Exam 15: Inference With Regression Models

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 ________.

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?

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 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.)

In a multiple regression based on 30 observations, the following information is provided: = 469 - 2x₁ + 6x₂ - 0.5x₃ and s_e = 16. Also, when x₁ = 30, x₂ = 10, and x₃ = 65 se( ₀) = 37. A) Construct a 90% confidence interval for E(y) if x₁ = 30, x₂ = 10, and x₃ = 65. B) Construct a 90% prediction interval for y if x₁ = 30, x₂ = 10, and x₃ = 65. C) Which interval is narrower? Explain.

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 ________.

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 Capital Asset Pricing Model (CAPM) model for Pfizer's return. a. At the 5% significance level, is the beta coefficient less than one? Show the relevant steps of the appropriate hypothesis test. B) At the 5% significance level, are there abnormal returns? Show the relevant steps of the appropriate hypothesis test.

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?

Test statistic for the test of linear restrictions uses all of the following, except ________.

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 ________.

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 ________.

Which of the following violates the assumptions of regression analysis?

In a simple linear regression based on 30 observations, the following information is provided: = 32.3 + 1.45x and s_e = 3.2. Also, se( ₀) evaluated at x = 20 is 1.3. A) Construct a 95% confidence interval for E(y) if x = 20. B) Construct a 95% prediction interval for y if x = 20.

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

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 ________.

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.

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 simple linear regression, Sales = β₀ + β₁ Advertising + ε, 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.

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

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 ________.