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Exam 13: Multiple Regression

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Question 41

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A regression model involving 3 independent variables for a sample of 20 periods resulted in the following sum of squares. Sum of Squares Regression 90 Residual Error) 100 a. Compute the coefficient of determination and fully explain its meaning. b. At α = 0.05 level of significance, test to determine whether or not there is a significant relationship between the independent variables and the dependent variable.

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a. 0.4737; 47.37% of variation in the de...

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Question 42

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Exhibit 13-6 Below you are given a partial computer output based on a sample of 16 observations. $\begin{array}{lcc} & \text { Coefficient } & \text { Standard Error } \\\text { Intercept } & 12.924&4.425\\\mathrm{X}_{1} & -3.682&2.63. \\\mathrm{X}_{2} &45.216&12.560\\\end{array}$ $\text { Analysis of Variance }$ $\begin{array}{lccc}\text { Source of } & \text { Degrees } &\text { Sum of } &\text { Mean }\\\text { Variation } & \text { of Freedom }&\text { Squares } & \text { Square }&F\\\text { Regression }&&4,853&2,426.5\\\text {Error }&&&485.3\end{array}$ -Refer to Exhibit 13-6. The test statistic used to determine if there is a relationship among the variables equals

A) -1.4
B) 0.2
C) 0.77
D) 5

E) All of the above
F) C) and D)

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Question 43

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The estimate of the multiple regression equation based on the sample data, which has the form of Ey) = $\hat { \mathrm { y } }$ = b? + b?x1 + b2x2 + ... + bpxp is

A term used to describe the case when the independent variables in a multiple regression model are correlated is

The following model Y=β₀+β₁X1+ε is referred to as a

A multiple regression model has the form Y = 7 + 2X1 + 9X2 As X1 increases by 1 unit holding X2 constant) , Y is expected to

Exhibit 13-8 The following estimated regression model was developed relating yearly income Y in $1,000s) of 30 individuals with their age X1) and their gender X2) 0 if male and 1 if female) . $\hat { Y }$ =30+0.7X1+3X2 Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 13-8. The multiple coefficient of determination is

Exhibit 13-9 In a regression analysis involving 25 observations, the following estimated regression equation was developed. $\hat { Y }$ =10 - 18X1+3X2+14X3 Also, the following standard errors and the sum of squares were obtained. Sb₁ = 3 Sb2 = 6 Sb3 = 7 SST = 4,800 SSE = 1,296 -Refer to Exhibit 13-9. The test statistic for testing the significance of the model is

A regression model involved 18 independent variables and 200 observations. The critical value of t for testing the significance of each of the independent variable's coefficients will have

Exhibit 13-6 Below you are given a partial computer output based on a sample of 16 observations. $\begin{array}{lcc} & \text { Coefficient } & \text { Standard Error } \\\text { Intercept } & 12.924&4.425\\\mathrm{X}_{1} & -3.682&2.63. \\\mathrm{X}_{2} &45.216&12.560\\\end{array}$ $\text { Analysis of Variance }$ $\begin{array}{lccc}\text { Source of } & \text { Degrees } &\text { Sum of } &\text { Mean }\\\text { Variation } & \text { of Freedom }&\text { Squares } & \text { Square }&F\\\text { Regression }&&4,853&2,426.5\\\text {Error }&&&485.3\end{array}$ -Refer to Exhibit 13-6. The degrees of freedom for the sum of squares explained by the regression SSR) are

Exhibit 13-9 In a regression analysis involving 25 observations, the following estimated regression equation was developed. $\hat { Y }$ =10 - 18X1+3X2+14X3 Also, the following standard errors and the sum of squares were obtained. Sb₁ = 3 Sb2 = 6 Sb3 = 7 SST = 4,800 SSE = 1,296 -Refer to Exhibit 13-9. If you want to determine whether or not the coefficients of the independent variables are significant, the critical value of t statistic at ? = 0.05 is

Exhibit 13-3 In a 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. -Refer to Exhibit 13-3. The critical F value at 95% confidence is

In a multiple regression analysis SSR = 1,000 and SSE = 200. The F statistic for this model is

Below you are given a computer output based on a sample of 30 days of the price of a company's stock Y in dollars), the Dow Jones industrial average X1), and the stock price of the company's major competitor X2 in dollars). $\begin{array}{lr}&\text { Coefilicient }&\text { Standard Error }\\\text { Constant } & 20.000 & 5.455 \\\mathrm{X}_{1} & 0.006 & 0.002 \\\mathrm{X}_{2} & -0.70 & 0.200\end{array}$ a. Use the output shown above and write an equation that can be used to predict the price of the stock. b. If the Dow Jones Industrial Average is 10,000 and the price of the competitor is $50, what would you expect the price of the stock to be? c. At α = 0.05, test to determine if the Dow Jones average is a significant variable. d. At α = 0.05, test to determine if the stock price of the major competitor is a significant variable.

Exhibit 13-2 A regression model between sales Y in $1,000) , 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. -Refer to Exhibit 13-2. To test for the significance of the model, the test statistic F is

A measure of goodness of fit for the estimated regression equation is the

The adjusted multiple coefficient of determination is adjusted for

Exhibit 13-5 Below you are given a partial Minitab output based on a sample of 25 observations. $\begin{array}{lcc}&\text { Coefficient }&\text { Standard Error }\\\text { Constant } & 145.321 & 48.682 \\\mathrm{X}_{1} & 25.625 & 9.150 \\\mathrm{X}_{2} & -5.720 & 3.575 \\\mathrm{X}_{3} & 0.823 & 0.183\end{array}$ -Refer to Exhibit 13-5. The estimated regression equation is

Exhibit 13-3 In a 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. -Refer to Exhibit 13-3. The conclusion is that the

Exhibit 13-8 The following estimated regression model was developed relating yearly income Y in $1,000s) of 30 individuals with their age X1) and their gender X2) 0 if male and 1 if female) . $\hat { Y }$ =30+0.7X1+3X2 Also provided are SST = 1,200 and SSE = 384. -Refer to Exhibit 13-8. The yearly income of a 24-year-old male individual is