Exam 15: Inference With Regression Models

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 real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x₁), the number of bathrooms (x₂), and its square footage (x₃). She estimates the following model: Rent = β₀ + β₁Bedroom + β₂Bath + β₃Sqft + ε. The following table shows a portion of the regression results. When testing whether the explanatory variables Bath and Sqft are jointly significant, the p-value associated with the test is 0.0039. At the 5% significance level, she ________.

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 ________.

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 ________.

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 + β₁Turnover + β₂Expense + 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. a. At the 10% significance level, are the explanatory variables jointly significant in explaining Return? Explain. B) At the 10% significance level, is each explanatory variable individually significant in explaining Return? Explain.

Multicollinearity is suspected when ________.

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?

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

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 ________.

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

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

Which of the following is the correct expression for computing a 100(1 - α)% confidence interval of the expected value of y?

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. Using the 95% confidence interval, what is the conclusion to the following hypothesis test: H₀: b₁ = 0; H_A: b₁ ≠ 0?

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

A sociologist studies the relationship between a district's average score on a standardized test for 10th grade students (y), the average school expenditures per student (x₁ in $1,000s), and an index of socioeconomic status of the district (x₂). The results of the regression are = 10.16 + 8.50x₁ + 4.30x₂; n = 25; SSE = 450; He would like to determine whether the influence of expenditures on test scores differs from the influence of the index on test scores, or β₁ ≠ β₂. The results of the restricted model for this test are = 12.25 + 6.05(x₁ + x₂); n = 25; SSE = 600. A) Formulate the hypotheses to determine whether Expenditures and Index Rate have the same influence on Scores. B) Calculate the value of the test statistic. C) At the 5% significance level, find the critical value(s). D) What is the conclusion to the test?

A sociologist wishes to study the relationship between happiness and age. He interviews 24 individuals and collects data on age and happiness, measured on a scale from 0 to 100. He estimates the following model: Happiness = β₀ + β₁Age + ε. The following table summarizes a portion of the regression results. When defining whether age is significant in explaining happiness, the competing hypotheses are ________.

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 real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x₁), the number of bathrooms (x₂), and its square footage (x₃). She estimates the following model: Rent = β₀ + β₁Bedroom + β₂Bath + β₃Sqft + ε. The following table shows a portion of the regression results. When testing whether Bath is significant at the 5% significance level, she ________.

A real estate analyst believes that the three main factors that influence an apartment's rent in a college town are the number of bedrooms, the number of bathrooms, and the apartment's square footage. For 40 apartments, she collects data on the rent (y, in $), the number of bedrooms (x₁), the number of bathrooms (x₂), and its square footage (x₃). She estimates the following model: Rent = β₀ + β₁Bedroom + β₂Bath + β₃Sqft + ε. The following table shows a portion of the regression results. Which of the following is the value of the test statistic for testing the joint significance of the linear regression model?

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 ________.