Exam 15: Inference With Regression Models

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 ______________.

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?

With the partial F test,we basically analyze the ratio of (SSE_{R - SSEU})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 error sum of squares for the restricted model is SSE_R = 12,343.78.Which of the following is the value of the test statistic when conducting this test?

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. When testing whether the slope coefficient differs from 3,the value of the test statistic is ____.

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 Price is significant in explaining Attendance,the value of the test statistic is _____.

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 _____________________.

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. When testing whether the explanatory variables are jointly significant at the 5% significance level,he _______________________________________________________________________.

Test statistic for the test of linear restrictions is using all of the following,except ______________________.

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 a 95% prediction interval for y when x equals 2? (Note that t_0,025,10 = 2.228. )

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 value of the test statistic for testing the joint significance of the linear regression model?

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 Bath and Sq ft are jointly significant,the p-value associated with the test is 0.0039.At the 5% significance level,she __________________________________________________________.

A researcher analyzes the factors that may influence the poverty rate and estimates the following model: y = β₀ + β₁x₁ + β₂x₂ + β₃x₃ + ε,where y is the poverty rate (y,in %),x₁ is the percent of the population with at least a high school education,x₂ is the median income (in $1,000s),and x₃ is the mortality rate (per 1,000 residents).The researcher would like to construct interval estimates for y when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively.The researcher estimates a modified model where poverty rate is the response variable and the explanatory variables are 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 the poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively. b.According to the modified model,what is a 95% confidence interval for the expected poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively? ? (Note that t_0.025,35 = 2.030. ) c.According to the modified model,what is a 95% prediction interval for the poverty rate when x₁,x₂,and x₃ equal 85%,$50,000,and 10,respectively? (Note that t_0.025,35 = 2.030. )

Serial correlation is typically observed in __________________.

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 are jointly significant at the 5% level,she ______________________________________________________________________.

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 _____________________________________________________________.

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 Bath is significant at the 5% significance 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?

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 are the hypotheses to test if the explanatory variables Bath and Sqft are jointly significant in explaining Rent?

A researcher analyzes the factors that may influence amusement park attendance and estimates the following model: Attendance = β₀ + β₁ Price + β₂ Rides + 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 andRides equal $85 and 30,respectively? (Note that t_0,025,27 = 2.052. )