Chapter 4: BASIC ESTIMATION TECHNIQUES

Multiple Choice

4-1 For the equation Y = a + bX, the objective of regression analysis is to

1. estimate the parameters a and b.
2. estimate the variables Y and X.
3. fit a straight line through the data scatter in such a way that the sum of the squared errors is minimized.
4. both a and c

Difficulty: 01 Easy

Topic: The Simple Linear Regression Model

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-01

4-2 In a linear regression equation of the form Y = a + bX, the slope parameter b shows

1. ΔX / ΔY.
2. ΔY / ΔX.
3. ΔY / Δb.
4. ΔX / Δb.
5. none of the above

Difficulty: 01 Easy

Topic: The Simple Linear Regression Model

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-01

4-3 In a linear regression equation of the form Y = a + bX, the intercept parameter a shows

• 1. the value of X when Y is zero.
  2. the value of Y when X is zero.
  3. the amount that Y changes when X changes by one unit.
  4. the amount that X changes when Y changes by one unit.

Difficulty: 01 Easy

Topic: The Simple Linear Regression Model

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-01

4-4 In a regression equation, the ______ captures the effects of factors that might influence the dependent variable but aren't used as explanatory variables.

1. intercept
2. slope parameter
3. R-square
4. random error term

Difficulty: 01 Easy

Topic: The Simple Linear Regression Model

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-01

4-5 The sample regression line

• 1. shows the actual (or true) relation between the dependent and independent variables.
  2. is used to estimate the population regression line.
  3. connects the data points in a sample.
  4. is estimated by the population regression line.
  5. maximizes the sum of the squared differences between the data points in a sample and the sample regression line.

Difficulty: 01 Easy

Topic: The Simple Linear Regression Model

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-01

4-6 Which of the following is an example of a time-series data set?

a. amount of labor employed in each factory in the U.S. in 2010

b. amount of labor employed yearly in a specific factory from 1990 through 2010

c. average amount of labor employed at specific times of the day at a specific factory in 2010

d. All of the above are time-series data sets.

Difficulty: 01 Easy

Topic: The Simple Linear Regression Model

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-01

4-7 The method of least squares

a. can be used to estimate the explanatory variables in a linear regression equation.

b. can be used to estimate the slope parameters of a linear equation.

1. minimizes the distance between the population regression line and the sample regression line.
2. all of the above

Difficulty: 01 Easy

Topic: Fitting a Regression Line

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-02

4-8 In a linear regression equation Y = a + bX, the fitted or predicted value of Y is

• 1. the value of Y obtained by substituting specific values of X into the sample regression equation.
  2. the value of X associated with a particular value of Y.
  3. the value of X that the regression equation predicts.
  4. the values of the parameters predicted by the estimators.
  5. the value of Y associated with a particular value of X in the sample.

Difficulty: 01 Easy

Topic: The Simple Linear Regression Model

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-01

4-9 A parameter estimate is said to be statistically significant if there is sufficient evidence that the

• 1. sample regression equals the population regression.
  2. parameter estimated from the sample equals the true value of the parameter.
  3. value of the t-ratio equals the critical value.
  4. true value of the parameter does not equal zero.

Difficulty: 02 Medium

Topic: Testing for Statistical Significance

AACSB: Reflective Thinking

Blooms: Understand

Learning Objective: 04-03

4-10 An estimator is unbiased if it produces

a. a parameter from the sample that equals the true parameter.

b. estimates of a parameter that are close to the true parameter.

c. estimates of a parameter that are statistically significant.

d. estimates of a parameter that are on average equal to the true parameter.

e. both b and c

Difficulty: 01 Easy

Topic: Fitting a Regression Line

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-02

4-11 The critical value of t is the value that a t-statistic must exceed in order to

a. reject the hypothesis that the true value of a parameter equals zero.

b. accept the hypothesis that the estimated value of parameter equals the true value.

c. reject the hypothesis that the estimated value of the parameter equals the true value.

d. reject the hypothesis that the estimated value of the parameter exceeds the true value.

Difficulty: 02 Medium

Topic: Testing for Statistical Significance

AACSB: Reflective Thinking

Blooms: Understand

Learning Objective: 04-03

4-12 To test whether the overall regression equation is statistically significant one uses

a. the t-statistic.

1. the R²-statistic.
2. the F-statistic.

d. the standard error statistic.

Difficulty: 01 Easy

Topic: Evaluation of the Regression Equation

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-04

4-13 In the regression model , a test of the hypothesis that parameter c equals zero is

a. an F-test.

1. an R²-test.

c. a zero-statistic.

1. a t-test.
2. a Z-test.

