Exam 13: Multiple Regression

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 model

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 sum of squares due to error SSE) equals

The following regression model has been proposed to predict sales at a fast food outlet. $\hat { Y }$ =18 - 2X1+7X2+15X3 where X1 = the number of competitors within 1 mile X2 = the population within 1 mile X3 = 1 if drive-up windows are present, 0 if otherwise $\hat { Y }$ = sales in $1,000s) a. What is the interpretation of 15 the coefficient of X3) in the regression equation? b. Predict sales for a store with 2 competitors, a population of 10,000 within one mile, and one drive-up window give the answer in dollars). c. Predict sales for the store with 2 competitors, a population of 10,000 within one mile, and no drive-up window give the answer in dollars).

The multiple coefficient of determination is

A multiple regression model has the form Y = 12 - 8X1 + 3X2 As X1 increases by 2 units holding X2 constant), Y is expected to

In multiple regression analysis,

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. Carry out the test of significance for the parameter ?? at the 1% level. The null hypothesis should be

In multiple regression analysis, the correlation among the independent variables is termed

In a multiple regression model, the values of the error term ,ε, are assumed to be

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 SSR are

A multiple regression model has the form $\hat { Y }$ =5+6X+7W As X increases by 1 unit holding W constant), Y is expected to

A regression was performed on a sample of 20 observations. Two independent variables were included in the analysis, X and Z. The relationship between X and Z is Z = X2. The following estimated equation was obtained. =23.72+12.61X+0.798Z $\hat { Y }$ The standard errors for the coefficients are Sb₁ = 4.85 and Sb2 = 0.21 For this model, SSR = 520.2 and SSE = 340.6 a. Estimate the value of Y when X = 5. b. Compute the appropriate t ratios. c. Test for the significance of the coefficients at the 5% level. Which variables) is are) significant? d. Compute the coefficient of determination and the adjusted coefficient of determination. Interpret the meaning of the coefficient of determination. e. Test the significance of the relationship among the variables at the 5% level of significance.

The numerical value of the coefficient of determination

All the variables in a multiple regression analysis

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 coefficient of determination for the above model is approximately

For a multiple regression model, SST = 200 and SSE = 50. The multiple coefficient of determination is

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. The coefficient of the unit price indicates that if the unit price is

The mathematical equation that explains how the dependent variable y is related to several independent variables x1, x2, …, xp and the error term ε is

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. We want to test whether the parameter ?? is significant. The test statistic equals

In a multiple regression model, the variance of the error term ε is assumed to be