Exam 15: Inference With Regression Models

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

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: a.Specify the competing hypotheses to determine whether Service is significant in explaining Salary. b.At the 5% significance level,is Service significant? Explain.

Which of the following statements in statistical terminology is equivalent to the statement: "There is no exact linear relationship among the explanatory variables"?

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. At the 1% significance level,which of the following is the correct confidence interval of the regression coefficient β₁?

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

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 1,000s)and Commercial Construction (in 1,000s)as the explanatory variables.The results of the regression are as follows: a.At the 5% significance level,are the explanatory variables jointly significant in explaining Lumber Sales? Explain. b.At the 5% significance level,is Commercial Construction significant in explaining Lumber Sales? Explain. c.At the 5% significance level,can you conclude that the slope coefficient attached to Housing Starts differs from 1? Explain.

The term BLUE stands for Best Linear Unbiased Estimator.

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.

In a simple linear regression based on 30 observations,the following information is provided: = 32.3 + 1.45x and s_e = 3.2.Also, 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.

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. To determine whether abnormal returns exist,which of the following competing hypotheses do you set up?

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

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

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 researcher studies the relationship between SAT scores,the test-taker's family income,and his or her grade point average (GPA).Data are collected from 24 students.He estimates the following model: SAT = β₀ + β₁ GPA + β₂ Income + ε.The following table summarizes a portion of the regression results. Which of the following is the correct hypotheses for testing the joint significance?

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

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 + β₁ Bedroom + β₂ Bath + β₃Sqft + ε.The following table shows a portion of the regression results. When testing whether the explanatory variables jointly influence the response variable,the null hypothesis is ________.

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

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

Consider the following regression results based on 30 observations. = 238.33 - 0.95x + 7.13x₂ + 4.76x₃;SSE = 3,439 = 209.56 - 1.03x₁ + 5.24(x₂ + x₃);SSE = 3,559 a.Formulate the hypotheses to determine whether the influences of x₂ and x₃ differ in explaining y. b.Calculate the value of the test statistic. c.At the 5% significance level,find the critical value(s). d.What is your conclusion to the test?

An economist estimates the following model: y = β₀ + β₁x + ε.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 x⁺ = x - 2.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 of y when x equals 2?