Difficulty: 01 Easy

Topic: Testing for Statistical Significance

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-03

4-14 If an analyst believes that more than one explanatory variable explains the variation in the dependent variable, what model should be used?

a. a simple linear regression model

b. a multiple regression model

c. a nonlinear regression model

d. a log-linear model

Difficulty: 01 Easy

Topic: Multiple Regression

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-05

4-15 The linear regression equation, Y = a + bX, was estimated. The following computer printout was

obtained:

Given the above information, the parameter estimate of a indicates

a. when X is zero, Y is 5.09.

b. when X is zero, Y is 15.48.

c. when Y is zero, X is –21.36.

d. when Y is zero, X is 8.03.

Difficulty: 01 Easy

Topic: The Simple Linear Regression Model

AACSB: Reflective Thinking

Blooms: Remember

Learning Objective: 04-01

4-16 The linear regression equation, Y = a + bX, was estimated. The following computer printout was

obtained:

Given the above information, the parameter estimate of b indicates

a. X increases by 8.03 units when Y increases by one unit.

b. X decreases by 21.36 units when Y increases by one unit.

c. Y decreases by 2.66 units when X increases by one unit.

d. a 10-unit decrease in X results in a 213.6 unit increase in Y.

Difficulty: 02 Medium

Topic: The Simple Linear Regression Model

AACSB: Reflective Thinking

Blooms: Understand

Learning Objective: 04-01

4-17 The linear regression equation, Y = a + bX, was estimated. The following computer printout was

obtained:

Given the above information, what is the critical value of t at the 1% level of significance?

a. 1.746

b. 2.120

c. 2.878

d. 2.921

Difficulty: 02 Medium

Topic: Testing for Statistical Significance

AACSB: Reflective Thinking

Blooms: Apply

Learning Objective: 04-03

4-18 The linear regression equation, Y = a + bX, was estimated. The following computer printout was

obtained:

Given the above information, which of the following statements is correct at the 1% level of significance?

a. Both and are statistically significant.

b. Neither nor is statistically significant.

c. is statistically significant, but is not.

d. is statistically significant, but is not.

Difficulty: 02 Medium

Topic: Testing for Statistical Significance

AACSB: Reflective Thinking

Blooms: Understand

Learning Objective: 04-03

4-19 The linear regression equation, Y = a + bX, was estimated. The following computer printout was

obtained:

Given the above information, the value of the R² statistic indicates that

a. 0.3066% of the total variation in Y is explained by the regression equation.

b. 0.3066% of the total variation in X is explained by the regression equation.

c. 30.66% of the total variation in Y is explained by the regression equation.

d. 30.66% of the total variation in X is explained by the regression equation.

Difficulty: 02 Medium

Topic: Evaluation of Regression Equation

AACSB: Reflective Thinking

Blooms: Understand

Learning Objective: 04-04

4-20 The linear regression equation, Y = a + bX, was estimated. The following computer printout was

obtained:

Given the above information, the exact level of significance of is

a. 0.171 percent.

b. 1 percent.

1. 1.71 percent.
2. 2.66 percent.
3. 2.921 percent.

Difficulty: 02 Medium

Topic: Testing for Statistical Significance

AACSB: Reflective Thinking

Blooms: Understand

Learning Objective: 04-03

4-21 The linear regression equation, Y = a + bX, was estimated. The following computer printout was

obtained:

Given the above information, if X equals 20, what is the predicted value of Y?

a. 186.42

b. 165.69

c. −186.42

d. −411.72

Difficulty: 02 Medium

Topic: The Simple Linear Regression Model

AACSB: Analytical Thinking

Blooms: Understand

Learning Objective: 04-01

4-22 A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results:

Based on the above information, which of the following is correct at the 1% level of significance?

a. The regression equation as a whole is statistically significant because the p-value of F is smaller than 0.01.

b. The estimates of the parameters a, b, and c are all statistically significant because the absolute values of their t-ratios exceed 2.797.

c. The estimates of the parameters a, b, and c are all statistically significant because the p- values for,, and are all less than 0.01.

d. The critical value of t is 2.797.

e. all of the above

Difficulty: 03 Hard

Topic: Multiple Regression

AACSB: Analytical Thinking

Blooms: Apply

Learning Objective: 04-05

4-23 A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results:

Based on the above information, hiring one more guard per week will decrease the losses due to theft at the warehouse by _________ per week.

a. $5,150

b. $211

c. $130

d. $480.92

Difficulty: 02 Medium

Topic: Multiple Regression

AACSB: Analytical Thinking

Blooms: Apply

Learning Objective: 04-05

4-24 A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results:

Based on the above information, if the firm hires 6 guards and the unemployment rate in the county is 10% (U = 10), what is the predicted dollar loss to theft per week?

a. $4,375 per week

b. $5,150 per week

c. $8,300 per week

d. $9,955 per week

Difficulty: 02 Medium

Topic: Multiple Regression

AACSB: Analytical Thinking

Blooms: Apply

Learning Objective: 04-05

4-25 A firm is experiencing theft problems at its warehouse. A consultant to the firm believes that the dollar loss from theft each week (T) depends on the number of security guards (G) and on the unemployment rate in the county where the warehouse is located (U measured as a percent). In order to test this hypothesis, the consultant estimated the regression equation T = a + bG + cU and obtained the following results:

Based on the above information, a one percent increase in the level of unemployment in the county results in an increase in losses due to theft of __________ more losses per week.

