Deck 15: Inference With Regression Models

Question 1

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

Answer 1

False

Question 2

One of the required assumptions of regression analysis states that the error term has a(an) ________ value of zero.

Answer 2

expected

Question 3

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

Answer 3

False

Question 4

It is common to refer to the interval estimate for an individual value of y as the ________ interval.

Question 5

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether there is a one-to-one relationship between x and y, the null hypothesis takes the form ________.

A) H₀: β₁ = 0
B) H₀: β₁ = 1
C) H₀: b₁ = 0
D) H₀: b₁ = 1

Question 6

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether there is a positive linear relationship between x and y, the alternative hypothesis takes the form ________.

A) H_A: β₁ = 0
B) H_A: β₁ > 0
C) H_A: β₁ < 0
D) H_A: b₁ > 1

Question 7

If the residuals are correlated, then the residuals should show no pattern around the horizontal axis.

Question 8

The term BLUE stands for Best Linear Unbiased Estimator.

Question 9

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

Question 10

With the partial F test, we basically analyze the ratio of (SSE_R - SSE_U) to ________.

Question 11

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 y holding the other explanatory variables constant.

Question 12

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether x significantly influences y, the null hypothesis takes the form ________.

A) H₀: β₁ = 0
B) H₀: β₁ = 1
C) H₀: b₁ = 0
D) H₀: b₁ = 1

Question 13

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 14

The ________ model is a complete model that imposes no restrictions on the coefficients.

Question 15

If the confidence interval does not contain the value zero, then the ________ variable associated with the regression coefficient is significant.

Question 16

The F test can be applied for any number of linear restrictions; the resulting test is often referred to as the ________ F test.

Question 17

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

Question 18

________ plots can be used to detect common violations, and they can be used to detect outliers.

Question 19

Conditional on x₁, x₂, ..., x_k, the error term ε is ________ distributed.

Question 20

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

Question 21

Refer to below regression results. When testing the overall significance of the regression model at the 5%, the decision is to ________.

A) reject H₀; we can conclude that the explanatory variables are jointly significant.
B) not reject H₀; we can conclude that the explanatory variables are jointly significant.
C) reject H₀; we cannot conclude that the explanatory variables are jointly significant.
D) not reject H₀; we cannot conclude the explanatory variables are jointly significant.

Question 22

The accompanying table shows the regression results when estimating y = β₀ + β₁x + ε Which of the following 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 23

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 F_0.05,(2,20) = 3.49, the decision is to ________.

A) reject H₀; we can conclude that the explanatory variables are jointly significant.
B) not reject H₀; we can conclude that the explanatory variables are jointly significant.
C) reject H₀; we cannot conclude that the explanatory variables are jointly significant.
D) not reject H₀; we cannot conclude the explanatory variables are jointly significant.

Question 24

When testing r linear restrictions imposed on the model y = β₀ + β₁x₁ + ... + β_k x_k + ε, 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 25

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 26

Given the following portion of regression results, which of the following is the value of the F_2,20 test statistic?

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

Question 27

The accompanying table shows the regression results when estimating y = β₀ + β₁x + ε. 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 28

Given the following portion of regression results, which of the following is the value of the F_(2,20) test statistic?

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

Question 29

When estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε, you wish to test H₀: β₁ = β₂ = 0 versus . The value of the test statistic is F_(2,20) = 2.50 and its associated p-value is 0.1073. At the 5% significance level, the conclusion is to ________.

A) reject the null hypothesis; we can conclude that x₁ and x₂ are jointly significant
B) reject the null hypothesis; we cannot conclude that x₁ and x₂ are jointly significant
C) not reject the null hypothesis; we can conclude that x₁ and x₂ are jointly significant
D) not reject the null hypothesis; we cannot conclude that x₁ and x₂ are jointly significant

Question 30

A sample of 200 monthly observations is used to run a simple linear regression: Returns = β₀ + β₁ Leverage + ε. A 5% 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 t₁₉₈ = -1.09, with an associated p-value of 0.2770. The correct decision is to ________.

