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Exam 15: Inference With Regression Models

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Exam 1: Statistics and Data68 Questionsadd course
Exam 2: Tabular and Graphical Methods99 Questionsadd course
Exam 3: Numerical Descriptive Measures123 Questionsadd course
Exam 4: Basic Probability Concepts107 Questionsadd course
Exam 5: Discrete Probability Distributions118 Questionsadd course
Exam 6: Continuous Probability Distributions114 Questionsadd course
Exam 7: Sampling and Sampling Distributions110 Questionsadd course
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Exam 10: Statistical Inference Concerning Two Populations104 Questionsadd course
Exam 11: Statistical Inference Concerning Variance96 Questionsadd course
Exam 12: Chi-Square Tests100 Questionsadd course
Exam 13: Analysis of Variance89 Questionsadd course
Exam 14: Regression Analysis116 Questionsadd course
Exam 15: Inference With Regression Models117 Questionsadd course
Exam 16: Regression Models for Nonlinear Relationships95 Questionsadd course
Exam 17: Regression Models With Dummy Variables117 Questionsadd course
Exam 18: Time Series and Forecasting103 Questionsadd course
Exam 19: Returns, Index Numbers and Inflation98 Questionsadd course
Exam 20: Nonparametric Tests99 Questionsadd course
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Exhibit 15-7.A manager at a local bank analyzed the relationship between monthly salary (y,in $)and length of service (x,measured in months)for 30 employees.She estimates Exhibit 15-7.A manager at a local bank analyzed the relationship between monthly salary (y,in $)and length of service (x,measured in months)for 30 employees.She estimates .The following table summarizes a portion of the regression results: Refer to Exhibit 15-7.Using the 95% confidence interval,what is the conclusion to the following hypothesis test: ? .The following table summarizes a portion of the regression results: Exhibit 15-7.A manager at a local bank analyzed the relationship between monthly salary (y,in $)and length of service (x,measured in months)for 30 employees.She estimates .The following table summarizes a portion of the regression results: Refer to Exhibit 15-7.Using the 95% confidence interval,what is the conclusion to the following hypothesis test: ? Refer to Exhibit 15-7.Using the 95% confidence interval,what is the conclusion to the following hypothesis test: Exhibit 15-7.A manager at a local bank analyzed the relationship between monthly salary (y,in $)and length of service (x,measured in months)for 30 employees.She estimates .The following table summarizes a portion of the regression results: Refer to Exhibit 15-7.Using the 95% confidence interval,what is the conclusion to the following hypothesis test: ? ?

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Exhibit 15-4.A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: Exhibit 15-4.A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: , where Attendance is the daily attendance (in 1000s),Price is the gate price (in $),and Rides is the number of rides at the amusement park.The researcher would like to construct interval estimates for Attendance when Price and Rides equal $85 and 30,respectively.The researcher estimates a modified model where Attendance is the response variable and the explanatory variables are now defined as and .A portion of the regression results is shown in the accompanying table. Refer to Exhibit 15-4.According to the modified model,what is the predicted value for Attendance when Price and Rides equal $85 and 30,respectively. , where Attendance is the daily attendance (in 1000s),Price is the gate price (in $),and Rides is the number of rides at the amusement park.The researcher would like to construct interval estimates for Attendance when Price and Rides equal $85 and 30,respectively.The researcher estimates a modified model where Attendance is the response variable and the explanatory variables are now defined as Exhibit 15-4.A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: , where Attendance is the daily attendance (in 1000s),Price is the gate price (in $),and Rides is the number of rides at the amusement park.The researcher would like to construct interval estimates for Attendance when Price and Rides equal $85 and 30,respectively.The researcher estimates a modified model where Attendance is the response variable and the explanatory variables are now defined as and .A portion of the regression results is shown in the accompanying table. Refer to Exhibit 15-4.According to the modified model,what is the predicted value for Attendance when Price and Rides equal $85 and 30,respectively. and Exhibit 15-4.A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: , where Attendance is the daily attendance (in 1000s),Price is the gate price (in $),and Rides is the number of rides at the amusement park.The researcher would like to construct interval estimates for Attendance when Price and Rides equal $85 and 30,respectively.The researcher estimates a modified model where Attendance is the response variable and the explanatory variables are now defined as and .A portion of the regression results is shown in the accompanying table. Refer to Exhibit 15-4.According to the modified model,what is the predicted value for Attendance when Price and Rides equal $85 and 30,respectively. .A portion of the regression results is shown in the accompanying table. Exhibit 15-4.A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: , where Attendance is the daily attendance (in 1000s),Price is the gate price (in $),and Rides is the number of rides at the amusement park.The researcher would like to construct interval estimates for Attendance when Price and Rides equal $85 and 30,respectively.The researcher estimates a modified model where Attendance is the response variable and the explanatory variables are now defined as and .A portion of the regression results is shown in the accompanying table. Refer to Exhibit 15-4.According to the modified model,what is the predicted value for Attendance when Price and Rides equal $85 and 30,respectively. Refer to Exhibit 15-4.According to the modified model,what is the predicted value for Attendance when Price and Rides equal $85 and 30,respectively.

