Ch.19 | Full Test Bank – Correlation Analysis and Regression

Test Bank

CHAPTER 19 Correlation Analysis and Regression Analysis

True-False

1. Regression is an analysis of dependence technique since it involves

a dependent variable as the focus of analysis.

2. A regression model can be used to explain, predict and control the dependent variable,

on the basis of independent variables.

3. In regression analysis, the dependent variable is sometimes called

the predictor variable.

4. The model: Y = α + βX2 + e hypothesizes a curvilinear relationship

between X and Y.

5. A regression model can accurately predict the level of a dependent

variable in a changing market environment.

6. A least squares criterion minimizes the squared vertical deviations

from the regression line.

7. In the expression Ŷ = 7.26 + 28.9 X, the estimated value of α = 28.9

and the estimated value of β = 7.26.

8. Correlation analysis provides a measure of the strength of association between two

variables, but tells us nothing about the nature of the relationship between them

9. When an understanding of the relationship between X and Y is the

motivation behind data analysis, the estimate of the β parameter is of primary importance.

10. If the standard deviation of X is approximated by s, then the

standard deviation of the mean (based on a sample size of n) is s/√n.

11. If the parameter β is zero, the value of b must also always be zero.

12. When testing the hypothesis that, in fact, β = 0, the researcher is

actually testing the hypothesis that the independent variable has no

(linear) effect on the dependent variable.

13. The unexplained variation in Y is estimated by

n

Σ (Y_i - Ŷ₁)²

i=1

14. The total variation in Y, the dependent variable, can be expressed

as the sum of the explained variance, the unexplained variance, and an unknown error.

15. r2 = Total variation - Unexplained variation

Total variation

16. r2 is the square of the correlation between X and Y and also the

square of the correlation between Ŷ and Y.

17. An independent variable which takes a small number (3 or 4) of

discrete values is often termed a dummy variable.

18. The larger the beta coefficient value, the stronger the effect of

that variable upon the dependent variable.

19. If a variable that is excluded from the model is correlated with an

independent variable in the model, the regression coefficient will

reflect the impact of the excluded variable on the dependent variable.

20. A regression model can be used to accurately predict the level of

dependent variable, given extreme values of an independent variable.

21. In interpreting parameter coefficients, β indicates that if the

independent variable X is changed by one unit, the dependent

variable Y will change by β units. In multiple regression, we add

the constraint that the values of all other independent variables remain constant.

22. Correlation analysis involves measuring the strength of the

relationship between two variables.

23. The Pearson correlation coefficient measures the degree to which

there is a linear association between two intervally scaled variables.

24. Correlation coefficient implies a causal relationship between variables.

25. Partial correlation coefficient is the measure of association

between two variables controlling for the effect of one or more additional variables.

26. The coefficient of determination (r2) measure the ability of the model to predict, and is

the ratio of the explained variation to the total variation

27. The difference between the actual and the predicted values in

regression equation is called residuals.

28. The point estimates b0 and b1 in a regression analysis, tend to

increase the total sum of squares.

29. The knowledge of the regression coefficient and the t value can suggest the extent of

association an independent variable has on the dependent variable.

30. Although the least-squares regression line provides a reasonable fit of the data

points, there are some deviations in the sample data about the line.

Multiple Choice

1. The degree of linear association between two intervally scaled variables is

measured by

1. Pearson correlation coefficient
2. significance level
3. analysis of variance
4. β
5. The measures of association represented by r and r2 are
6. symmetric
7. dependent
8. asymmetric
9. independent
10. To examine the association between two variables after controlling for

the other variables the researcher should use

1. bivariate correlation
2. partial correlation
3. product moment correlation
4. simple correlation
5. Which of the following is not an assumption of the regression model?
6. the error term is normally distributed
7. the error terms are independent of each other
8. the values of independent variable are fixed
9. the independent variable is normally distributed
10. Which one of the following is the same as standard deviation of regression coefficient?
11. sum of squares of errors
12. standard error
13. predicted value
14. standard error of the estimate

