Exam 15: Inference With Regression Models

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

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

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: 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 accompanying table shows the regression results when estimating

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

Exhibit 15-8.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: .The following table shows a portion of the regression results. Refer to Exhibit 15-8.When testing whether the explanatory variables are jointly significant at the 5% level,she

Exhibit 15-7.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 table summarizes a portion of the regression results: Refer to Exhibit 15-7.Which of the hypotheses will determine whether the intercept differs from zero?

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:

Exhibit 15-7.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 table summarizes a portion of the regression results: Refer to Exhibit 15-7.Using the 95% confidence interval,what is the conclusion to the following hypothesis test: ?

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

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:

Consider the following regression results based on 30 observations. 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?

A marketing manager examines the relationship between the attendance at amusement parks and the price of admission.He estimates the following model: , where Attendance is the average daily number of people who attend an amusement park in July (in 1000s)and Price is the price of admission.The marketing manager would like to construct interval estimates for Attendance when Price equals $80.The researcher estimates a modified model where Attendance is the response variable and the Price is now defined as .A portion of the regression results is shown in the accompanying table. a.According to the modified model,what is the point estimate for Attendance when Price equals $80? B)According to the modified model,what is a 95% confidence interval for Attendance when Price equals $80? (Note that . ) C)According to the modified model,what is a 95% prediction interval for Attendance when Price equals $80? (Note that . )

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

Exhibit 15-8.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: .The following table shows a portion of the regression results. Refer to Exhibit 15-8.When testing whether Bath is significant at the 5% level,she

Consider the following regression results based on 30 observations. Notes: Parameter estimates are in the main body of the table with the p-values in parentheses;* represents significance at 5% level.The last row presents the error sum of squares. A)Formulate the hypotheses to determine whether x₂ and x₃ are jointly significant in explaining y. B)Define the restricted and the unrestricted models needed to conduct the test. C)Calculate the value of the test statistic. D)At the 5% significance level,find the critical value(s). E)What is your conclusion to the test?

Exhibit 15-8.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: .The following table shows a portion of the regression results. Refer to Exhibit 15-8.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

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

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.

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.