chapter 5: basic estimation techniques2019/04/12 · intercept 15.48 5.09 3.04 0.0008 x −21.36...
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Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Chapter 4: BASIC ESTIMATION TECHNIQUES Multiple Choice
4-1 For the equation Y = a + bX, the objective of regression analysis is to
a. estimate the parameters a and b.
b. estimate the variables Y and X.
c. fit a straight line through the data scatter in such a way that the sum of the squared errors
is minimized.
d. both a and c
Answer: d
Difficulty: 01 Easy
Topic: The Simple Linear Regression Model
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-01
4-2 In a linear regression equation of the form Y = a + bX, the slope parameter b shows
a. X / Y.
b. Y / X.
c. Y / b.
d. X / b.
e. none of the above
Answer: b
Difficulty: 01 Easy
Topic: The Simple Linear Regression Model
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-01
4-3 In a linear regression equation of the form Y = a + bX, the intercept parameter a shows
a. the value of X when Y is zero.
b. the value of Y when X is zero.
c. the amount that Y changes when X changes by one unit.
d. the amount that X changes when Y changes by one unit.
Answer: b
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.
a. intercept
b. slope parameter
c. R-square
d. random error term
Answer: d
Difficulty: 01 Easy
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Topic: The Simple Linear Regression Model
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-01
4-5 The sample regression line
a. shows the actual (or true) relation between the dependent and independent variables.
b. is used to estimate the population regression line.
c. connects the data points in a sample.
d. is estimated by the population regression line.
e. maximizes the sum of the squared differences between the data points in a sample and the
sample regression line.
Answer: b
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.
Answer: b
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.
c. minimizes the distance between the population regression line and the sample regression
line.
d. all of the above
Answer: b
Difficulty: 01 Easy
Topic: Fitting a Regression Line
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-02
4-8 In a linear regression equation Y = a + bX, the fitted or predicted value of Y is
a. the value of Y obtained by substituting specific values of X into the sample regression
equation.
b. the value of X associated with a particular value of Y.
c. the value of X that the regression equation predicts.
d. the values of the parameters predicted by the estimators.
e. the value of Y associated with a particular value of X in the sample.
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Answer: a
Difficulty: 01 Easy
Topic: The Simple Linear Regression Model
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-01
4-9 A parameter estimate is said to be statistically significant if there is sufficient evidence that the
a. sample regression equals the population regression.
b. parameter estimated from the sample equals the true value of the parameter.
c. value of the t-ratio equals the critical value.
d. true value of the parameter does not equal zero.
Answer: d
Difficulty: 02 Medium
Topic: Fitting a Regression Line
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-02
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
Answer: d
Difficulty: 01 Easy
Topic: Fitting a Regression Line
AACSB: Reflective Thinking
Blooms: Understand
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.
Answer: a
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.
b. the R 2 -statistic.
c. the F-statistic.
d. the standard error statistic.
Answer: c
Difficulty: 01 Easy
Topic: Evaluation of the Regression Equation
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-04
4-13 In the regression model Y = a + bX + cZ , a test of the hypothesis that parameter c equals zero is
a. an F-test.
b. an R 2 -test.
c. a zero-statistic.
d. a t-test.
e. a Z-test.
Answer: d
Difficulty: 01 Easy
Topic: Testing For Statistical Significance
AACSB: Reflective Thinking
Blooms: Understand
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
Answer: b
Difficulty: 01 Easy
Topic: Multiple Regression
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-05
4-15 The linear regression equation, Y = a + bX, was estimated. The following computer printout was
obtained:
DEPENDENT VARIABLE: Y R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.3066 7.076 0.0171 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 15.48 5.09 3.04 0.0008
X −21.36 8.03 −2.66 0.0171
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.
Answer: b
Difficulty: 01 Easy
Topic: Evaluation of the Regression Equation
AACSB: Reflective Thinking
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Blooms: Understand
Learning Objective: 04-04
4-16 The linear regression equation, Y = a + bX, was estimated. The following computer printout was
obtained:
DEPENDENT VARIABLE: Y R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.3066 7.076 0.0171 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 15.48 5.09 3.04 0.0008
X −21.36 8.03 −2.66 0.0171
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.