1. $75
2. $211
3. $280
4. $460

Difficulty: 02 Medium

Topic: Multiple Regression

AACSB: Analytical Thinking

Blooms: Apply

Learning Objective: 04-05

4-26 In the nonlinear function , the parameter c measures

a. ΔY /ΔZ.

b. the percent change in Y for a 1 percent change in Z.

c. the elasticity of Y with respect to Z.

d. both a and c

e. both b and c

Difficulty: 03 Hard

Topic: Nonlinear Regression Analysis

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-27 Tests for statistical significance must be performed

a. because the TRUE values of the intercept and slope parameters are random variables.

b. because the ESTIMATED values of the intercept and slope parameters are not, in general, equal to the true values of the intercept and slope parameters.

c. because the computed t-ratios are random variables and may be too large to provide evidence that b is not equal to zero.

d. in order to determine whether or not the parameter estimates are far enough away from zero to conclude that the true parameter values are not equal to zero.

e. both b and d

Difficulty: 03 Hard

Topic: Testing for Statistical Significance

AACSB: Reflective Thinking

Blooms: Analyze

Learning Objective: 04-03

4-28 If the p-value is 10%, then the

a. level of significance is 10%.

b. level of confidence is 90%.

c. probability of a Type I error is 90%.

d. both a and b

e. null hypothesis should not be rejected if the level of significance is 5%

Difficulty: 02 Medium

Topic: Testing for Statistical Significance

AACSB: Reflective Thinking

Blooms: Understand

Learning Objective: 04-03

4-29 Suppose you are testing the statistical significance (at the 5% significance level) of a parameter estimate from the regression equation:

Y = a + bR + cS + dW

which is estimated using a time-series sample containing monthly observations over a 30−month time period. The critical value of the appropriate test statistic is

a. t_critical = 2.042.

b. t_critical = 2.056.

c. F_critical = 4.22.

d. F_critical = 7.76.

Difficulty: 02 Medium

Topic: Testing for Statistical Significance

AACSB: Reflective Thinking

Blooms: Apply

Learning Objective: 04-03

4-30 Suppose you are testing the statistical significance (at the 1% significance level) of a parameter estimate from the regression model:

M = a + bR + cI

which is estimated using a cross−section data set on 22 firms. The critical value of the appropriate test statistic is

a. t_critical = 2.861.

b. t_critical = −2.845.

c. t_critical = 2.845.

d. F_critical = 5.93.

e. F_critical = 19.44.

Difficulty: 02 Medium

Topic: Testing for Statistical Significance

AACSB: Reflective Thinking

Blooms: Apply

Learning Objective: 04-03

4-31 Refer to the following computer output from estimating the parameters of the nonlinear model

The computer output from the regression analysis is:

Based on the info above, the nonlinear relation can be transformed into the following linear regression model:

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-32 Refer to the following computer output from estimating the parameters of the nonlinear model

The computer output from the regression analysis is:

Based on the info above, the estimated value of a is

a. −0.6931

b. 0.50

c. −3.67

d. 2.66

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-33 Refer to the following computer output from estimating the parameters of the nonlinear model

The computer output from the regression analysis is:

Based on the info above, which of the parameter estimates are statistically significant at the 90% level of confidence?

a. All the parameter estimates are statistically significant.

b. All parameter estimates except and are statistically significant.

c. is not statistically significant, but all the rest of the parameter estimates are significant.

d. is not statistically significant, but all the rest of the parameter estimates are significant.

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-34 Refer to the following computer output from estimating the parameters of the nonlinear model

The computer output from the regression analysis is:

Based on the info above, if R = 1, S = 2, and T = 3, what value do you expect Y will have?

1. 143
2. 1,345
3. 3,289
4. 6,578
5. −4,559

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-35 Refer to the following computer output from estimating the parameters of the nonlinear model

The computer output from the regression analysis is:

Based on the info above, if R decreases by 10% (all other things constant), Y will

1. increase by 4.66%.
2. increase by 46.6%.
3. decrease by 4.66%.
4. decrease by 46.6%.

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-36 Refer to the following computer output from estimating the parameters of the nonlinear model

The computer output from the regression analysis is:

Based on the info above, if S increases by 8% (all other things constant), Y will

1. decrease by 3.52%.
2. decrease by 0.44%.

c. decrease by 4.4%.

d. increase by 0.44%.

