		5.195
Observations		50

ANOVA Table
	df	SS		MS		F	Sig. F
Regression			3605.7736		901.4434			0.0001
Error			1214.2264		29.9892
Total	49		4820.0000

	Coefficient		Std. Error		T-test		P-Value
Intercept		−1.6335		5.8078		−0.281		0.7798
Income		0.4485		0.1137		3.9545		0.0003
Size		4.2615		0.8062		5.286		0.0001
School		−0.6517		0.4319		−1.509		0.1383

Dependent variable is House.

Referring to the Real Estate Builder regression results, one individual in the sample had an annual income of $10,000, a family size of 1, and an education of 8 years. This individual owned a home with an area of 1,000 square feet (House = 10.00). What is the residual (i.e., error) in hundreds of square feet for this data point?

A) 8.10

B) 5.40

C) −5.40

D) −8.10

88) Regression Statistics


R Square		0.748
Adjusted R Square		0.726
Standard Error		5.195
Observations		50

ANOVA Table
	df	SS		MS		F	Sig. F
Regression			3605.7736		901.4434			0.0001
Error			1214.2264		29.9892
Total	49		4820.0000

	Coefficient		Std. Error		T-test		P-Value
Intercept		−1.6335		5.8078		−0.281		0.7798
Income		0.4485		0.1137		3.9545		0.0003
Size		4.2615		0.8062		5.286		0.0001
School		−0.6517		0.4319		−1.509		0.1383

Dependent variable is House.

Referring to the Real Estate Builder regression results, suppose the builder wants to test whether the coefficient on Income is significantly different from 0. What is the value of the relevant diagnostic statistic?

A) 0.4485

B) 5.195

C) 3.9545

D) −0.281

89) In a linear regression problem, we are using "R-squared" to measure goodness-of-fit. We add a feature in linear regression model and retrain the same model.

Which of the following options is true?

A) If R Squared increases, this variable is significant.

B) If R Squared decreases, this variable is not significant.

C) Individually, R squared cannot tell about variable importance. We can't say anything about it right now.

D) None of the options are correct.

90) Which of the following indicates a fairly strong relationship between X and Y?

A) The Correlation coefficient = 0.9

B) The p-value for the coefficient = 0 is 0.0001

C) The t-statistic for the coefficient = 0 is 30

D) None of the options are correct.

91) To test linear relationship of y(dependent) and x(independent) continuous variables, which of the following plots is best suited?

A) Scatter Plot

B) Barchart

C) Histogram

D) None of the options are correct.

92) A correlation between age and health of a person is found to be −1.09. On the basis of this, you would tell the doctors that

A) age is a good predictor of health.

B) age is a poor predictor of health.

C) None of the options are correct.

93) Which of the following metrics can be used for evaluating regression models?

1) t Statistics

2) Adjusted R Squared

3) F Statistics

4) RMSE

A) 2 and 3 are correct.

B) 1 and 2 are correct.

C) 2, 3, and 4 are correct.

D) All (1, 2, 3, and 4) are correct.

94) How does number of observations influence overfitting? Choose the correct answer(s).

Note: the rest of all parameters are same.

1) In case of fewer observations, it is easy to overfit the data.

2) In case of fewer observations, it is hard to overfit the data.

3) In case of more observations, it is easy to overfit the data.

4) In case of more observations, it is hard to overfit the data.

A) 1 and 4 are correct.

B) 2 and 3 are correct.

C) 1 and 3 are correct.

D) None of the options are correct.

95) Consider the following dataset

Which identified point, if removed, will have the largest effect on fitted regression line as shown in the above figure (the dashed line is the regression line)?

A) a

B) b

C) c

D) d

96) In a simple linear regression model (One independent variable), if we change the input variable by 1 unit, how much will the output variable value change?

A) By 1

B) No change

C) By the value of the intercept

D) By the value of the slope

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Created Date:

Aug 21, 2025

Chapter Name:

Chapter 5 Regression Forecasting – Causal

Author:

Barry Keating

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