Statistics Ch 15 Test Bank - Multiple Regression

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 The predicted yearly income of a 24-year-old female individual is a. $13.80 b. $13,800 c. $46,800 d. $49,800

$46,800

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 Refer to Exhibit 15-3. The predicted yearly income of a 24-year-old male individual is a. $19.80 b. $19,800 c. $49.80 d. $49,800

$49,800

In a regression model involving 30 observations, the following estimated regression equation was obtained: . For this model, SSR = 700 and SSE = 100. The multiple coefficient of determination is approximately a. -0.875 b. 0.875 c. 0.125 d. 0.144

0.875

Below you are given a partial statistical software output based on a sample of 25 observations. Coefficient Standard Error Constant 145.321 48.682 x1 25.625 9.150 x2 -5.720 3.575 x3 0.823 0.183 Refer to Exhibit 15-2. The interpretation of the coefficient on x1 is that a. a one unit decrease in x1 will lead to a predicted 25.625 unit increase in y b. a one unit increase in x1 will lead to a predicted 25.625 unit increase in y when all other variables are held constant c. a one unit increase in x1 will lead to a predicted 25.625 unit increase in x1 when all other variables are held constant d. It is impossible to interpret the coefficient.

a one unit increase in x1 will lead to a predicted 25.625 unit increase in y when all other variables are held constant

A variable that takes on the values of 0 or 1 and is used to incorporate the effect of categorical variables in a regression model is called a. an interaction b. a constant variable c. a dummy variable d. None of these alternatives is correct.

a dummy variable

An estimated regression equation has the form: . As x1 increases by 1 unit (holding x2 constant), y is expected to a. increase by 9 units b. decrease by 9 units c. increase by 2 units d. decrease by 2 units

increase by 2 units

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 At a 1% significance level, the regression model a. is significant b. is not significant c. would be significant is the sample size was larger than 30 d. None of these alternatives is correct.

is significant

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 The 95% confidence interval for β_2 (the slope of Gender) extends from a. 1.3584 to 4.6416 b. - 1.3584 to -4.6416 c. -2.0567 to 3.5491 d. 1.9872 to 4.8981

1.3584 to 4.6416

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 If we want to test the significance of an individual variable at a 5% significance level, the (positive) critical t value is a. 2.052 b. 1.703 c. 1.96 d. 1.645

2.052

Below you are given a partial statistical software output based on a sample of 25 observations. Coefficient Standard Error Constant 145.321 48.682 x1 25.625 9.150 x2 -5.720 3.575 x3 0.823 0.183 The (positive) critical t-value to test a significance of an independent variable at a 5% significance level is a. 1.960 b. 2.069 c. 2.074 d. 2.080

2.080

Below you are given a partial statistical software output based on a sample of 25 observations. Coefficient Standard Error Constant 145.321 48.682 x1 25.625 9.150 x2 -5.720 3.575 x3 0.823 0.183 The value of the test statistics for testing a significance of x1 equals a. 0.357 b. 2.8 c. 14 d. 1.96

2.8

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 Refer to Exhibit 15-3. The value of the test statistic for testing the overall significance of the regression model is a. 0.73 b. 1.47 c. 28.69 d. 5.22

28.69

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 Refer to Exhibit 15-3. If we want to test the significance of Gender, the value of the test statistic is a. 3 b. 0.80 c. 1.96 d. 3.75

3.75

In a regression model involving 30 observations, the following estimated regression equation was obtained: . For this model, SSR = 700 and SSE = 100. At 1% significance level, the critical F value for testing the overall significance of the model is a. 2.53 b. 2.76 c. 4.18 d. 3.35

4.18

In a regression model involving 30 observations, the following estimated regression equation was obtained: . For this model, SSR = 700 and SSE = 100. The value of the F statistic for testing the overall significance of the regression model is a. 43.75 b. 0.875 c. 50.19 d. 7.00

43.75

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 If we want to test for the overall significance of the regression model, the critical F value at a 1% significance level is a. 3.33 b. 5.49 c. 3.35 d. 1.96

5.49

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 What is the percentage of variation in the yearly income explained by the age and the gender? a. 92% b. 42% c. 68% d. 50%

