Deck 15: Inference With Regression Models

Question 1

In a multiple regression based on 30 observations,the following information is provided:

Answer 1

with .Also, evaluated at and is 2.8.
a.Construct a 95% confidence interval for if x₁ equals 40 and x₂ equals 30.
b.Construct a 95% prediction interval for y if x₁ equals 40 and x₂ equals 30.
c.Which interval is narrower? Explain.

Question 2

The accompanying table shows the regression results when estimating

Answer 2

. a.Specify the competing hypotheses to determine whether the explanatory variables are jointly significant.
b.At the 5% significance level,are the explanatory variables jointly significant? Explain.
c.At the 5% significance level,is x₂ significant in explaining y? Explain.
d.At the 5% significance level,is the slope coefficient attached to x₃ different from -2?

Question 3

Consider the following regression results based on 40 observations.

Answer 3

a.Specify the hypotheses to determine if the slope differs from one.
b.Calculate the value of the test statistic.
c.At the 5% significance level,find the critical value(s).
d.Does the slope differ from one? Explain.

Question 4

A simple linear regression, ,is estimated using time-series data over the last 10 years.The residuals e,and the time variable t are shown in the accompanying table. a.Graph the residuals e against time and look for any discernible pattern.
b.Which assumption is being violated? Discuss its consequences and suggest a possible remedy.

Question 5

In a multiple regression based on 30 observations,the following information is provided:

Question 6

Consider the following regression results based on 30 observations.

Question 7

An investment analyst wants to examine the relationship between a mutual fund's return,its turnover rate and its expense ratio.She randomly selects 10 mutual funds and estimates: Return = β₀ + β₁ Turnover + β₂ Expense + ε,where Return is the average five-year return (in %),Turnover is the annual holdings turnover (in %),Expense is the annual expense ratio (in %),and ε is the random error component.A portion of the regression results is shown in the accompanying table.

Question 8

The accompanying table shows the regression results when estimating

Question 9

A sociologist studies the relationship between a district's average score on a standardized test for 10^th grade students (y),the average school expenditures per student (x₁in $1000s),and an index of socioeconomic status of the district (x₂).The results of the regression are:

Question 10

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

Question 11

In a simple linear regression based on 30 observations,the following information is provided:

Question 12

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

Question 13

A simple linear regression, ,is estimated using cross-sectional data from 10 firms.The resulting residuals e,along with the values of the explanatory variable Advertising (x,in $100s),are shown in the accompanying table. a.Graph the residuals e against Advertising (x)and look for any discernible pattern.
b.Which assumption is being violated? Discuss its consequences and suggest a possible remedy.

Question 14

Consider the following regression results based on 30 observations.

Question 15

An analyst examines the effect that various variables have on crop yield.He estimates

Question 16

When estimating a multiple regression model based on 30 observations,the following results were obtained.

Question 17

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:

Question 18

A sociologist estimates the following regression relating Poverty (y)to Education (x₁):

Question 19

Pfizer Inc.is the world's largest research-based pharmaceutical company.Monthly data for Pfizer'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 Pfizer's return.

Question 20

Assume you ran a multiple regression to gain a better understanding of the relationship between lumber sales,housing starts,and commercial construction.The regression uses Lumber Sales (in $100,000s)as the response variable with Housing Starts (in 1000s)and Commercial Construction (in 1000s)as the explanatory variables.The results of the regression are:

Question 21

The term multicollinearity refers to the condition when the variance of the error term,conditional on x₁,x₂,…,x_n,is the same for all observations.

Question 22

A wavelike movement in residuals suggests positive serial correlation.

Question 23

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

A)0.66
B)1.42
C)1.96
D)2.25

Question 24

The term BLUE stands for Best Linear Unbiased Estimator.

Question 25

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?

A)Neither of the explanatory variables is related to the response variable.
B)Both of the explanatory variables are related to the response variable.
C)Exactly one of the explanatory variables is related to the response variable.
D)At least one of the explanatory variables is significantly related to the response variable.

Question 26

A crucial assumption in a regression model is that the error term is not correlated with any of the explanatory variables.

Question 27

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

A)for a two-tailed test that assesses whether the regression coefficient differs from one.
B)for a right-tailed test that assesses whether the regression coefficient is greater than zero.
C)for a two-tailed test that assesses whether the regression coefficient differs from zero.
D)for a left-tailed test that assesses whether the regression coefficient is less than zero.

Question 28

Find the 95% confidence interval for the regression coefficient β₁,if df = 30,b = -2 and .