Answer: d
Difficulty: 02 Medium
Topic: Fitting a Regression Line
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-02
4-17 The linear regression equation, Y = a + bX, was estimated. The following computer printout was
obtained:
DEPENDENT VARIABLE: Y R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.3066 7.076 0.0171 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 15.48 5.09 3.04 0.0008
X −21.36 8.03 −2.66 0.0171
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
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Answer: d
Difficulty: 03 Hard
Topic: Testing For Statistical Significance
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-03
4-18 The linear regression equation, Y = a + bX, was estimated. The following computer printout was
obtained:
DEPENDENT VARIABLE: Y R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.3066 7.076 0.0171 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 15.48 5.09 3.04 0.0008
X −21.36 8.03 −2.66 0.0171
Given the above information, which of the following statements is correct at the 1% level of
significance?
a. Both a and b are statistically significant.
b. Neither a nor b is statistically significant.
c. a is statistically significant, but b is not.
d. b is statistically significant, but a is not.
Answer: c
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:
DEPENDENT VARIABLE: Y R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.3066 7.076 0.0171 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 15.48 5.09 3.04 0.0008
X −21.36 8.03 −2.66 0.0171
Given the above information, the value of the R 2 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.
Answer: c
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Difficulty: 02 Medium
Topic: Evaluation of the 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:
DEPENDENT VARIABLE: Y R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.3066 7.076 0.0171 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 15.48 5.09 3.04 0.0008
X −21.36 8.03 −2.66 0.0171
Given the above information, the exact level of significance of b is
a. 0.171 percent.
b. 1 percent.
c. 1.71 percent.
d. 2.66 percent.
e. 2.921 percent.
Answer: c
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:
DEPENDENT VARIABLE: Y R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.3066 7.076 0.0171 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 15.48 5.09 3.04 0.0008
X −21.36 8.03 −2.66 0.0171
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
Answer: d
Difficulty: 02 Medium
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Topic: The Simple Linear Regression Model
AACSB: Analytic
Blooms: Apply
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:
DEPENDENT VARIABLE: T R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 27 0.7793 42.38 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 5150.43
1740.72 2.96 0.0068
G −480.92 130.66 −3.68 0.0012
U 211.0 75.0 2.81 0.0096
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, a , b and c are all less than 0.01. d. The critical value of t is 2.797. e. all of the above
Answer: e
Difficulty: 03 Hard
Topic: Multiple Regression
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-05
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
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:
DEPENDENT VARIABLE: T R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 27 0.7793 42.38 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 5150.43
1740.72 2.96 0.0068
G −480.92 130.66 −3.68 0.0012
U 211.0 75.0 2.81 0.0096
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
Answer: d
Difficulty: 01 Easy
Topic: Multiple Regression
AACSB: Analytic
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:
DEPENDENT VARIABLE: T R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 27 0.7793 42.38 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 5150.43
1740.72 2.96 0.0068
G −480.92 130.66 −3.68 0.0012
U 211.0 75.0 2.81 0.0096
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
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
Answer: a
Difficulty: 02 Medium
Topic: Multiple Regression
AACSB: Analytic
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:
DEPENDENT VARIABLE: T R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 27 0.7793 42.38 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 5150.43
1740.72 2.96 0.0068
G −480.92 130.66 −3.68 0.0012
U 211.0 75.0 2.81 0.0096
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.
a. $75
b. $211
c. $280
d. $460
Answer: b
Difficulty: 02 Medium
Topic: Multiple Regression
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-05
4-26 In the nonlinear function Y = aXbZ
c , the parameter c measures
a. Y /Z.
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
Answer: e
Difficulty: 03 Hard
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Topic: Nonlinear Regression Analysis
AACSB: Analytic
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
Answer: e
Difficulty: 03 Hard
Topic: Testing For Statistical Significance
AACSB: Reflective Thinking
Blooms: Understand
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%
Answer: e
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. tcritical = 2.042.
b. tcritical = 2.056.
c. Fcritical = 4.22.
d. Fcritical = 7.76.
Answer: b
Difficulty: 03 Hard
Topic: Testing For Statistical Significance
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-03
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
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. tcritical = 2.861.
b. tcritical = −2.845.
c. tcritical = 2.845.
d. Fcritical = 5.93.
e. Fcritical = 19.44.