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A researcher analyzes the factors that may influence the poverty rate and estimates the following model:

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, where y is the poverty rate (y,in %),x<sub>1</sub> is the percent of the population with at least a high school education,x<sub>2</sub> is the median income ( in $1000s),and x<sub>3</sub> is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as ,and .A portion of the regression results is shown in the accompanying table. a.According to the modified model,what is the point estimate for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively. b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) c.According to the modified model,what is a 95% prediction interval for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) ,
where y is the poverty rate (y,in %),x1 is the percent of the population with at least a high school education,x2 is the median income ( in $1000s),and x3 is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x1,x2,and x3 equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as , where y is the poverty rate (y,in %),x<sub>1</sub> is the percent of the population with at least a high school education,x<sub>2</sub> is the median income ( in $1000s),and x<sub>3</sub> is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as ,and .A portion of the regression results is shown in the accompanying table. a.According to the modified model,what is the point estimate for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively. b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) c.According to the modified model,what is a 95% prediction interval for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) ,and , where y is the poverty rate (y,in %),x<sub>1</sub> is the percent of the population with at least a high school education,x<sub>2</sub> is the median income ( in $1000s),and x<sub>3</sub> is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as ,and .A portion of the regression results is shown in the accompanying table. a.According to the modified model,what is the point estimate for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively. b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) c.According to the modified model,what is a 95% prediction interval for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) .A portion of the regression results is shown in the accompanying table. , where y is the poverty rate (y,in %),x<sub>1</sub> is the percent of the population with at least a high school education,x<sub>2</sub> is the median income ( in $1000s),and x<sub>3</sub> is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as ,and .A portion of the regression results is shown in the accompanying table. a.According to the modified model,what is the point estimate for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively. b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) c.According to the modified model,what is a 95% prediction interval for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) a.According to the modified model,what is the point estimate for the poverty rate when x1,x2,and x3 equal 85%,$50,000,and 10,respectively.
b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x1,x2,and x3 equal 85%,$50,000,and 10,respectively? (Note that , where y is the poverty rate (y,in %),x<sub>1</sub> is the percent of the population with at least a high school education,x<sub>2</sub> is the median income ( in $1000s),and x<sub>3</sub> is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as ,and .A portion of the regression results is shown in the accompanying table. a.According to the modified model,what is the point estimate for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively. b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) c.According to the modified model,what is a 95% prediction interval for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) . )
c.According to the modified model,what is a 95% prediction interval for the poverty rate when x1,x2,and x3 equal 85%,$50,000,and 10,respectively? (Note that , where y is the poverty rate (y,in %),x<sub>1</sub> is the percent of the population with at least a high school education,x<sub>2</sub> is the median income ( in $1000s),and x<sub>3</sub> is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are now defined as ,and .A portion of the regression results is shown in the accompanying table. a.According to the modified model,what is the point estimate for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively. b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) c.According to the modified model,what is a 95% prediction interval for the poverty rate when x<sub>1</sub>,x<sub>2</sub>,and x<sub>3</sub> equal 85%,$50,000,and 10,respectively? (Note that . ) . )

