Question 1

True or False: In data mining where huge data sets are being explored to discover relationships among a large number of variables,the best-subsets approach is more practical than the stepwise regression approach.

Accepted Answer

The stepwise regression approach is generally more practical than the best-subsets approach in data mining as it is less computationally intensive and provides a more manageable number of variables for analysis.

Question 2

True or False: In stepwise regression,an independent variable is not allowed to be removed from the model once it has entered into the model.

Accepted Answer

The answer of True or False: In stepwise regression,an independent...

Question 3

The logarithm transformation can be used
A)to overcome violations to the autocorrelation assumption.
B)to test for possible violations to the autocorrelation assumption.
C)to change a nonlinear model into a linear model.
D)to change a linear independent variable into a nonlinear independent variable.

Accepted Answer

The logarithm transformation can be used to transform a nonlinear model into a linear model. This is useful when trying to fit a linear regression model to data that has a nonlinear relationship between the independent and dependent variables. It can also be used to transform data that is heavily skewed to have a more normal distribution, which can improve the accuracy of the regression model. However, it is not used to overcome or test for violations to the autocorrelation assumption or to change a linear independent variable into a nonlinear independent variable.

Question 4

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state.
Let Y = % Passing as the dependent variable,XS1U1B11S1U1B0 = % Attendance,XS1U1B12S1U1B0 = Salaries and XS1U1B13S1U1B0 = Spending.
The coefficient of multiple determination (  )of each of the 3 predictors with all the other remaining predictors are,respectively,0.0338,0.4669,and 0.4743.
The output from the best-subset regressions is given below:  Following is the residual plot for % Attendance:  Following is the output of several multiple regression models:
Model (I):  Model (II):  Model (III): 
-True or False: Referring to Table 15-4,the residual plot suggests that a nonlinear model on % attendance may be a better model.

Accepted Answer

A residual plot that shows a pattern or curvature suggests that the relationship between the variables may not be linear, indicating that a nonlinear model might better fit the data.

Question 5

True or False: The goals of model building are to find a good model with the fewest independent variables that is easier to interpret and has lower probability of collinearity.

Accepted Answer

The statement is true. The goals of model building include finding a model that is both accurate and easy to interpret, which often involves minimizing the number of independent variables in the model and reducing collinearity.

Question 6

The logarithm transformation can be used
A)to overcome violations to the autocorrelation assumption.
B)to test for possible violations to the autocorrelation assumption.
C)to overcome violations to the homoscedasticity assumption.
D)to test for possible violations to the homoscedasticity assumption.

Accepted Answer

The logarithm transformation can be used to overcome violations to the homoscedasticity assumption by reducing the heteroscedasticity in the data, making it more homoscedastic. While autocorrelation may also be addressed with logarithm transformation in some cases, it is not the primary purpose of this transformation. Testing for violations to the assumptions is typically done using diagnostic plots and statistical tests, not transformations.

Question 7

Which of the following will not change a nonlinear model into a linear model?
A)Quadratic regression model
B)Logarithmic transformation
C)Square-root transformation
D)Variance inflationary factor

Accepted Answer

Variance inflationary factor is a measure of multicollinearity in linear regression models and has no effect on the linearity of the model. A quadratic regression model, logarithmic transformation, and square-root transformation all have the potential to transform a nonlinear model into a linear model.

Question 8

TABLE 15-4 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Let Y = % Passing as the dependent variable,XS1U1B11S1U1B0 = % Attendance,XS1U1B12S1U1B0 = Salaries and XS1U1B13S1U1B0 = Spending. The coefficient of multiple determination ( )of each of the 3 predictors with all the other remaining predictors are,respectively,0.0338,0.4669,and 0.4743. The output from the best-subset regressions is given below: Following is the residual plot for % Attendance: Following is the output of several multiple regression models: Model (I): Model (II): Model (III): -Referring to Table 15-4,which of the following models should be taken into consideration using the Mallows' C_p statistic? A)X₁,X₃ B)X₁,X₂,X₃ C)Both of the above D)None of the above

Accepted Answer

We can determine the best model using Mallows' Cp statistic, which gives an estimate of the prediction error of each model. In this case, the best models are the ones with the lowest value of Cp. Model I has a Cp of 4.93, Model II has a Cp of 4.67, and Model III has a Cp of 5.05. Therefore, Model II, which includes all three predictors X₁, X₂, and X₃, should be considered. Additionally, Model I, which only includes X₁ and X₃, should also be considered as it has a relatively low Cp value.