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-37 Refer to the following nonlinear model which relates W to P, Q, and R:

The computer output form the regression analysis is:

Based on the info above, the nonlinear relation can be transformed into the following linear regression model:

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-38 Refer to the following nonlinear model which relates W to P, Q, and R:

The computer output form the regression analysis is:

Based on the info above, which of the parameter estimates are statistically significant at the 5% level of significance?

a. All the parameter estimates are statistically significant.

b. All parameter estimates except and are statistically significant.

c. is not statistically significant, but all the rest of the parameter estimates are significant.

d. is not statistically significant, but all the rest of the parameter estimates are significant.

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-39 Refer to the following nonlinear model which relates W to P, Q, and R:

The computer output from the regression analysis is:

Based on the info above, the estimated value of a is

1. 0.916
2. 12.182
3. 2.50
4. 2.66

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-40 Refer to the following nonlinear model which relates W to P, Q, and R:

The computer output for the regression analysis is:

Based on the info above, if P = 0.5, Q = 1.5, and R = 0.8, what value do you expect W will have?

a. 16,712

b. 243,200

c. 1,345

d. 3,289

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-41 Refer to the following nonlinear model which relates W to P, Q, and R:

The computer output for the regression analysis is:

Based on the info above, if R decreases by 12% (all other things constant), W will

a. decrease by 72%.

b. decrease by 6%.

c. increase by 6%.

d. increase by 72%.

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-42 Refer to the following nonlinear model which relates W to P, Q, and R:

The computer output for the regression analysis is:

Based on the info above, if Q increases by 8% (all other things constant), W will

a. decrease by 99.2%.

b. decrease by 12.5%.

c. increase by 0.99%.

d. increase by 99.2%.

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-43 Refer to the following nonlinear model which relates W to P, Q, and R:

The computer output for the regression analysis is:

Based on the info above, if P = Q = R = 1, what value do you expect W will have?

a. 0

b. 1

c. 12.182

d. 2.50

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-44 Refer to the following nonlinear model which relates W to P, Q, and R:

The computer output for the regression analysis is:

Based on the info above, the value of R² tells us that

a. 0.9023% of the total variation in ln W is explained by the regression equation.

b. 90.23% of the total variation in ln W is explained by the regression equation.

c. 0.9023% of the total variation in P, W, and R is explained by the regression equation.

d. 0.9023% of the total variation in ln P, ln Q, and ln R is explained by the regression equation.

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-45 In a multiple regression model, the coefficients on the independent variables measure

1. the percent of the variation in the dependent variable explained by a change in that independent variable, all other influences held constant.
2. the change in the dependent variable from a one-unit change in that independent variable, all other influences held constant.
3. the change in that independent variable from a one-unit change in the dependent variable, all other influences held constant.
4. the change in the dependent variable explained by the random error, all other influences held constant.

Difficulty: 02 Medium

Topic: Multiple Regression

AACSB: Reflective Thinking

Blooms: Understand

Learning Objective: 04-05

4-46 The quadratic equation Y = a + bX +cX² can be estimated using linear regression by estimating

a. Y = a + bX + ZX where Z = c²

b. Y = a + ZX where Z = (b + c)

c. Y = a + bZ where Z = X²

d. Y = a + ZX where Z = (b + c)²

e. none of the above will work

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-47 A manager wishes to estimate an average cost equation of the following form:

where Q is the level of output. Letting Z = Q² and using least-squares estimation, the manager obtains the following computer output:

Given the above information, which of the parameter estimates are statistically significant at the 1% significance level?

a. All parameter estimates are statistically significant.

b. All parameter estimates except are statistically significant.

c. is not statistically significant, but all the rest of the parameter estimates are significant.

d. is not statistically significant, but all the rest of the parameter estimates are significant.

Difficulty: 02 Medium

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Understand

Learning Objective: 04-06

4-48 A manager wishes to estimate an average cost equation of the following form:

where Q is the level of output. Letting Z = Q² and using least-squares estimation, the manager obtains the following computer output:

Given the above information, the value of R² indicates that _______ of the total variation in C is explained by the regression equation.

a. 0.7679%

b. 76.79%

c. 7.679%

d. 7679%

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-49 A manager wishes to estimate an average cost equation of the following form:

where Q is the level of output. Letting Z = Q² and using least-squares estimation, the manager obtains the following computer output:

Given the above information, when output is 40 units, what is average cost?

a. $200

b. $280

c. $360

d. $480

e. $520

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06

4-50 A manager wishes to estimate an average cost equation of the following form:

where Q is the level of output. Letting Z = Q² and using least-squares estimation, the manager obtains the following computer output:

Given the above information, when output is 20 units, what is average cost?

a. $160

b. $200

c. $280

d. $340

e. $360

Difficulty: 03 Hard

Topic: Nonlinear Regression Models

AACSB: Analytical Thinking

Blooms: Analyze

Learning Objective: 04-06