A) reject the null hypothesis; we can conclude that leverage significantly explains returns
B) reject the null hypothesis; we cannot conclude that leverage significantly explains returns
C) not reject the null hypothesis; we cannot conclude that leverage significantly explains returns
D) not reject the null hypothesis; we can conclude that leverage significantly explains returns

Question 31

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 32

The accompanying table shows the regression results when estimating y = β₀ + β₁x + ε. Is x significantly related to y at the 5% significance level?

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

Question 33

The accompanying table shows the regression results when estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε. At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant?

A) Only x_1
B) Only x_{3
C) x1} and x_{2
D) x2} and x₃

Question 34

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 35

Which of the following is the 95% confidence interval for the regression coefficient β₁, if df = 30, b₁ = −2 and s = 3?

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

Question 36

Refer to below regression results. When testing the overall significance of the regression model at the 5% level given a critical value of F_0.05,(2.20) = 3.49, the decision is to ________.

A) reject H₀; we can conclude that the explanatory variables are jointly significant.
B) not reject H₀; we can conclude that the explanatory variables are jointly significant.
C) reject H₀; we cannot conclude that the explanatory variables are jointly significant.
D) not reject H₀; we cannot conclude the explanatory variables are jointly significant.

Question 37

When estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε, you wish to test H₀: β₁ = β₂ versus H_A: β₁ ≠ β₂. The value of the test statistic is F_(1,30) = 7.75 and its associated p-value is 0.0092. At the 1% significance level, the conclusion is to ________.

A) reject the null hypothesis; we cannot conclude that the influence of x₁ on y is different from the influence of x₂ on y.
B) reject the null hypothesis; we can conclude that the influence of x₁ on y is different from the influence of x₂ on y.
C) not reject the null hypothesis; we can conclude that the influence of x₁ on y is different from the influence of x₂ on y.
D) not reject the null hypothesis; we cannot conclude that the influence of x₁ on y is different from the influence of x₂ on y.

Question 38

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 39

Consider the following simple linear regression model: y = β₀ + β₁x + ε. When determining whether there is a negative linear relationship between x and y, the alternative hypothesis takes the form ________.

A) H_A: β₁ = 0
B) H_A: β₁ > 0
C) H_A: β₁ < 0
D) H_A: b₁ > 0

Question 40

In regression, the predicted values concerning y are subject to ________.

A) kurtosis
B) skewness
C) mean deviation
D) sampling variation

Question 41

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β₀ + β₁Price + β₂Temperature + β₃Rides + ε, where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), Temperature is the average daily temperature (in °F), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. When testing whether Temperature is significant at the 5% significance level, she ________.

A) rejects H₀: β₂ = 0, and concludes that Temperature is significant
B) does not reject H₀: β₂ = 0, and concludes that Temperature is significant
C) rejects H₀: β₂ = 0, and cannot conclude that Temperature is significant
D) does not reject H₀: β₂ = 0, and cannot conclude that Temperature is significant

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

A 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: Sales = β₀ + β₁ Advertising + ε. The following table shows a portion of the regression results. Which of the following are the competing hypotheses used to test whether Advertising is significant in predicting Sales?

A) H₀: b₁ = 0; H_A: b₁ ≠ 0.
B) H₀: b₁ = 2.88; H_A: b₁ ≠ 2.88.
C) H₀: β₁ = 0; H_A: β₁ ≠ 0.
D) H₀: β₁ ≠ 0; H_A: β₁ = 0.

Question 44

A 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: Sales = β₀ + β₁ Advertising + ε. The following table shows a portion of the regression results. When testing whether the slope coefficient differs from 3, the value of the test statistic is ________.