Answer: a
Difficulty: 03 Hard
Topic: Testing For Statistical Significance
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-03
4-31 Refer to the following computer output from estimating the parameters of the nonlinear model
Y = aRbS cT d
The computer output from the regression analysis is:
DEPENDENT VARIABLE: LNY R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 32 0.7766 32.44 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT −0.6931 0.32 −2.17 0.0390
LNR 4.66 1.36 3.43 0.0019
LNS −0.44 0.24 −1.83 0.0774
LNT 8.28 4.6 1.80 0.0826
Based on the info above, the nonlinear relation can be transformed into the following linear
regression model:
a. Y = ln(aRbS cT d )
b. lnY = ln(aRbScT d )
c. lnY = lna × ln R × lnS × lnT d. lnY = lna + bln R + c lnS + d lnT Answer: d
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-06
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
4-32 Refer to the following computer output from estimating the parameters of the nonlinear model
Y = aRbS cT d
The computer output from the regression analysis is:
DEPENDENT VARIABLE: LNY R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 32 0.7766 32.44 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT −0.6931 0.32 −2.17 0.0390
LNR 4.66 1.36 3.43 0.0019
LNS −0.44 0.24 −1.83 0.0774
LNT 8.28 4.6 1.80 0.0826
Based on the info above, the estimated value of a is
a. −0 .6931
b. 0.50
c. −3.67
d. 2.66
Answer: b
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-06
4-33 Refer to the following computer output from estimating the parameters of the nonlinear model
Y = aRbS cT d
The computer output from the regression analysis is:
DEPENDENT VARIABLE: LNY R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 32 0.7766 32.44 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT −0.6931 0.32 −2.17 0.0390
LNR 4.66 1.36 3.43 0.0019
LNS −0.44 0.24 −1.83 0.0774
LNT 8.28 4.6 1.80 0.0826
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 a and b are statistically significant. c. a is not statistically significant, but all the rest of the parameter estimates are significant. d. c is not statistically significant, but all the rest of the parameter estimates are significant.
Answer: a
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-06
4-34 Refer to the following computer output from estimating the parameters of the nonlinear model
Y = aRbS cT d
The computer output from the regression analysis is:
DEPENDENT VARIABLE: LNY R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 32 0.7766 32.44 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT −0.6931 0.32 −2.17 0.0390
LNR 4.66 1.36 3.43 0.0019
LNS −0.44 0.24 −1.83 0.0774
LNT 8.28 4.6 1.80 0.0826
Based on the info above, if R = 1, S = 2, and T = 3, what value do you expect Y will have?
a. 143
b. 1,345
c. 3,289
d. 6,578
e. −4 ,559
Answer: c
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-06
4-35 Refer to the following computer output from estimating the parameters of the nonlinear model
Y = aRbS cT d
The computer output from the regression analysis is:
DEPENDENT VARIABLE: LNY R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 32 0.7766 32.44 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT −0.6931 0.32 −2.17 0.0390
LNR 4.66 1.36 3.43 0.0019
LNS −0.44 0.24 −1.83 0.0774
LNT 8.28 4.6 1.80 0.0826
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
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Based on the info above, if R decreases by 10% (all other things constant), Y will
a. increase by 4.66%.
b. increase by 46.6%.
c. decrease by 4.66%.
d. decrease by 46.6%.
Answer: d
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Analyze
Learning Objective: 04-06
4-36 Refer to the following computer output from estimating the parameters of the nonlinear model
Y = aRbS cT d
The computer output from the regression analysis is:
DEPENDENT VARIABLE: LNY R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 32 0.7766 32.44 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT −0.6931 0.32 −2.17 0.0390
LNR 4.66 1.36 3.43 0.0019
LNS −0.44 0.24 −1.83 0.0774
LNT 8.28 4.6 1.80 0.0826
Based on the info above, if S increases by 8% (all other things constant), Y will
a. decrease by 3.52%.
b. decrease by 0.44%.
c. decrease by 4.4%.
d. increase by 0.44%.