Serial correlation is typically observed in:

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Question 4

Exhibit 15-5.The accompanying table shows the regression results when estimating Exhibit 15-5.The accompanying table shows the regression results when estimating . Refer to Exhibit 15-5.When testing whether or not x<sub>1</sub> and x<sub>2</sub> are jointly significant,the null hypothesis is . Exhibit 15-5.The accompanying table shows the regression results when estimating . Refer to Exhibit 15-5.When testing whether or not x<sub>1</sub> and x<sub>2</sub> are jointly significant,the null hypothesis is Refer to Exhibit 15-5.When testing whether or not x1 and x2 are jointly significant,the null hypothesis is

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Question 5

Exhibit 15-1.An marketing analyst wants to examine the relationship between sales (in $1,000s)and advertising (in $100s)for firms in the food and beverage industry and so collects monthly data for 25 firms.He estimates the model Exhibit 15-1.An marketing analyst wants to examine the relationship between sales (in $1,000s)and advertising (in $100s)for firms in the food and beverage industry and so collects monthly data for 25 firms.He estimates the model .The following table shows a portion of the regression results. Refer to Exhibit 15-1.When testing whether the slope coefficient differs from 3,the critical values at the 5% significance level are -2.069 and 2.069.The conclusion to the test is to .The following table shows a portion of the regression results. Exhibit 15-1.An marketing analyst wants to examine the relationship between sales (in $1,000s)and advertising (in $100s)for firms in the food and beverage industry and so collects monthly data for 25 firms.He estimates the model .The following table shows a portion of the regression results. Refer to Exhibit 15-1.When testing whether the slope coefficient differs from 3,the critical values at the 5% significance level are -2.069 and 2.069.The conclusion to the test is to Refer to Exhibit 15-1.When testing whether the slope coefficient differs from 3,the critical values at the 5% significance level are -2.069 and 2.069.The conclusion to the test is to

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Question 6

The accompanying table shows the regression results when estimating The accompanying table shows the regression results when estimating .When testing whether the slope coefficient differs from 1,the value of the test statistic is .When testing whether the slope coefficient differs from 1,the value of the test statistic is The accompanying table shows the regression results when estimating .When testing whether the slope coefficient differs from 1,the value of the test statistic is

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Question 7

Exhibit 15-6.Tiffany & Co.has been the world's premier jeweler since 1837.The performance of Tiffany's stock is likely to be strongly influenced by the economy.Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60).The accompanying table shows the regression results when estimating the CAPM model for Tiffany's return. Exhibit 15-6.Tiffany & Co.has been the world's premier jeweler since 1837.The performance of Tiffany's stock is likely to be strongly influenced by the economy.Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60).The accompanying table shows the regression results when estimating the CAPM model for Tiffany's return. Refer to Exhibit 15-6.When testing whether there are abnormal returns,or whether the alpha coefficient is significantly different from zero,the value of the test statistic is Refer to Exhibit 15-6.When testing whether there are abnormal returns,or whether the alpha coefficient is significantly different from zero,the value of the test statistic is

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Question 8

Consider the following regression results based on 30 observations.

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Question 9

A marketing manager examines the relationship between the attendance at amusement parks and the price of admission.He estimates the following model:

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Question 10

Exhibit 15-6.Tiffany & Co.has been the world's premier jeweler since 1837.The performance of Tiffany's stock is likely to be strongly influenced by the economy.Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60).The accompanying table shows the regression results when estimating the CAPM model for Tiffany's return. Exhibit 15-6.Tiffany & Co.has been the world's premier jeweler since 1837.The performance of Tiffany's stock is likely to be strongly influenced by the economy.Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60).The accompanying table shows the regression results when estimating the CAPM model for Tiffany's return. Refer to Exhibit 15-6.When testing whether the beta coefficient is significantly greater than one,the value of the test statistic is Refer to Exhibit 15-6.When testing whether the beta coefficient is significantly greater than one,the value of the test statistic is

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Question 11

The term BLUE stands for Best Linear Unbiased Estimator.