A) t₂₃ = -1.895
B) t₂₃ = -0.079
C) t₂₃ = 0.079
D) t₂₃ = 1.895

Question 45

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: Win = β₀ + β₁Double Faults + β₂Aces + ε, 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. When testing whether the explanatory variables are jointly significant at the 5% significance 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 cannot concludes that the explanatory variables are jointly significant
D) does not reject H₀, and cannot conclude that the explanatory variables are jointly significant

Question 46

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 47

Serial correlation is typically observed in ________.

A) outliers
B) sparse data
C) time series data
D) get estimators that are biased and cannot conduct tests of significance

Question 48

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 49

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: Win = β₀ + β₁ Double Faults + β₂Aces + ε, 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. 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 H₀: β₁ = 0, and concludes that DoubleFaults is significant
B) does not reject H₀: β₁ = 0, and concludes that DoubleFaults is significant
C) rejects H₀: β₁ = 0, and cannot conclude that DoubleFaults is significant
D) does not reject H₀: β₁ = 0, and cannot concludes DoubleFaults is significant

Question 50

A researcher gathers data on 25 households and estimates the following model: Expenditure = β₀ + β₁ Income + ε. A residual plot of the estimated model is shown in the accompanying graph. Which of the following 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 51

A 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: Sales = β₀ + β₁ Advertising + ε. The following table shows a portion of the regression results. When testing whether Advertising is significant at the 10% significance level, the conclusion is to ________.

A) reject H₀; we can conclude advertising is significant
B) not reject H₀; we cannot conclude advertising is significant
C) reject H₀; we cannot conclude advertising is significant
D) not reject H₀; we can conclude advertising is significant

Question 52

Serial correlation occurs when the error term is ________.

A) dispersed evenly
B) randomly distributed
C) correlated across observations
D) uncorrelated across observations

Question 53

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 these choices is correct.

Question 54

A 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: Sales = β₀ + β₁ Advertising + ε. The following table shows a portion of the regression results. 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; we can conclude the slope coefficient differs from 3
B) not reject H₀; we can conclude the slope coefficient differs from 3
C) reject H₀; we cannot conclude the slope coefficient differs from 3
D) not reject H₀; we cannot conclude the slope coefficient differs from 3

Question 55

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: Win = β₀ + β₁Double Faults + β₂Aces + ε, 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. When testing whether the explanatory variables jointly influence the response variable, the null hypothesis is ________.

A) H₀: β₁ = β₂ = 0
B) H₀: β₁ + β₂ = 0
C) H₀: β₀ = β₁ = β₂ = 0
D) H₀: β₀ + β₁ + β₂ + 0

Question 56

A 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 collects monthly data for 25 firms. He estimates the model: Sales = β₀ + β₁ Advertising + ε. The following table shows a portion of the regression results. Which of the following are the competing hypotheses used to test whether the slope coefficient differs from 3?

A) H₀: b₁ = 3; H_A: b₁ ≠ 3
B) H₀: b₁ = 2.88; H_A: b₁ ≠ 2.88
C) H₀: β₁ = 3; H_A: β₁ ≠ 3
D) H₀: β₁ = 2.88; H_A: β₁ ≠ 2.88

Question 57

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: Win = β₀ + β₁ Double Faults + β₂Aces + ε, 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. Is the relationship between Win and Aces significant at the 5% significance 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 58

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 59

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β₀ + β₁ Price + β₂ Temperature + β₃ Rides + ε, where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), Temperature is the average daily temperature (in ^oF), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. When testing whether Price is significant in explaining Attendance, the value of the test statistic is ________.

A) −4.085.
B) −1.201.
C) 1.201.
D) 4.085.

Question 60

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) Both get estimators that are biased and cannot conduct tests of significance are correct.

Question 61

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 Capital Asset Pricing Model (CAPM) model for Tiffany's return. 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) H₀: α = 0; H_A: α ≠ 0.
B) H₀: β = 0; H_A: β ≠ 0
C) H₀: α ≤ 1; H_A: α > 1
D) H₀: β ≤ 1; H_A: β > 1

Question 62

The accompanying table shows the regression results when estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε. When testing whether or not x₁ and x₂ are jointly significant, the null hypothesis is ________.

