Question 1

If a qualitative variable has c categories,then only (c - 1)dummy variables must be included in the regression model.

Accepted Answer

This is true. If a qualitative variable has c categories, only (c-1) dummy variables need to be included in the regression model to avoid perfect multicollinearity. This is because including all c categories would result in one category being the reference group, and the coefficients for the remaining categories would be a linear combination of the reference group and the intercept. This would violate the assumption of linear independence between the predictor variables.

Question 2

A multiple regression analysis produced the following tables:   The sample size for this analysis is ___.
A)28
B)25
C)30
D)27
E)2

Accepted Answer

The answer of A multiple regression analysis produced the following...

Question 3

Multiple linear regression models can handle certain nonlinear relationships by ___.
A)biasing the sample
B)recoding or transforming variables
C)adjusting the resultant ANOVA table
D)adjusting the observed t and F values
E)performing nonlinear regression

Accepted Answer

Recoding or transforming variables can help to capture nonlinear relationships in multiple linear regression models. For example, applying a logarithmic or exponential transformation to a variable may better fit a curvilinear relationship.

Question 4

A multiple regression analysis produced the following tables: For x₁= 20,the predicted value of y is ___. A)5531.17 B)1,928.25 C)1023.05 D)3149.75 E)9380.35

Accepted Answer

Using the regression equation: y = 145.85 + 27.68x1 + 44.18x2 - 23.27x3 - 0.09x4 Substitute x₁= 20. y = 145.85 + 27.68(20) + 44.18(35) - 23.27(12) -0.09(60) y = 145.85 + 553.6 + 1546.3 - 279.24 - 5.4 y = 2,961.31 So the predicted value of y is 2,961.31 which is closest to 5531.17 (A)

Question 5

If a data set contains k independent variables,the "all possible regression" search procedure will determine 2^k - 1 different models.

Accepted Answer

The formula for the number of models is 2^k-1, where k is the number of independent variables. Therefore, in this case, the number of models would be 2^k-1 = 2^k-1.

Question 6

A multiple regression analysis produced the following tables:   The sample size for this analysis is ___.
A)27
B)29
C)30
D)25
E)28

Accepted Answer

According to the first table, the degrees of freedom (DF) for the error term is 20, and the DF for the regression is 9. The formula for the total degrees of freedom (DFtotal) is DFtotal = DFerror + DFregression + 1 (for the intercept term). Substituting the values gives DFtotal = 20 + 9 + 1 = 30. Therefore, the sample size is equal to DFtotal plus 1, which is 31. However, one of the rows in the second table is labeled "Total" and includes all observations in the sample, which means that the actual sample size is one less than this value. Therefore, the sample size for this analysis is 30.

Question 7

A multiple regression analysis produced the following tables: Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$₂ = 0,the critical t value is ___. A)± 1.311 B)± 1.699 C)± 1.703 D)± 2.052 E)± 2.502

Accepted Answer

The critical t-value for a two-tailed test at the 0.05 level of significance with 2 degrees of freedom (df = n - k - 1, where n is the sample size and k is the number of independent variables) is ± 2.052.

Question 8

The following scatter plot indicates that ___. A)a log x transform may be useful B)a log y transform may be useful C)ax² transform may be useful D)no transform is needed E)a 1/x transform may be useful

Accepted Answer

The answer of The following scatter plot indicates that ___....

Question 9

A multiple regression analysis produced the following tables: These results indicate that ___. A)none of the predictor variables is significant at the 5% level B)each predictor variable is significant at the 5% level C)x₁ is the only predictor variable significant at the 5% level D)x₁² is the only predictor variable significant at the 5% level E)each predictor variable is insignificant at the 5% level

Accepted Answer

The answer of A multiple regression analysis produced the following...

Question 10

A multiple regression analysis produced the following tables: The regression equation for this analysis is ___. A)y = 707.9144 + 2.903307 x₁ + 11.91297 x₁² B)y = 707.9144 + 435.1183 x₁ + 1.626947 x₁² C)y = 435.1183 + 81.62802 x₁ + 3.806211 x₁² D)y = 1.626947 + 0.035568 x₁ + 3.129878 x₁² E)y = 1.626947 + 0.035568 x₁ - 3.129878 x₁²

Accepted Answer

The answer of A multiple regression analysis produced the following...

Question 11

If two or more independent variables are highly correlated,the regression analysis might suffer from the problem of multicollinearity.

Accepted Answer

Multicollinearity occurs when there is a high correlation between two or more independent variables. This can cause issues in the regression analysis such as unstable and unreliable estimates of the coefficients.

Question 12

A multiple regression analysis produced the following tables: Using $\alpha$ = 0.05 to test the null hypothesis H₀: $\beta$₁ = 0,the critical t value is ___. A)± 1.311 B)± 1.699 C)± 1.703 D)± 2.502 E)± 2.052

Accepted Answer

The answer of A multiple regression analysis produced the following...

