Exam 13: Multiple Regression

The mathematical equation relating the expected value of the dependent variable to the value of the independent variables, which has the form of Ey) = β₀ + β₁x1 + β2x2 + ... + βpxp is

In a multiple regression model, the error term ε is assumed to be a random variable with a mean of

Exhibit 13-4 a. Y=β₀ + β₁X1 + β2X2 + ε b. EY)=β₀ + β₁X1 + β2X2 + ε c. $\hat { Y }$ =b₀ + b₁X1 + b2X2 d. EY)=β₀ + β₁X1 + β2X2 -Refer to Exhibit 13-4. Which equation gives the estimated regression line?

In a multiple regression analysis involving 5 independent variables and 30 observations, SSR = 360 and SSE = 40. The coefficient of determination is

For a multiple regression model, SSR = 600 and SSE = 200. The multiple coefficient of determination is

Exhibit 13-11 Below you are given a partial computer output based on a sample of 25 observations. Coefficient Standard Error Constant 145 29 20 5 -18 6 4 4 -Refer to Exhibit 13-11. We want to test whether the parameter ?2 is significant. The test statistic equals

Exhibit 13-12 In a laboratory experiment, data were gathered on the life span Y in months) of 33 rats, units of daily protein intake X1), and whether or not agent X2 a proposed life extending agent) was added to the rats diet X2 = 0 if agent X2 was not added, and X2 = 1 if agent was added.) From the results of the experiment, the following regression model was developed. $\hat { Y }$ =36+0.8X1 - 1.7X2 Also provided are SSR = 60 and SST = 180. -Refer to Exhibit 13-12. The degrees of freedom associated with SSE are

In a regression analysis involving 20 observations and five independent variables, the following information was obtained. ANALYSIS OF VARIANCE Source of Degrees Sum of Mean Variation of Freedom Squares Square F Regression \_\_\_? \_\_\_? \_\_\_? \_\_\_? Error \_\_\_? \_\_\_? 30 Total 990 Fill in all the blanks in the above ANOVA table.

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. Coefilicient Standard Error Intercept 40.00 7.00 8.00 2.50 6.00 3.00 a. If the company uses $40,000 in advertisement and has 30 salespersons, what are the expected sales? Give your answer in dollars. b. At α = 0.05, test for the significance of the coefficient of advertising. c. At α = 0.05, test for the significance of the coefficient of the number of salespeople.

In order to test for the significance of a regression model involving 8 independent variables and 121 observations, the numerator and denominator degrees of freedom respectively) for the critical value of F are

A multiple regression model has

Exhibit 13-6 Below you are given a partial computer output based on a sample of 16 observations. Coefficient Standard Error Intercept 12.924 4.425 -3.682 2.63. 45.216 12.560 $\text { Analysis of Variance }$ Source of Degrees Sum of Mean Variation of Freedom Squares Square F Regression 4,853 2,426.5 Error 485.3 -Refer to Exhibit 13-6. The F value obtained from the table used to test if there is a relationship among the variables at the 5% level equals

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 sales people X2) for a corporation: ANALYSIS OF VARIANCE Source of Variation Degrees of Freedom Sum of Squares Mean Square F Regression 2 822.088 Error 7 736.012 a. At α = 0.05 level of significance, test to determine if the model is significant. That is, determine if there exists a significant relationship between the independent variables and the dependent variable. b. Determine the multiple coefficient of determination. c. Determine the adjusted multiple coefficient of determination. d. What has been the sample size for this regression analysis?

A variable that cannot be measured in terms of how much or how many but instead is assigned values to represent categories is called

Multiple regression analysis was used to study the relationship between a dependent variable, Y, and four independent variables; X1, X2, X3 and, X4. The following is a partial result of the regression analysis involving 31 observations. Coefficient Standard Error Intercept 18.00 6.00 12.00 8.00 24.00 48.00 -36.00 36.00 16.00 2.00 $\text { Analysis of Variance }$ Source DF SS MS F Regression 125 Error Total 760 a. Compute the coefficient of determination. b. Perform a t test and determine whether or not β₁ is significantly different from zero α = 0.05). c. Perform a t test and determine whether or not β4 is significantly different from zero α = 0.05). d. At α = 0.05, perform an F test and determine whether or not the regression model is significant.

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 model

Exhibit 13-5 Below you are given a partial Minitab output based on a sample of 25 observations. Coefficient Standard Error Constant 145.321 48.682 25.625 9.150 -5.720 3.575 0.823 0.183 -Refer to Exhibit 13-5. The t value obtained from the table to test an individual parameter at the 5% level is

The following regression model has been proposed to predict sales at a furniture store. $\hat { Y }$ = 10 - 4X1+7X2+18X3 where X1 = competitor's previous day's sales in $1,000s) X2 = population within 1 mile in 1,000s) X3 = 1 if any form of advertising was used, 0 if otherwise $\hat { Y }$ = sales in $1,000s) a. Fully interpret the meaning of the coefficient of X3. b. Predict sales in dollars) for a store with competitor's previous day's sale of $3,000, a population of 10,000 within 1 mile, and six radio advertisements.

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. Coefilicient Standard Error Constant -11.340 20.412 0.798 0.332 0.141 0.278 a. Write the regression equation. b. Interpret the coefficients of the estimated regression equation found in Part a). c. At α =0.05, test for the significance of the coefficient of advertising. d. At α =0.05, test for the significance of the coefficient of number of salespeople. e. If the company uses $50,000 in advertisement and has 800 salespersons, what are the expected sales? Give your answer in dollars.

Exhibit 13-10 In a regression model involving 30 observations, the following estimated regression equation was obtained. $\hat { Y }$ =170+34X1 - 3X2+8X3+58X4+3X5 For this model, SSR = 1,740 and SST = 2,000. -Refer to Exhibit 13-10. The value of MSR is