6. In analysis of variance, the hypothesis that the means are equal will be rejected if

1. the total mean square error is significantly greater than either the explained or unexplained mean square error
2. the total mean square error is significantly greater than the unexplained
3. the mean square error explained is significantly greater than the mean square unexplained
4. the mean square error unexplained is significantly greater than the mean square explained

7. Snow Belt Airlines weighed the baggage of 100 passengers and found the mean weight

to be 34.2 pounds with a standard deviation of 14 pounds. What is the 95% confidence interval for the actual weight of the baggage? (Round Z to the nearest whole number)

1. 20.0 - 48.2
2. 32.8 - 35.6
3. 31.4 - 37.0
4. 0.0 - 50.0

8. If you tested a null hypothesis on problem 7, and accepted it, the probability of

Type I error would be

1. .95
2. .50
3. .10
4. zero

9. A regression analysis has shown that there is a definite, positive

relationship between sales (dependent variable) and advertising and

sales promotion (all units in dollars). The estimated relationship

is sales = (3) advertising + (1) sales promotion + 1,500. Based on the given information

a. all marketing resources should be allocated to advertising, if possible.

b. all marketing resources should be allocated to sales promotion, if possible.

c. the allocation between advertising and sales promotion should be

split in the ratio 3 to 1 in all circumstances.

d. none of the above.

10. Consider the following model: Y = α + βX + e. Which of the

following statements is not true?

a. The model involves one dependent and one independent variable.

b. The parameters of the model are Y and X.

c. The parameters of the model are α and β.

d. e represents the error in the model.

11. In the simple linear regression model, Y = α + βX + e,

a. the errors are assumed to be as likely to occur above the line as below the line.

b. the errors are assumed to be more likely to occur above the line than below it.

c. the errors are assumed to be more likely to occur below the line than above it.

d. it is assumed that the error is larger for larger values of X.

12. Based on the regression model,

If Ŷ = 50 + 25X, where Ŷ = estimated sales level; X = advertising

1. the actual sales level, when X = 2, is 100.

2. when X = 3, the estimated sales level is 125.

3. when X = 3, the estimated sales level is 175.

4. when X = 3, the actual sales level is 125.

a. 1

b. 2

c. 3

d. 1 and 4

13. Consider the estimated relationship: Ŷ = 50 + 50X.

1. The average level of Y, if X = 0, is 50.

2. For each unit increase in α, Y will increase by 50 units.

3. For each unit increase in X, Y will increase by 50 units.

a. 1

b. 2

c. 1 and 2

d. 1 and 3

14. Consider the following: Y = 20 + 30X; Sb = 20

1. The value of t is 1.0.

2. The value of t is 1.5.

3. The evidence suggests that β = 0.

4. The evidence suggests that β ≠ 0.

a. 1

b. 2

c. 4

d. 2 and 4

15. Consider the following:

Based on the above information, which of these statements is not true?

a. The estimated model is Ŷ = -40 + 10X₁ - 5X₂ + 40X₃.

b. The t-value for β₂ is -1/3.

c. It can be concluded that X₃, X₁, and X₂ have the greatest impact on Y, in that order.

d. A unit increase in X₂ will result in a decrease of 5 units in

the value of Y, when the values of X₁ and X₃ are held constant.

16. Which of the following data analysis techniques can be termed

analysis of dependence techniques?

a. Correlation analysis

b. Regression analysis

c. Multidimensional scaling

d. Cluster analysis

17. In a scatter diagram, the sample correlation value is 1 if,

1. the points fall along a straight line running from the lower left to the upper right
2. the points are clustered in a pattern sloping from lower left to upper right
3. the points are clustered in a pattern sloping from upper left to lower right
4. the points are clustered in no clear, defined pattern

18. Which of the following is not a property of the product moment correlation coefficient?

a. it is independent of sample size and units of measurement.

b. it is a measure of association between two variables.

c. it always lies between 1 and -1.

d. it implies a causal relationship between two variables.