Question 9

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state.
Let Y = % Passing as the dependent variable,XS1U1B11S1U1B0 = % Attendance,XS1U1B12S1U1B0 = Salaries and XS1U1B13S1U1B0 = Spending.
The coefficient of multiple determination (  )of each of the 3 predictors with all the other remaining predictors are,respectively,0.0338,0.4669,and 0.4743.
The output from the best-subset regressions is given below:  Following is the residual plot for % Attendance:  Following is the output of several multiple regression models:
Model (I):  Model (II):  Model (III): 
-True or False: Referring to Table 15-4,there is reason to suspect collinearity between some pairs of predictors.

Accepted Answer

The answer of TABLE 15-4
The superintendent of a school district...

Question 10

TABLE 15-4 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Let Y = % Passing as the dependent variable,XS1U1B11S1U1B0 = % Attendance,XS1U1B12S1U1B0 = Salaries and XS1U1B13S1U1B0 = Spending. The coefficient of multiple determination ( )of each of the 3 predictors with all the other remaining predictors are,respectively,0.0338,0.4669,and 0.4743. The output from the best-subset regressions is given below: Following is the residual plot for % Attendance: Following is the output of several multiple regression models: Model (I): Model (II): Model (III): -Referring to Table 15-4,the "best" model using a 5% level of significance among those chosen by the C_p statistic is A)X₁,X₃. B)X₁,X₂,X₃. C)Either of the above D)None of the above

Accepted Answer

The answer of TABLE 15-4
The superintendent of a school district...

Question 11

An independent variable X_j is considered highly correlated with the other independent variables if A)VIF_j < 5. B)VIF_j > 5. C)VIF_j < VIF_i for i ≠ j. D)VIF_j > VIF_i for i ≠ j.

Accepted Answer

A high value of VIF (Variable Inflation Factor) indicates a high correlation between the independent variables. Therefore, if VIF_j > 5, it is considered to be highly correlated with the other independent variables.

Question 12

TABLE 15-4
The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state.
Let Y = % Passing as the dependent variable,XS1U1B11S1U1B0 = % Attendance,XS1U1B12S1U1B0 = Salaries and XS1U1B13S1U1B0 = Spending.
The coefficient of multiple determination (  )of each of the 3 predictors with all the other remaining predictors are,respectively,0.0338,0.4669,and 0.4743.
The output from the best-subset regressions is given below:  Following is the residual plot for % Attendance:  Following is the output of several multiple regression models:
Model (I):  Model (II):  Model (III): 
-Referring to Table 15-4,what are,respectively,the values of the variance inflationary factor of the 3 predictors?

Accepted Answer

The answer of TABLE 15-4
The superintendent of a school district...

Question 13

TABLE 15-4 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Let Y = % Passing as the dependent variable,XS1U1B11S1U1B0 = % Attendance,XS1U1B12S1U1B0 = Salaries and XS1U1B13S1U1B0 = Spending. The coefficient of multiple determination ( )of each of the 3 predictors with all the other remaining predictors are,respectively,0.0338,0.4669,and 0.4743. The output from the best-subset regressions is given below: Following is the residual plot for % Attendance: Following is the output of several multiple regression models: Model (I): Model (II): Model (III): -Referring to Table 15-4,the better model using a 5% level of significance derived from the "best" model above is A)X₁. B)X₃. C)X₁,X₃. D)X₁,X₂,X₃.

Accepted Answer

The answer of TABLE 15-4
The superintendent of a school district...