A) H₀: β₁ = β_2
B) H₀: β₁ ≠ β_2
C) H₀: β₁ + β₂ = 0
D) H₀: β₁ = β₂ = 0

Question 63

The accompanying table shows the regression results when estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε. At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant?

A) Only x_1
B) Only x_{3
C) x1} and x_{2
D) x2} and x₃

Question 64

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β₀ + β₁Price + β₂Temperature + β₃Rides + ε, where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), Temperature is the average daily temperature (in °F), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. When testing whether the explanatory variables Temperature and Rides are jointly significant, the p-value associated with the test is 0.0000. At the 1% significance level, the researcher ________.

A) rejects H₀, and concludes that at least one of the explanatory variables, Temperature and Rides, is significant in explaining Attendance
B) does not reject H₀, and concludes that at least one of the explanatory variables, Temperature and Rides, is significant in explaining Attendance
C) rejects H₀, and cannot conclude that at least one of the explanatory variables, Temperature and Rides, is significant in explaining Attendance
D) does not reject H₀, and cannot conclude at least one of the explanatory variables, Temperature and Rides, is significant in explaining Attendance

Question 65

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 Capital Asset Pricing Model (CAPM) model for Tiffany's return. When testing whether the beta coefficient is significantly greater than one, the value of the test statistic is ________.

A) −1.98
B) 1.98
C) 4.33
D) 9.58

Question 66

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β₀ + β₁Price + β₂Temperature + β₃Rides + ε, where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), Temperature is the average daily temperature (in °F), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. Which of the following are the hypotheses to test if the explanatory variables Temperature and Rides are jointly significant in explaining Attendance?

A) H₀: β₂ = β₃ = 0; H_A: At least one of the coefficients is nonzero.
B) H₀: β₂ = β₃ = 0; H_A: At least one of the coefficients is zero.
C) H₀: β₀ = β₁ = 0; H_A: At least one of the coefficients is nonzero.
D) H₀: β₀ = β₁ = 0; H_A: At least one of the coefficients is zero.

Question 67

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 . The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. When testing whether the beta coefficient is significantly greater than one, the relevant critical value at the 5% significance level is t_0.05,58 = 1.672. The conclusion to the test is to ________.

A) reject H₀; we can conclude that the return on Tiffany stock is riskier than the return on the market
B) not reject H₀; we can conclude that the return on Tiffany stock is riskier than the return on the market
C) reject H₀; we cannot conclude that the return on Tiffany stock is riskier than the return on the market
D) not reject H₀; we cannot conclude that the return on Tiffany stock is riskier than the return on the market

Question 68

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 model: Salary = β₀ + β₁Service + ε. The following table summarizes a portion of the regression results. Which of the following hypotheses will determine whether the intercept differs from zero?

A) H₀: β₀ = 0; H_A: β₀ ≠ 0
B) H₀: β₁ = 0; H_A: β₁ ≠ 0
C) H₀: b₀ = 0; H_A: b₀ ≠ 0
D) H₀: b₁ = 0; H_A: b₁ ≠ 0

Question 69

A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: Attendance = β₀ + β₁Price + β₂Rides + ε, where Attendance is the daily attendance (in 1,000s), 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 Price* = Price - 85 and Rides* = Rides - 30. A portion of the regression results is shown in the accompanying table. According to the modified model, which of the following 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 70

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β₀ + β₁Price + β₂Temperature + β₃Rides + ε, where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), Temperature is the average daily temperature (in °F), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. Which of the following is the value of the test statistic for testing the joint significance of the linear regression model?