Answer: a
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Analyze
Learning Objective: 04-06
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
4-37 Refer to the following nonlinear model which relates W to P, Q, and R:
W = aPbQc Rd
The computer output form the regression analysis is:
DEPENDENT VARIABLE: LNW R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.9023 43.12 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 2.50 0.45 5.56 0.0001
LNP −5.10 1.75 −2.91 0.0113
LNQ 12.4 3.2 3.88 0.0017
LNR −6.00 1.5 −4.00 0.0010
Based on the info above, the nonlinear relation can be transformed into the following linear
regression model:
a. W = ln(aPbQcRd )
b. lnW = ln(aPbQc Rd )
c. lnW = ln a × ln P × lnQ × ln R
d. lnW = ln a + bln P + c lnQ + d ln R
Answer: d
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-06
4-38 Refer to the following nonlinear model which relates W to P, Q, and R:
W = aPbQc Rd
The computer output form the regression analysis is:
DEPENDENT VARIABLE: LNW R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.9023 43.12 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 2.50 0.45 5.56 0.0001
LNP −5.10 1.75 −2.91 0.0113
LNQ 12.4 3.2 3.88 0.0017
LNR −6.00 1.5 −4.00 0.0010
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
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 a and bare statistically significant.
c. a is not statistically significant, but all the rest of the parameter estimates are significant.
d. c is not statistically significant, but all the rest of the parameter estimates are significant.
Answer: a
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-06
4-39 Refer to the following nonlinear model which relates W to P, Q, and R:
W = aPbQc Rd
The computer output form the regression analysis is:
DEPENDENT VARIABLE: LNW R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.9023 43.12 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 2.50 0.45 5.56 0.0001
LNP −5.10 1.75 −2.91 0.0113
LNQ 12.4 3.2 3.88 0.0017
LNR −6.00 1.5 −4.00 0.0010
Based on the info above, the estimated value of a is
a. 0.916
b. 12.182
c. 2.50
d. 2.66
Answer: b
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-06
4-40 Refer to the following nonlinear model which relates W to P, Q, and R:
W = aPbQc Rd
The computer output form the regression analysis is:
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
DEPENDENT VARIABLE: LNW R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.9023 43.12 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 2.50 0.45 5.56 0.0001
LNP −5.10 1.75 −2.91 0.0113
LNQ 12.4 3.2 3.88 0.0017
LNR −6.00 1.5 −4.00 0.0010
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
Answer: b
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-06
4-41 Refer to the following nonlinear model which relates W to P, Q, and R:
W = aPbQc Rd
The computer output form the regression analysis is:
DEPENDENT VARIABLE: LNW R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.9023 43.12 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 2.50 0.45 5.56 0.0001
LNP −5.10 1.75 −2.91 0.0113
LNQ 12.4 3.2 3.88 0.0017
LNR −6.00 1.5 −4.00 0.0010
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%.
Answer: d
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Learning Objective: 04-06
4-42 Refer to the following nonlinear model which relates W to P, Q, and R:
W = aPbQc Rd
The computer output form the regression analysis is:
DEPENDENT VARIABLE: LNW R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.9023 43.12 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 2.50 0.45 5.56 0.0001
LNP −5.10 1.75 −2.91 0.0113
LNQ 12.4 3.2 3.88 0.0017
LNR −6.00 1.5 −4.00 0.0010
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%.
Answer: d
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-06
4-43 Refer to the following nonlinear model which relates W to P, Q, and R:
W = aPbQc Rd
The computer output form the regression analysis is:
DEPENDENT VARIABLE: LNW R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.9023 43.12 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 2.50 0.45 5.56 0.0001
LNP −5.10 1.75 −2.91 0.0113
LNQ 12.4 3.2 3.88 0.0017
LNR −6.00 1.5 −4.00 0.0010
Based on the info above, if P = Q = R = 1, what value do you expect W will have?
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
a. 0
b. 1
c. 12.182
d. 2.50
Answer: c
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-06
4-44 Refer to the following nonlinear model which relates W to P, Q, and R:
W = aPbQc Rd
The computer output form the regression analysis is:
DEPENDENT VARIABLE: LNW R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 18 0.9023 43.12 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 2.50 0.45 5.56 0.0001
LNP −5.10 1.75 −2.91 0.0113
LNQ 12.4 3.2 3.88 0.0017
LNR −6.00 1.5 −4.00 0.0010
Based on the info above, the value of R 2 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.
