Exam 12: Multiple Regression

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In a study of foreign holdings in Egyptian banks,the following sample regression results were obtained,based on 14 annual observations: = -3.25 + - + ,and R² = 0.92, Where the numbers in parentheses under the coefficient estimates are the estimated coefficient standard errors,and y = Year-end share of assets in Egyptian bank subsidiaries held by foreigners,as a percentage of total assets x₁ = Annual change,in billions of Egyptian pounds,in foreign direct investment in Egypt x₂ = Bank price-earnings ratio x₃ = Index of the exchange value of the Egyptian pounds -Test the null hypothesis that β₂ is zero,against the alternative that it is negative at the 5% significance level,and interpret your result.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: The computer output for the multiple regression model,y = β₀ + β₁X₁ + β₂X₂ + ε is shown below.However,because of a printer malfunction some of the results are not shown.These are identified by asterisks. S = * R-Sq = * ANALYSIS OF VARIANCE -Calculate the unbiased estimate of error variance.

The value of is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A professor investigated some of the factors that affect an individual student's final grade in his course.He proposed the multiple regression model Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + ε ,where Y is the final mark (out of 100),X₁ is the number of lectures skipped,X₂ is the number of late assignments,and X₃ is the mid-term test mark (out of 100).The professor recorded the data for 50 randomly selected students.The computer output is shown below. The regression equation is = 41.6 - 3.18x₁ - 1.17x₂ + 0.63x₃. S = 13.74 R-Sq = 30.0% ANALYSIS OF VARIANCE -Interpret the coefficient b₂.

The coefficient of multiple correlation is the square root of the coefficient of determination.

The coefficient of determination is:

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: A regression analysis has produced the following partial analysis of variance table: Analysis of Variance -Compute the mean squares for regression.

In a multiple regression analysis,six independent variables are used in the equation based on a sample of 45 observations.What are the degrees of freedom associated with the F statistic?

What would you conclude if you fail to reject H₀ : β₁ = β₂ = ∙ ∙ ∙ ∙ ∙ ∙ = β_k = 0?

In a multiple regression model with K independent variables on n observations,the standard error of the estimate is = .

A multiple regression analysis that includes 25 data points and 4 independent variables produces SST = 400 and SSR = 300.The multiple standard error of the estimate for the analysis is 5.

The standard multiple regression assumption states that the error terms have the same variance.This is known as homoscedasticity.

A multiple regression equation includes 5 independent variables,and the coefficient of determination is 0.81.The percentage of the variation in y that is explained by the regression equation is 90%.

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Assume that x₁ is a continuous variable and x₂ is a dummy variable with a value of 0 or 1. -The t statistic and the partial F statistic are closely related.Explain this relationship.Which would you prefer to use?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: As director of the local tourist board,you are interested in determining the factors that influence the hotel occupancy rate in your city each month.Hotel occupancy can be measured as the percentage of available hotel rooms that are occupied by paying customers.You develop the following model: Y = β₀ + β₁X₁ + β₂X₂ + β₃X₃ + β₄X₄ + ε,where Y is the hotel occupancy rate,X₁ is the total number of passengers arriving at the airport,X₂ is a price index 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.You look at data from the past 36 months and obtain the following results: = 67.1 + 0.02x₁ - 0.055x₂ + 0.08x₃ + 12.3x₄,R² = 0.67, = 58.3, = 0.008, = 0.01, = 0.06, = 4.7,and SSE = 576. -Calculate the regression sum of squares.

In a regression model involving 30 observations,the following estimated regression model was obtained: = 5.1 + 1.5x₁ + 1.2x₂.For this model,the following statistics were given: SST = 162.1 and SSE = 73.9.What is the value of the F statistic for testing the validity of this model?

How many degrees of freedom are associated with a multiple regression model involving K predictors and n observations when running a t-test for the individual coefficients?

For a particular regression,the adjusted coefficient of determination, ² can never be larger than the coefficient of determination,R².

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: Assume that x₁ is a continuous variable and x₂ is a dummy variable with a value of 0 or 1. -Adjusting the coefficient of determination is considered particularly important in multiple regression situations.Why?

THE NEXT QUESTIONS ARE BASED ON THE FOLLOWING INFORMATION: In a study of foreign holdings in Egyptian banks,the following sample regression results were obtained,based on 14 annual observations: = -3.25 + - + ,and R² = 0.92, Where the numbers in parentheses under the coefficient estimates are the estimated coefficient standard errors,and y = Year-end share of assets in Egyptian bank subsidiaries held by foreigners,as a percentage of total assets x₁ = Annual change,in billions of Egyptian pounds,in foreign direct investment in Egypt x₂ = Bank price-earnings ratio x₃ = Index of the exchange value of the Egyptian pounds -Find a 95% confidence interval for β₁.