Question 14

TABLE 15-4 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Let Y = % Passing as the dependent variable,XS1U1B11S1U1B0 = % Attendance,XS1U1B12S1U1B0 = Salaries and XS1U1B13S1U1B0 = Spending. The coefficient of multiple determination ( )of each of the 3 predictors with all the other remaining predictors are,respectively,0.0338,0.4669,and 0.4743. The output from the best-subset regressions is given below: Following is the residual plot for % Attendance: Following is the output of several multiple regression models: Model (I): Model (II): Model (III): -Referring to Table 15-4,the "best" model chosen using the adjusted R-square statistic is A)X₁,X₃. B)X₁,X₂,X₃. C)Either of the above D)None of the above

Accepted Answer

The answer of TABLE 15-4
The superintendent of a school district...

Question 15

True or False: Using the C_pstatistic in model building,all models with C_p ≤ (k + 1)are equally good.

Accepted Answer

The C_p statistic is used to assess the significance of individual predictors in a model. It is not used to compare models with different numbers of predictors, so there is no fixed threshold value (k + 1) that determines whether one model is better than another.

Question 16

The _______ (larger/smaller)the value of the Variance Inflationary Factor,the higher is the collinearity of the X variables.

Accepted Answer

The answer of The _______ (larger/smaller)the value of the Variance...

Question 17

TABLE 15-4 The superintendent of a school district wanted to predict the percentage of students passing a sixth-grade proficiency test.She obtained the data on percentage of students passing the proficiency test (% Passing),daily mean of the percentage of students attending class (% Attendance),mean teacher salary in dollars (Salaries),and instructional spending per pupil in dollars (Spending)of 47 schools in the state. Let Y = % Passing as the dependent variable,XS1U1B11S1U1B0 = % Attendance,XS1U1B12S1U1B0 = Salaries and XS1U1B13S1U1B0 = Spending. The coefficient of multiple determination ( )of each of the 3 predictors with all the other remaining predictors are,respectively,0.0338,0.4669,and 0.4743. The output from the best-subset regressions is given below: Following is the residual plot for % Attendance: Following is the output of several multiple regression models: Model (I): Model (II): Model (III): -Referring to Table 15-4,which of the following predictors should first be dropped to remove collinearity? A)X₁ B)X₂ C)X₃ D)None of the above

Accepted Answer

Without the actual data from Table 15-4, it's not possible to determine which predictor should be dropped. Typically, collinearity is assessed using statistical measures like VIF (Variance Inflation Factor), and the predictor with the highest VIF is considered for removal. "None of the above" suggests that the table might not indicate any collinearity issues.

Question 18

Using the best-subsets approach to model building,models are being considered when their A)C_p > k. B)C_p ≤ k. C)C_p > (k + 1). D)C_p ≤ (k + 1).

Accepted Answer

The answer of Using the best-subsets approach to model building,models...

Question 19

A regression diagnostic tool used to study the possible effects of collinearity is ________.

Accepted Answer

The answer of A regression diagnostic tool used to study...

Question 20

True or False: The stepwise regression approach takes into consideration all possible models.

Accepted Answer

The stepwise regression approach only considers a subset of all possible models by iteratively adding or removing variables based on certain criteria, such as the p-value or adjusted R-squared. It does not consider all possible models.

Quiz 15: Multiple Regression Model Building

True or False: In data mining where huge data sets are being explored to discover relationships among a large number of variables,the best-subsets approach is more practical than the stepwise regression approach.

True or False: In stepwise regression,an independent variable is not allowed to be removed from the model once it has entered into the model.

The logarithm transformation can be used

True or False: The goals of model building are to find a good model with the fewest independent variables that is easier to interpret and has lower probability of collinearity.

The logarithm transformation can be used

Which of the following will not change a nonlinear model into a linear model?

An independent variable Xj is considered highly correlated with the other independent variables if

True or False: Using the Cp statistic in model building,all models with Cp ≤ (k + 1)are equally good.

The _______ (larger/smaller)the value of the Variance Inflationary Factor,the higher is the collinearity of the X variables.

Using the best-subsets approach to model building,models are being considered when their

A regression diagnostic tool used to study the possible effects of collinearity is ________.

True or False: The stepwise regression approach takes into consideration all possible models.

An independent variable X_j is considered highly correlated with the other independent variables if

True or False: Using the C_pstatistic in model building,all models with C_p ≤ (k + 1)are equally good.