A)[-5.00,-1.00]
B)[-7.88,3.88]
C)[-7.09,3.09]
D)[-8.13,4.13]

Question 29

When some explanatory variables of a regression model are strongly correlated,this phenomenon is called serial correlation.

Question 30

The accompanying table shows the regression results when estimating .Is x significantly related to y at the 5% significance level?

A)Yes,since the p-value of 0.0745 is greater than 0.05.
B)No,since the p-value of 0.0745 is greater than 0.05.
C)Yes,since the slope coefficient of 1.417 is less than the test statistic of 2.25.
D)No,since the slope coefficient of 1.417 is less than the test statistic of 2.25.

Question 31

Consider the following simple linear regression model: .When determining whether there is a positive linear relationship between x and y,the alternative hypothesis takes the form

A)
B)
C)
D)

Question 32

Consider the following simple linear regression model: .When determining whether x significantly influences y,the null hypothesis takes the form

A)
B)
C)
D)

Question 33

If in the multiple linear model the slope coefficient β_i is negative,it suggests an inverse (negative)relationship between the explanatory variable x_i and the response variable.

Question 34

Consider the following simple linear regression model: .When determining whether there is a negative linear relationship between x and y,the alternative hypothesis takes the form

A)
B)
C)
D)

Question 35

The restricted model is a reduced model where we estimate the coefficients that are restricted under the null hypothesis.

Question 36

Consider the following simple linear regression model: .When determining whether there is a one-to-one relationship between x and y,the null hypothesis takes the form

A)
B)
C)
D)

Question 37

Given the following portion of regression results,what is the value of the test statistic?

A)1.96
B)3.49
C)8.04
D)10

Question 38

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

A)0.66
B)1.42
C)1.96
D)2.25

Question 39

The test statistic for testing the individual significance is assumed to follow the t distribution with n - k - 2 degrees of freedom,where n is the sample size and k is the number of explanatory variables.

Question 40

The alternative hypothesis for the test of joint significance is specified as: H_A: At least two β_j ≠ 0.

Question 41

When confronted with multicollinearity,a good remedy is to ____ if we can justify its redundancy.

A)add one more collinear variable.
B)drop one of the collinear variables.
C)remove both the collinear variables.
D)add as many collinear variables as possible.

Question 42

Which of the following violates the assumptions of regression analysis?

A)The error term is normally distributed.
B)The error term has a zero mean.
C)The error term is correlated with an explanatory variable.
D)The error term has a constant variance.

Question 43

Serial correlation is typically observed in:

A)Outliers.
B)Sparse data.
C)Time series data.
D)Cross sectional data.

Question 44

When estimating ,you wish to test versus .The value of the test statistic is and its associated p-value is 0.0092.At the 1% significance level,the conclusion is to:

A)Reject the null hypothesis and conclude that the influence of x₁ and x₂ on y is the same.
B)Reject the null hypothesis and conclude that the influence of x₁ and x₂ on y is not the same.
C)Do not reject the null hypothesis and conclude that the influence of x₁ and x₂ on y is the same.
D)Do not reject the null hypothesis and conclude that the influence of x₁ and x₂ on y is not the same.

Question 45

In regression,the two types of interval estimates concerning y are called:

A)significance interval and prediction interval.
B)confidence interval and significance interval.
C)confidence interval and prediction interval.
D)significance interval and frequency interval.

Question 46

If the variance of the error term is not the same for all observations,we

A)Get estimators that are biased.
B)Can perform tests of significance.
C)Cannot conduct tests of significance.
D)A and C

Question 47

Multicollinearity is suspected when

A)there is a low R² coupled with significant explanatory variables.
B)there is a high R² coupled with significant explanatory variables.
C)there is a low R² coupled with insignificant explanatory variables.
D)there is a high R² coupled with insignificant explanatory variables.

Question 48

A sample of 200 monthly observations is used to run a simple linear regression: Returns = β₀ + β₁ Leverage + ε.A five percent level of significance is used to study if leverage has a significant influence on returns.The value of the test statistic for the regression coefficient of Leverage is calculated as ,with an associated p-value of 0.2770.The correct decision is to:

A)Reject the null hypothesis and conclude that leverage significantly explains returns.
B)Reject the null hypothesis and conclude that leverage does not significantly explain returns.
C)Do not reject the null hypothesis and conclude that leverage does not significantly explain returns.
D)Do not reject the null hypothesis and conclude that leverage significantly explains returns.

Question 49

One of the assumptions of regression analysis is:

A)there is perfect multicollinearity among some explanatory variables.
B)there is no perfect multicollinearity among any explanatory variables.
C)there is some degree of multicollinearity among some explanatory variables.
D)None of the above.

