Exam 15: Inference With Regression Models

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. Which of the following is the value of the test statistic for testing the joint significance of the linear regression model?

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.

Consider the following regression results based on 40 observations. a.Specify the hypotheses to determine if the slope differs from one. b.Calculate the value of the test statistic. c.At the 5% significance level,find the critical value(s). d.Does the slope differ from one? Explain.

A simple linear regression,Sales = β₀ + β₁ Advertising + ε,is estimated using cross-sectional data from 10 firms.The resulting residuals e,along with the values of the explanatory variable Advertising (x,in $100s),are shown in the accompanying table. a.Graph the residuals e against Advertising (x)and look for any discernible pattern. b.Which assumption is being violated? Discuss its consequences and suggest a possible remedy.

A sociologist estimates the regression relating Poverty (y)to Education (x₁).The estimated regression equation is: = 71.68 - 0.69x₁;n = 39;SSE = 152. In an attempt to improve the results,he adds two more explanatory variables: Median Income (x₂,in $1,000s)and the Mortality Rate (x₃,per 1,000 residents).The estimated regression equation is: = 59.80 - 0.44x₁- 0.18x₂ + 0.17x₃;n = 39;SSE = 60. .a.Formulate the hypotheses to determine whether Median Income and the Mortality Rate are jointly significant in explaining Poverty. b.Calculate the value of the test statistic. c.At the 5% significance level,find the approximate value of the critical value(s). d.What is the conclusion to the test?

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

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. When testing whether there are abnormal returns,the conclusion to the test is at the 5% significance level is to ___________________________________________________.

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,whereAttendance 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 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 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 the slope coefficient differs from 3?

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 = 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 + β₁x + ε. Which of the following is the value of the test statistic when testing whether x significantly influences 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 + β₁ Service + 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?

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

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 + β₁ Service + 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 marketing manager examines the relationship between the attendance at amusement parks and the price of admission.He estimates the following model: Attendance = β₀ + β₁ price + ε,where Attendance is the average daily number of people who attend an amusement park in July (in 1,000s)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 Price* = Price - 80.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 t_0.025,28 = 2.048. ) c.According to the modified model,what is a 95% prediction interval for Attendance when Price equals $80? (Note that t_0.025,28 = 2.048. )

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. Which of the following is the estimate of Happiness for the person who is 65 years old?

When confronted with multicollinearity,a good remedy is to _______________________ if we can justify its redundancy.

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 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.

When estimating a multiple regression model based on 30 observations,the following results were obtained. a.Specify the hypotheses to determine whether x₁ is linearly related to y.At the 5% significance level,use the p-value approach to complete the test.Are x₁ andy linearly related? b.Construct the 95% confidence interval for β₂.Using this confidence interval,is x₂ significant in explaining y? Explain. c.At the 5% significance level,can you conclude that β₁ differs from −1? Show the relevant steps of the appropriate hypothesis test.