Answer: b
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Apply
Learning Objective: 04-06
4-45 In a multiple regression model, the coefficients on the independent variables measure
a. the percent of the variation in the dependent variable explained by a change in that
independent variable, all other influences held constant.
b. the change in the dependent variable from a one-unit change in that independent variable,
all other influences held constant.
c. the change in that independent variable from a one-unit change in the dependent variable,
all other influences held constant.
d. the change in the dependent variable explained by the random error, all other influences
held constant.
Answer: b
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Difficulty: 02 Medium
Topic: Multiple Regression
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-05
4-46 The quadratic equation Y = a + bX +cX 2 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 = X 2
d. Y = a + ZX where Z = (b + c)2
e. none of the above will work
Answer: e
Difficulty: 03 Hard
Topic: Nonlinear Regression Analysis
AACSB: Analytic
Blooms: Analyze
Learning Objective: 04-06
4-47 A manager wishes to estimate an average cost equation of the following form:
C = a + bQ + cQ2
where Q is the level of output. Letting Z = Q 2 and using least-squares estimation, the manager
obtains the following computer output:
DEPENDENT VARIABLE: C R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 28 0.7679 26.47 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 200 38.00 5.26 0.0001
Q −12.00 4.36 −2.75 0.0111
Z 0.50 0.16 3.13 0.0046
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 b are statistically significant.
c. a is not statistically significant, but all the rest of the parameter estimates are significant.
d. c is not statistically significant, but all the rest of the parameter estimates are significant.
Answer: b
Difficulty: 02 Medium
Topic: Multiple Regression
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-05
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
4-48 A manager wishes to estimate an average cost equation of the following form:
C = a + bQ + cQ2
where Q is the level of output. Letting Z = Q 2 and using least-squares estimation, the manager
obtains the following computer output:
DEPENDENT VARIABLE: C R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 28 0.7679 26.47 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 200 38.00 5.26 0.0001
Q −12.00 4.36 −2.75 0.0111
Z 0.50 0.16 3.13 0.0046
Given the above information, the value of R 2 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%
Answer: b
Difficulty: 02 Medium
Topic: Evaluation of the Regression Equation
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-04
4-49 A manager wishes to estimate an average cost equation of the following form:
C = a + bQ + cQ2
where Q is the level of output. Letting Z = Q 2 and using least-squares estimation, the manager
obtains the following computer output:
DEPENDENT VARIABLE: C R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 28 0.7679 26.47 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 200 38.00 5.26 0.0001
Q −12.00 4.36 −2.75 0.0111
Z 0.50 0.16 3.13 0.0046
Given the above information, when output is 40 units, what is average cost?
a. $200
b. $280
c. $360
d. $480
e. $520
Chapter 4: BASIC ESTIMATION TECHNIQUES © 2016 by McGraw-Hill Education. This is proprietary material solely for authorized instructor use. Not authorized for sale or distribution in
any manner. This document may not be copied, scanned, duplicated, forwarded, distributed, or posted on a website, in whole or part.
Answer: d
Difficulty: 02 Medium
Topic: Multiple Regression
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-05
4-50 A manager wishes to estimate an average cost equation of the following form:
C = a + bQ + cQ2
where Q is the level of output. Letting Z = Q 2 and using least-squares estimation, the manager
obtains the following computer output:
DEPENDENT VARIABLE: C R−SQUARE F−RATIO P−VALUE ON F
OBSERVATIONS: 28 0.7679 26.47 0.0001 VARIABLE
PARAMETER ESTIMATE
STANDARD ERROR
T−RATIO
P−VALUE
INTERCEPT 200 38.00 5.26 0.0001
Q −12.00 4.36 −2.75 0.0111
Z 0.50 0.16 3.13 0.0046
Given the above information, when output is 20 units, what is average cost?
a. $160
b. $200
c. $280
d. $340
e. $360
Answer: a
Difficulty: 02 Medium
Topic: Multiple Regression
AACSB: Reflective Thinking
Blooms: Understand
Learning Objective: 04-05