Question 50

In regression,the predicted values concerning y are subject to:

A)Kurtosis.
B)Skewness.
C)Mean deviation.
D)Sampling variation.

Question 51

In regression,multicollinearity is considered problematic when two or more explanatory variables are:

A)Not correlated.
B)Rarely correlated.
C)Highly correlated.
D)Moderately correlated.

Question 52

Given the following portion of regression results,what is the value of the test statistic?

A)1.96
B)2.59
C)3.49
D)10

Question 53

The accompanying table shows the regression results when estimating .At the 5% significance level,which explanatory variable(s)is(are)individually significant?

A)Only x₁
B)Only x₃
C)x₁ and x₂
D)x₂ and x₃

Question 54

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?

A)Neither of the explanatory variables is significantly related to the response variable.
B)Both of the explanatory variables are significantly related to the response variable.
C)Exactly one of the explanatory variables is significantly related to the response variable.
D)At least one of the explanatory variables is significantly related to the response variable.

Question 55

When testing r linear restrictions imposed on the model ,the test statistic is assumed to follow the distribution with

A)df₁ = k and df₂ = n - k - 1.
B)df₁ = k - 1 and df₂ = n - k - 1.
C)df₁ = r and df₂ = n - k.
D)df₁ = r and df₂ = n - k - 1.

Question 56

A researcher gathers data on 25 households and estimates the following model: .A residual plot of the estimated model is shown in the accompanying graph.What can be inferred from the residual plot?

A)The residuals have little variation.
B)The residuals do not exhibit any pattern.
C)The residuals seem to fan out across the horizontal axis.
D)The residuals are evenly distributed across the horizontal axis.

Question 57

For a given confidence level,the prediction interval is always wider than the confidence interval because

A)The confidence interval is for a particular value of y rather than for the expected value E(y).
B)The prediction interval is for a particular value of y rather than for the expected value E(y).
C)The confidence interval is for a particular value of x rather than for the expected value E(x).
D)The prediction interval is for a particular value of x rather than for the expected value E(x).

Question 58

When estimating ,you wish to test versus .The value of the test statistic is and its associated p-value is 0.1073.At the 5% significance level,the conclusion is to:

A)Reject the null hypothesis and conclude that x₁ and x₂ are jointly significant.
B)Reject the null hypothesis and conclude that x₁ and x₂ are not jointly significant.
C)Do not reject the null hypothesis and conclude that x₁ and x₂ are jointly significant.
D)Do not reject the null hypothesis and conclude that x₁ and x₂ are not jointly significant.

Question 59

Refer to the portion of regression results in the accompanying table.When testing the overall significance of the regression model at the 5% level given a critical value of ,the decision is to:

A)Reject H₀ and conclude that the explanatory variables are jointly significant.
B)Do not reject H₀ and conclude that the explanatory variables are jointly significant.
C)Reject H₀ and conclude that the explanatory variables are not jointly significant.
D)Do not reject H₀ and conclude that the explanatory variables are not jointly significant.

Question 60

Refer to the portion of regression results in the accompanying table.When testing the overall significance of the regression model at the 5% level given a critical value of ,the decision is to:

A)Reject H₀ and conclude that the explanatory variables are jointly significant.
B)Do not reject H₀ and conclude that the explanatory variables are jointly significant.
C)Reject H₀ and conclude that the explanatory variables are not jointly significant.
D)Do not reject H₀ and conclude that the explanatory variables are not jointly significant.

Question 61

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:

A)
B)
C)
D)

Question 62

Exhibit 15-5.The accompanying table shows the regression results when estimating . Refer to Exhibit 15-5.At the 5% significance level,which explanatory variable(s)is(are)individually significant?

A)Only x₁
B)Only x₃
C)x₁ and x₂
D)x₂ and x₃

Question 63

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 relevant critical value at the 5% significance level is .The conclusion to the test is:

A)Reject H₀,and conclude that the return on Tiffany stock is riskier than the return on the market.
B)Do not reject H₀,and conclude that the return on Tiffany stock is riskier than the return on the market.
C)Reject H₀,and conclude that the return on Tiffany stock is less risky than the return on the market.
D)Do not reject H₀,and conclude that the return on Tiffany stock is less risky than the return on the market.