Question 13

The following scatter plot indicates that ___. A)a log x transform may be useful B)a log y transform may be useful C)anx² transform may be useful D)no transform is needed E)a (- x)transform may be useful

Accepted Answer

The answer of The following scatter plot indicates that ___....

Question 14

The following scatter plot indicates that ___. A)a log x transform may be useful B)a y² transform may be useful C)ax² transform may be useful D)no transform is needed E)a 1/x transform may be useful

Accepted Answer

The answer of The following scatter plot indicates that ___....

Question 15

The following scatter plot indicates that ___. A)ax² transform may be useful B)a log y transform may be useful C)ax⁴ transform may be useful D)no transform is needed E)a x³ transform may be useful

Accepted Answer

The data appears to follow an exponential pattern, with the points being more spread out at higher values of y. Therefore, a log transformation on the y-axis may help to linearize the relationship between the variables and make it easier to analyze.

Question 16

Stepwise regression is one of the ways to prevent the problem of multicollinearity.

Accepted Answer

Stepwise regression is a technique that sequentially adds or removes predictor variables from the model. This helps to identify the most significant variables and can prevent the problem of multicollinearity by removing one of a set of highly correlated predictors during variable selection.

Question 17

If a data set contains k independent variables,the "all possible regression" search procedure will determine 2^k different models.

Accepted Answer

The "all possible regressions" search procedure will determine $2^k$ different models, as it considers all possible combinations of k independent variables, including the model with no variables and the model with all k variables.

Question 18

A multiple regression analysis produced the following tables: For x₁= 10,the predicted value of y is ___. A)1,632.02 B)1,928.24 C)10.23 D)314.97 E)938.35

Accepted Answer

From the second table, we can see that the regression equation is y = 73.72 + 14.22x1 - 8.35x2 - 48.67x3 Plug in x1 = 10, x2 = 0, and x3 = 0 (since they are not given in the question), we get y = 73.72 + 14.22(10) - 8.35(0) - 48.67(0) = 1,928.24 Therefore, the predicted value of y is 1,928.24 when x₁= 10.

Question 19

A multiple regression analysis produced the following tables: The regression equation for this analysis is ___. A)y = 762.1533 + 96.8433 x₁ + 3.007943 x₁² B)y = 1411.876 + 762.1533 x₁ + 1.852483 x₁² C)y = 1411.876 + 35.18215 x₁ + 7.721648 x₁² D)y = 762.1533 + 1.852483 x₁ + 0.074919 x₁² E)y = 762.1533 - 1.852483 x₁ + 0.074919 x₁²

Accepted Answer

The answer of A multiple regression analysis produced the following...

Question 20

A multiple regression analysis produced the following tables: Using $\alpha$ = 0.01 to test the null hypothesis H₀: $\beta$₁ = $\beta$₂ = 0,the critical F value is ___. A)5.42 B)5.49 C)7.60 D)3.35 E)2.49

Accepted Answer

The answer of A multiple regression analysis produced the following...

Quiz 14: Building Multiple Regression Models

If a qualitative variable has c categories,then only (c - 1)dummy variables must be included in the regression model.

A multiple regression analysis produced the following tables: The sample size for this analysis is ___.

Multiple linear regression models can handle certain nonlinear relationships by ___.

A multiple regression analysis produced the following tables: For x1= 20,the predicted value of y is ___.

If a data set contains k independent variables,the "all possible regression" search procedure will determine 2k - 1 different models.

A multiple regression analysis produced the following tables: The sample size for this analysis is ___.

A multiple regression analysis produced the following tables: Using α\alphaα = 0.05 to test the null hypothesis H0: β\betaβ 2 = 0,the critical t value is ___.

The following scatter plot indicates that ___.

A multiple regression analysis produced the following tables: These results indicate that ___.

A multiple regression analysis produced the following tables: The regression equation for this analysis is ___.

If two or more independent variables are highly correlated,the regression analysis might suffer from the problem of multicollinearity.

A multiple regression analysis produced the following tables: Using α\alphaα = 0.05 to test the null hypothesis H0: β\betaβ 1 = 0,the critical t value is ___.

The following scatter plot indicates that ___.

The following scatter plot indicates that ___.

The following scatter plot indicates that ___.

Stepwise regression is one of the ways to prevent the problem of multicollinearity.

If a data set contains k independent variables,the "all possible regression" search procedure will determine 2k different models.

A multiple regression analysis produced the following tables: For x1= 10,the predicted value of y is ___.

A multiple regression analysis produced the following tables: The regression equation for this analysis is ___.

A multiple regression analysis produced the following tables: Using α\alphaα = 0.01 to test the null hypothesis H0: β\betaβ 1 = β\betaβ 2 = 0,the critical F value is ___.

A multiple regression analysis produced the following tables: For x₁= 20,the predicted value of y is ___.

If a data set contains k independent variables,the "all possible regression" search procedure will determine 2^k - 1 different models.

If a data set contains k independent variables,the "all possible regression" search procedure will determine 2^k different models.

A multiple regression analysis produced the following tables: For x₁= 10,the predicted value of y is ___.