68%

A student used multiple regression analysis to study how family spending (y) is influenced by income (x1), family size (x2), and additions to savings (x3). The variables y, x1, and x3 are measured in thousands of dollars. The following results were obtained. ANOVA DF SS Regression 45.9634 Residual 11 2.6218 Total Coefficients Standard Error Intercept 0.0136 x1 0.7992 0.074 x2 0.2280 0.190 x3 -0.5796 0.920 a. Write out the estimated regression equation for the linear relationship between the variables. b. What is the expected spending of family of size 4 making 90,000 a year, and adding $5,000 annually to their savings? c. c. Compute R2. What can you say about the strength of this relationship? d. Carry out a test of whether the regression model is significant. Use a 0.05 level of significance. e. e. Carry out a test to see if x3 and y are significantly related. Use a 0.05 level of significance.

ANS: a. = 0.0136 + 0.7992x1 + 0.228x2 - 0.5796x3 b. = 0.0136 + 0.7992(90) + 0.228(4) - 0.579(5) = 69.956, that is, $69,956 c. R2 = 0.9460. Therefore, 94.6% of the variability in y is explained by the independent variables. d. F = 64.28; p-value < 0.01 (almost zero); reject Ho; the model is significant (critical F = 3.59) e. t = -0.63; p-value > 0.4; do not reject Ho; the relationship is not significant (critical positive t = 2.201)

In a regression model involving more than one independent variable, which of the following tests must be used in order to determine if the regression model is significant? a. t test b. F test c. Either a t test or a chi-square test can be used. d. chi-square test

F test

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 If we want to test for the overall significance of the regression model, the p-value of the test is a. Less than 0.01 b. Between 0.01 and 0.05 c. Between 0.05 and 0.10 d. More than 0.10

Less than 0.01

Below you are given a partial statistical software output based on a sample of 25 observations. Coefficient Standard Error Constant 145.321 48.682 x1 25.625 9.150 x2 -5.720 3.575 x3 0.823 0.183 If one carries out the test of significance for the variable x at the 5% level, then the null hypothesis should be a. Rejected because |2.8| ≥ 2.08 b. not rejected c. Revised d. None of these alternatives is correct.

Rejected because |2.8| ≥ 2.08

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 If we want to test the significance of Gender, the p-value of the test is a. less than 0.01 b. between 0.01 and 0.05 c. between 0.05 and 0.10 d. More than 0.10

less than 0.01

30 individuals were randomly selected to develop a linear regression equation relating their yearly income (in $1,000s) with their age and their gender (1 if male and 0 if female). This led to the following information: ANOVA df SS MS F Regression Error 384 Total 1200 Coefficients Standard Error t Stat Intercept 30 Age 0.7 0.20 Gender 3 0.80 From the above output, it can be said that, for the same age, the predicted yearly income of a. males is $3 more than females b. females is $3 more than males c. males is $3,000 more than females d. females is $3,000 more than males

males is $3,000 more than females

In a regression model involving 30 observations, the following estimated regression equation was obtained: . For this model, SSR = 700 and SSE = 100. At 1% significance level, the conclusion is that the a. model is not significant b. model is significant c. x1 is significant d. x2 is significant

model is significant

In multiple regression analysis, the correlation among the independent variables is termed a. homoscedasticity b. linearity c. multicollinearity d. adjusted coefficient of determination

multicollinearity

In multiple regression analysis, a. there can be any number of dependent variables but only one independent variable b. there must be only one independent variable c. the coefficient of determination must be larger than 1 d. there can be several independent variables, but only one dependent variable

there can be several independent variables, but only one dependent variable

Below you are given a partial statistical software output based on a sample of 25 observations. Coefficient Standard Error Constant 145.321 48.682 x1 25.625 9.150 x2 -5.720 3.575 x3 0.823 0.183 The estimated regression equation is a. y^ = B0+B1x1+B2x2+b3x3+e b. E(y) = B0+B1x1+B2x2+B3x3 c. y^ = 145.321+25.625x1-5720x2+0.823x3 d. y^ = 48.682+9.15x1+3.575x2+1.183x3

y^ = 145.321+25.625x1-5720x2+0.823x3