Question 64

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 a 95% prediction interval for Attendance when Price and Rides equal $85 and 30,respectively? (Note that . )

A)[12,740,56,080]
B)[16,330,53,450]
C)[26,080,42,740]
D)[28,900,41,500]

Question 65

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

A)
B)
C)
D)

Question 66

Exhibit 15-5.The accompanying table shows the regression results when estimating . Refer to Exhibit 15-5.When testing whether or not x₁ and x₂ have the same influence on y,the null hypothesis is

A)
B)
C)
D)

Question 67

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

A)Reject H₀;the slope coefficient differs from 3.
B)Not reject H₀;the slope coefficient differs from 3.
C)Reject H₀;the slope coefficient does not differ from 3.
D)Not reject H₀;the slope coefficient does not differ from 3.

Question 68

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)25,670
B)34,410
C)40,910
D)55,600

Question 69

Exhibit 15-2.A sports analyst wants to exam the factors that may influence a tennis player's chances of winning.Over four tournaments,he collects data on 30 tennis players and estimates the following model: , where Win is the proportion of winning,Double Faults is the percentage of double faults made,and Aces is the number of Aces.A portion of the regression results are shown in the accompanying table. Refer to Exhibit 15-2.When testing whether the explanatory variables are jointly significant at the 5% level,he

A)Rejects H₀,and concludes that the explanatory variables are jointly significant.
B)Does not reject H₀,and concludes that the explanatory variables are jointly significant.
C)Rejects H₀,and concludes that the explanatory variables are not jointly significant.
D)Does not reject H₀,and concludes that the explanatory variables are not jointly significant.

Question 70

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.Specify the competing hypotheses in order to test whether the slope coefficient differs from 3.

A)
B)
C)
D)

Question 71

Exhibit 15-2.A sports analyst wants to exam the factors that may influence a tennis player's chances of winning.Over four tournaments,he collects data on 30 tennis players and estimates the following model: , where Win is the proportion of winning,Double Faults is the percentage of double faults made,and Aces is the number of Aces.A portion of the regression results are shown in the accompanying table. Refer to Exhibit 15-2.Excel shows that the 95% confidence interval for β₁ is [-0.12,-0.002].When determining whether or not Double Faults is significant at the 5% significance level,he

A)Rejects ,and concludes that Double Faults is significant.
B)Does not reject ,and concludes that Double Faults is significant.
C)Rejects ,and concludes that Double Faults is not significant.
D)Does not reject

Question 72

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.Specify the competing hypotheses in order to test whether Advertising is significant in predicting Sales.

A)
B)
C)
D)

Question 73

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 value of the test statistic is:

A)
B)
C)
D)

Question 74

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 a 95% confidence interval for expected Attendance when Price and Rides equal $85 and 30,respectively? (Note that . )

A)[12,740,56,780]
B)[16,330,53,450]
C)[26,080,42,740]
D)[28,900,41,500]

Question 75

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:

A)Reject H₀,and conclude that the explanatory variables are jointly significant.
B)Not reject H₀,and conclude that the explanatory variables are jointly significant.
C)Reject H₀,and conclude that the explanatory variables are not jointly significant.
D)Not reject H₀,and conclude that the explanatory variables are not jointly significant.

Question 76

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

A)-98.
B)1.98.
C)4.33.
D)9.58.

Question 77

Exhibit 15-2.A sports analyst wants to exam the factors that may influence a tennis player's chances of winning.Over four tournaments,he collects data on 30 tennis players and estimates the following model: , where Win is the proportion of winning,Double Faults is the percentage of double faults made,and Aces is the number of Aces.A portion of the regression results are shown in the accompanying table. Refer to Exhibit 15-2.When testing whether the explanatory variables jointly influence the response variable,the null hypothesis is

A)
B)
C)
D)

Question 78

Serial correlation occurs when the error term is:

A)Dispersed evenly.
B)Randomly distributed.
C)Correlated across observations.
D)Uncorrelated across observations.

Question 79

Exhibit 15-2.A sports analyst wants to exam the factors that may influence a tennis player's chances of winning.Over four tournaments,he collects data on 30 tennis players and estimates the following model: , where Win is the proportion of winning,Double Faults is the percentage of double faults made,and Aces is the number of Aces.A portion of the regression results are shown in the accompanying table. Refer to Exhibit 15-2.Is the relationship between Win and Aces significant at the 5 percent level?

A)No,because the relevant p-value is less than 0.05.
B)Yes,because the relevant p-value is less than 0.05.
C)No,because the relevant p-value is greater than 0.05.
D)Yes,because the relevant p-value is greater than 0.05.

Question 80

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 Advertising is significant at the 10% significance level,the conclusion is to

A)Reject H₀;Advertising is significant.
B)Not reject H₀;Advertising is significant.
C)Reject H₀;Advertising is not significant.
D)Not reject H₀;Advertising is not significant.