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Question 12

The accompanying table shows the regression results when estimating The accompanying table shows the regression results when estimating .What is the value of the test statistic when testing whether x significantly influences y? .What is the value of the test statistic when testing whether x significantly influences y? The accompanying table shows the regression results when estimating .What is the value of the test statistic when testing whether x significantly influences y?

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Question 13

Exhibit 15-9.An economist estimates the following model: Exhibit 15-9.An economist estimates the following model: .She would like to construct interval estimates for y when x equals 2.She estimates a modified model where y is the response variable and the explanatory variable is now defined as .A portion of the regression results is shown in the accompanying table. Refer to Exhibit 15-9.According to the modified model,what is the predicted value of y when x equals 2. .She would like to construct interval estimates for y when x equals 2.She estimates a modified model where y is the response variable and the explanatory variable is now defined as Exhibit 15-9.An economist estimates the following model: .She would like to construct interval estimates for y when x equals 2.She estimates a modified model where y is the response variable and the explanatory variable is now defined as .A portion of the regression results is shown in the accompanying table. Refer to Exhibit 15-9.According to the modified model,what is the predicted value of y when x equals 2. .A portion of the regression results is shown in the accompanying table. Exhibit 15-9.An economist estimates the following model: .She would like to construct interval estimates for y when x equals 2.She estimates a modified model where y is the response variable and the explanatory variable is now defined as .A portion of the regression results is shown in the accompanying table. Refer to Exhibit 15-9.According to the modified model,what is the predicted value of y when x equals 2. Refer to Exhibit 15-9.According to the modified model,what is the predicted value of y when x equals 2.

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Question 14

Exhibit 15-5.The accompanying table shows the regression results when estimating Exhibit 15-5.The accompanying table shows the regression results when estimating . Refer to Exhibit 15-5.When testing whether the explanatory variables are jointly significant at the 5% level,the conclusion is to: . Exhibit 15-5.The accompanying table shows the regression results when estimating . Refer to Exhibit 15-5.When testing whether the explanatory variables are jointly significant at the 5% level,the conclusion is to: Refer to Exhibit 15-5.When testing whether the explanatory variables are jointly significant at the 5% level,the conclusion is to:

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Question 15

Find the 95% confidence interval for the regression coefficient β1,if df = 30,b = -2 and Find the 95% confidence interval for the regression coefficient β<sub>1</sub>,if df = 30,b = -2 and . .

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Question 16

A manager at a local bank analyzed the relationship between monthly salary (y,in $)and length of service (x,measured in months)for 30 employees.The following table summarizes a portion of the regression results:

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Question 17

Given the following portion of regression results,which of the following conclusions is true with regard to the F test at the 5% significance level? Given the following portion of regression results,which of the following conclusions is true with regard to the F test at the 5% significance level?

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Question 18

Exhibit 15-6.Tiffany & Co.has been the world's premier jeweler since 1837.The performance of Tiffany's stock is likely to be strongly influenced by the economy.Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60).The accompanying table shows the regression results when estimating the CAPM model for Tiffany's return. Exhibit 15-6.Tiffany & Co.has been the world's premier jeweler since 1837.The performance of Tiffany's stock is likely to be strongly influenced by the economy.Monthly data for Tiffany's risk-adjusted return and the risk-adjusted market return are collected for a five-year period (n = 60).The accompanying table shows the regression results when estimating the CAPM model for Tiffany's return. Refer to Exhibit 15-6.You would like to determine whether an investment in Tiffany's is riskier than the market.When conducting this test,you set up the following competing hypotheses: Refer to Exhibit 15-6.You would like to determine whether an investment in Tiffany's is riskier than the market.When conducting this test,you set up the following competing hypotheses:

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Question 19

Excel and virtually all other statistical packages report the p-value

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Question 20
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