A) −4.09
B) 0.04
C) 9.95
D) 99.78

Question 71

A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: Attendance = β₀ + β₁Price + β₂Rides + ε, where Attendance is the daily attendance (in 1,000s), 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
Price* = Price - 85 and Rides* = Rides - 30. A portion of the regression results is shown in the accompanying table. According to the modified model, which of the following is a 95% confidence interval for expected Attendance when Price and Rides equal $85 and 30, respectively? (Note that t_0,025,27 = 2.052.)

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

Question 72

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 . The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. When testing whether there are abnormal returns, or whether the alpha coefficient is significantly different from zero, the value of the test statistic is ________.

A) −1.98
B) 1.98
C) 4.33
D) 9.58

Question 73

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 . The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. When testing whether there are abnormal returns, or whether the alpha coefficient is significantly different from zero, the value of the test statistic is ________.

A) H₀: α = 0; H_A: α ≠ 0
B) H₀: β = 0; H_A: β ≠ 0
C) H₀: α ≤ 1; H_A: α > 1
D) H₀: β ≤ 1; H_A: β > 1

Question 74

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β₀ + β₁Price + β₂Temperature + β₃Rides + ε, where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), Temperature is the average daily temperature (in °F), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. When testing whether the explanatory variables are jointly significant at the 5% significance level, the researcher ________.

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 cannot conclude that the explanatory variables are jointly significant
D) does not reject H₀, and cannot conclude that the explanatory variables are jointly significant

Question 75

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β₀ + β₁Price + β₂Temperature + β₃Rides + ε, where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), Temperature is the average daily temperature (in °F), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. When testing whether the explanatory variables Temperature and Rides are jointly significant, the error sum of squares for the restricted model is SSE_R = 12,343.78. Which of the following is the value of the test statistic when conducting this test?

A) −4.09
B) 25.33
C) 49.58
D) 99.78

Question 76

The accompanying table shows the regression results when estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε. When testing whether the explanatory variables are jointly significant at the 5% significance 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 cannot conclude that the explanatory variables are jointly significant
D) not reject H₀, and cannot conclude that the explanatory variables are jointly significant

Question 77

The accompanying table shows the regression results when estimating y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε. When testing whether or not x₁ and x₂ have the same influence on y, the null hypothesis is ________.

A) H₀: β₁ = β_{2
B) H0}: β₁ ≠ β_{2
C) H0}: β₁ + β₂ = β_{3
D) H0}: β₁ + β₂ = 0

Question 78

A researcher analyzes the factors that may influence amusement park attendance. She estimates the following model: Attendance = β₀ + β₁Price + β₂Temperature + β₃Rides + ε, where Attendance is the daily attendance (in 1,000s), Price is the gate price (in $), Temperature is the average daily temperature (in °F), and Rides is the number of rides at the amusement park. A portion of the regression results is shown in the accompanying table. When testing whether Rides is significant at the 1% significance level, she ________.

A) rejects H₀: β₃ = 0, and concludes that Rides is significant
B) does not reject H₀: β₃ = 0, and concludes that Rides is significant
C) rejects H₀: β₃ = 0, and cannot conclude that Rides is significant
D) does not reject H₀: β₃ = 0, and cannot conclude that Rides is significant

Question 79

A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: Attendance = β₀ + β₁Price + β₂Rides + ε, where Attendance is the daily attendance (in 1,000s), 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 Price* = Price - 85 and Rides* = Rides - 30. A portion of the regression results is shown in the accompanying table. According to the modified model, which of the following is a 95% prediction interval for Attendance when Price and Rides equal $85 and 30, respectively? (Note that t_0.025,27 = 2.052.)

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

Question 80

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 . The accompanying table shows the regression results when estimating the Capital Asset Pricing Model (CAPM) model for Tiffany's return. When testing whether there are abnormal returns, the conclusion to the test is at the 5% significance level is to ________.

A) reject H₀; we can conclude there are abnormal returns
B) not reject H₀; we can conclude there are abnormal returns
C) reject H₀; we cannot conclude there are abnormal returns
D) not reject H₀, we cannot conclude there are abnormal returns