Exam 12: Multiple Regression

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose you are interested in determining the factors that influence the time required to prepare a tax return,and developed the model: Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄ + ε,where Y is the amount of time (in minutes),X₁ is the income of the individual (in thousands of dollars),X₂ is the age of the individual,X₃ is the number of people living in the household,and X₄ is a dummy variable that takes the value 1,if the individual owns his or her own home.After interviewing 40 accountants,you get the following results: = 17.2 + 3.8x₁ - 1.04x₂ + 2.15x₃ + 15.1x₄, = 5.3, = 0.13, = 0.33, = 1.51, = 4.7,SSR = 164.2,SSE = 200.7,and R² = 0.45. -Test H₀ : β₁ = 0 against H₁ : β₁ ≠ 0 and interpret your result.

A multiple regression analysis involving three independent variables and 25 data points results in a value of 0.769 for the unadjusted multiple coefficient of determination.The adjusted multiple coefficient of determination is:

The test on all parameters of a regression model has the following null and alternative hypotheses: H₀ : β₁ = β₂ = β₃ = ∙ ∙ ∙ ∙ ∙ ∙ = β_k = 0 and H₁ : β₁ ≠ β₂ ≠ β₃ ≠ ∙ ∙ ∙ ∙ ∙ ∙ ≠ β_k ≠ 0.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose you are interested in determining the factors that influence the time required to prepare a tax return.You develop the model Y = β₀ + β₁X₁ + β₂X₂ + β₃ + β₄X₃ + β₅X₄ + β₆(X₁ ∙ X₄) + ε,where Y is the amount of time in minutes,X₁ is the income of the individual (in thousands of dollars),X₂ is the age of the individual,X₃ is the number of people living in the household,and X₄ is a dummy variable that takes the value 1 if the individual owns his or her own home.After interviewing 40 accountants,you obtained = 17.2 + 0.38x₁ + 1.04x₂ - 0.04 + 2.15x₃ + 0.11x₄ - 0.22(x₁ ∙ x₄), = 5.3, = 0.13, = 0.33, = 1.51, = 4.7, = 0.05,and = 0.07. -Test the hypothesis H₀ : β₁ = 0 and interpret your result.

What is the value of ?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Consider the following regression model: Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + ε.Suppose that you have estimated the coefficients for the model,and obtained the partial ANOVA table shown below. Analysis of Variance -Complete the missing values identified by asterisks in the table.

What is the 95% confidence interval associated with β₁?

How should the loan officer interpret the coefficient on x₃?

In a regression model involving 34 observations,the following estimated regression model was obtained: = 48 + 2.5x₁ + 1.2x₂ - 0.7x₃.For this model,the following statistics were given: SST = 960 and SSE = 270.What is the value of the F statistic for testing the validity of this model?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The model y = β₀ + β₁X₁ + β₂X₂ + ε was fitted to a sample of 25 families in order to explain household milk consumption: where y = Milk consumption,in quarts,per week,x₁ = Weekly income,in hundreds of dollars,and x₂ = Family size.The least squares estimates of the regression parameters were b₀ = -0.03,b₁ = 0.05,and b₂ = 1.1,with coefficient standard errors = 0.02; = 0.38.The total sum of squares and the error sum of squares were found to be 165.8 and 66.32 respectively. -For a fixed weekly income,test the null hypothesis that milk consumption does not depend linearly on the size of the family against an appropriate one-sided alternative.Use α = 0.025.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The director of a local tourist board is interested in determining the factors that influence the hotel occupancy rate in his city each month.Hotel occupancy can be measured as the percentage of available hotel rooms that are occupied by paying customers.He develops the model: lnY = β₀ + β₁lnX₁ + β₂lnX₂ + β₃lnX₃ + β₄X₄ + ε,where Y is the hotel occupancy rate (as a percentage),X₁ is the total number of passengers arriving at the airport (measured in thousands),X₂ is an average of local hotel room rates,X₃ is the consumer confidence index,and X₄ is a dummy variable = 1 during the months of June,July,and August.He looks at the data from the past 36 months and obtains ln = 4.2 + 1.23lnx₁ - 2.2lnx₂ + 0.34ln x₃ + 2.3x₄ and R² = 0.63. -Interpret the estimate b₃.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Suppose you are interested in determining the factors that influence the time required to prepare a tax return.You develop the model Y = β₀ + β₁X₁ + β₂X₂ + β₃ + β₄X₃ + β₅X₄ + β₆(X₁ ∙ X₄) + ε,where Y is the amount of time in minutes,X₁ is the income of the individual (in thousands of dollars),X₂ is the age of the individual,X₃ is the number of people living in the household,and X₄ is a dummy variable that takes the value 1 if the individual owns his or her own home.After interviewing 40 accountants,you obtained = 17.2 + 0.38x₁ + 1.04x₂ - 0.04 + 2.15x₃ + 0.11x₄ - 0.22(x₁ ∙ x₄), = 5.3, = 0.13, = 0.33, = 1.51, = 4.7, = 0.05,and = 0.07. -Test the hypothesis H₀ : β₅ = 0 and interpret your result.