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Exam 15: Multiple Regression

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Question 41

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Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. $\begin{array}{l}\begin{array} { l l } \text { Coefficients } & \text { Standard Error } \\12.924 & 4.425 \\- 3.682 & 2.630 \\45.216 & 12.560\end{array}\\\text { Analysis of Variance }\\\begin{array} { l l l l l } \text { Source of } & \text { Degrees of } & \text { Sum of } & \text { Mean } \\\text { Variation } & \text { Freedom } & \text { Squares } & \text { Square }\end{array} \quad F\end{array}$ The test statistic used to determine if there is a relationship among the variables equals

A) 1.40.
B) .2.
C) .77.
D) 5.

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Question 42

Multiple Choice

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In order to test for the significance of a regression model involving 4 independent variables and 36 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are

A) 4 and 36.
B) 3 and 35.
C) 4 and 31.
D) 4 and 32.

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Question 43

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In a multiple regression model involving 30 observations, the following estimated regression equation was obtained: $\hat { y }$ = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model, SSR = 700 and SSE = 100.The multiple coefficient of determination for the above model is

A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares. SSR = 165 SSE = 60 ​ The test statistic obtained from the information provided is

In a multiple regression analysis involving 12 independent variables and 166 observations, SSR = 878 and SSE = 122.The multiple coefficient of determination is

A regression model between sales (y in $1000) , unit price (x₁ in dollars) , and television advertisement (x₂ in dollars) resulted in the following function: $\hat { y }$ = 7 - 3x₁ + 5x₂ For this model, SSR = 3500, SSE = 1500, and the sample size is 18.If we want to test for the significance of the regression model, the critical value of F at the 5% level of significance is?

A regression analysis involved 6 independent variables and 27 observations.The critical value of t for testing the significance of each of the independent variable's coefficients will have

The multiple coefficient of determination is

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female) . $\hat { y }$ = 30 + .7x₁ + 3x₂ Also provided are SST = 1200 and SSE = 384.The test statistic for testing the significance of the model is

A regression model involving 8 independent variables for a sample of 69 observations resulted in the following sum of squares. $\begin{array} { l } \mathrm { SSE } = 306 \\\mathrm { SST } = 1800\end{array}$ ​ a. Compute the multiple coefficient of determination. b. At α = .05, test to determine whether or not the model is significant.

In a multiple regression analysis, SSR = 1000 and SSE = 200.The F statistic for this model is

Below you are given a partial computer output from a multiple regression analysis based on a sample of 16 observations. $\begin{array}{l}\begin{array} { l l } \text { Coefficients } & \text { Standard Error } \\12.924 & 4.425 \\- 3.682 & 2.630 \\45.216 & 12.560\end{array}\\\text { Analysis of Variance }\\\begin{array} { l l l l l } \text { Source of } & \text { Degrees of } & \text { Sum of } & \text { Mean } \\\text { Variation } & \text { Freedom } & \text { Squares } & \text { Square }\end{array} \quad F\end{array}$ We want to test whether the parameter $\beta$ ₁ is significant.The test statistic equals

A multiple regression model has

In logistic regression,

The following is part of the results of a regression analysis involving sales (y in millions of dollars), advertising expenditures (x₁ in thousands of dollars), and number of salespeople (x₂) for a corporation.The regression was performed on a sample of 10 observations. $\begin{array} { c l l } & \text { Coefficients } & \text { Standard Error } \\\text { Intercept } & 40.00 & 7.00 \\\mathrm { x } _ { 1 } & 8.00 & 2.50 \\\mathrm { x } _ { 2 } & 6.00 & 3.00\end{array}$ ​ a. If the company uses $40,000 in advertisement and has 30 salespeople, what are the expected sales? Give your answer in dollars. b. At α = .05, test for the significance of the coefficient of advertising. c. At α = .05, test for the significance of the coefficient of the number of salespeople.

A regression model between sales (y in $1000) , unit price (x₁ in dollars) , and television advertisement (x₂ in dollars) resulted in the following function: $\hat { y }$ = 7 - 3x₁ + 5x₂ For this model, SSR = 3500, SSE = 1500, and the sample size is 18.The adjusted multiple coefficient of determination for this problem is

The following estimated regression equation was developed relating yearly income (y in $1000s) of 30 individuals with their age (x₁) and their gender (x₂) (0 if male and 1 if female) . $\hat { y }$ = 30 + .7x₁ + 3x₂ Also provided are SST = 1200 and SSE = 384.The multiple coefficient of determination is

A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares. SSR = 165 SSE = 60 ​ The multiple coefficient of determination is

In a multiple regression model involving 30 observations, the following estimated regression equation was obtained: $\hat { y }$ = 17 + 4x₁ - 3x₂ + 8x₃ + 8x₄ For this model, SSR = 700 and SSE = 100.The critical F value at $\alpha$ = .05 is

In order to test for the significance of a regression model involving 3 independent variables and 47 observations, the numerator and denominator degrees of freedom (respectively) for the critical value of F are