Identify the variable that can be eliminated first to possibly improve the given model.

Question

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Answer 1

Question

Chapter 10.3, Problem 58E

a.

To determine

Identify the variable that can be eliminated first to possibly improve the given model.

a.

Expert Solution

Answer to Problem 58E

The variable that can be eliminated first to possibly improve the given model is X2.

Explanation of Solution

In order to improve a regression model, the most insignificant independent variable in the model should be eliminated first. The high p-value indicates that the variable is insignificant.

From the multiple regression model, it is clear that the variable X2 has the highest p-value. Hence, one should try to eliminate the variable X2 to possibly improve the given model.

b.

To determine

Describe about the R2 of the model.

Explain whether the change in R2 represents that removing the variable chosen in Part (a) is a good or bad idea.

b.

Expert Solution

Answer to Problem 58E

The coefficient of determination R2 is 15.0%.

Explanation of Solution

The larger value of R2 indicates that the model is better. From the multiple regression output, it is clear that the coefficient of determination R2 is 15.0%.

Generally, even eliminating an insignificant variable tends to decrease the value of R2. However, if R2 is not decreased by any substantial amount, it indicates that removing X2 is a good idea. If there is a substantial decrease in R2, it is an indication that removing X2 is a bad idea.

c.

To determine

Obtain the p-value of ANOVA for the original 3-predictor model.

Explain whether the type of change in the p-value for ANOVA represents that removing the variable chosen in Part (a) is a good or bad idea.

c.

Expert Solution

Answer to Problem 58E

The p-value of ANOVA for the original 3-predictor model is 0.322.

Explanation of Solution

From the multiple regression output, it is clear that the p-value of ANOVA for the original 3-predictor model is 0.322.

In common, removing an insignificant variable tends to improve the model. Thus, it causes the p-value of ANOVA to decrease.

Thus, if the p-value decreases after removing X2, it is an indication that removing X2 is a good idea. If the p-value increases after removing X2, it is an indication that removing X2 is a bad idea.

d.

To determine

Obtain the F-statistic from ANOVA for the given model.

Explain whether there is a change in F-statistic for ANOVA when removing an insignificant variable.

d.

Expert Solution

Answer to Problem 58E

The F-statistic of ANOVA for the given model is 1.23.

Explanation of Solution

From the multiple regression output, it is clear that the F-statistic of ANOVA for the given model is 1.23.

In the F-statistic, the numerator is divided by fewer degrees of freedom and the denominator is divided by more degrees of freedom.

The variable that explains little variation than other variables is dropped out as it is an insignificant variable. Hence, if an insignificant variable is dropped out, it causes the F-statistic to increase.

If the F-statistics is increased after removing the insignificant variable, then removing that variable is good idea. Otherwise, it is a bad idea.

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Answer 2

Question

Chapter 10.3, Problem 58E

a.

To determine

Identify the variable that can be eliminated first to possibly improve the given model.

a.

Expert Solution

Answer to Problem 58E

The variable that can be eliminated first to possibly improve the given model is X2.

Explanation of Solution

In order to improve a regression model, the most insignificant independent variable in the model should be eliminated first. The high p-value indicates that the variable is insignificant.

From the multiple regression model, it is clear that the variable X2 has the highest p-value. Hence, one should try to eliminate the variable X2 to possibly improve the given model.

b.

To determine

Describe about the R2 of the model.

Explain whether the change in R2 represents that removing the variable chosen in Part (a) is a good or bad idea.

b.

Expert Solution

Answer to Problem 58E

The coefficient of determination R2 is 15.0%.

Explanation of Solution

The larger value of R2 indicates that the model is better. From the multiple regression output, it is clear that the coefficient of determination R2 is 15.0%.

Generally, even eliminating an insignificant variable tends to decrease the value of R2. However, if R2 is not decreased by any substantial amount, it indicates that removing X2 is a good idea. If there is a substantial decrease in R2, it is an indication that removing X2 is a bad idea.

c.

To determine

Obtain the p-value of ANOVA for the original 3-predictor model.

Explain whether the type of change in the p-value for ANOVA represents that removing the variable chosen in Part (a) is a good or bad idea.

c.

Expert Solution

Answer to Problem 58E

The p-value of ANOVA for the original 3-predictor model is 0.322.

Explanation of Solution

From the multiple regression output, it is clear that the p-value of ANOVA for the original 3-predictor model is 0.322.

In common, removing an insignificant variable tends to improve the model. Thus, it causes the p-value of ANOVA to decrease.

Thus, if the p-value decreases after removing X2, it is an indication that removing X2 is a good idea. If the p-value increases after removing X2, it is an indication that removing X2 is a bad idea.

d.

To determine

Obtain the F-statistic from ANOVA for the given model.

Explain whether there is a change in F-statistic for ANOVA when removing an insignificant variable.

d.

Expert Solution

Answer to Problem 58E

The F-statistic of ANOVA for the given model is 1.23.

Explanation of Solution

From the multiple regression output, it is clear that the F-statistic of ANOVA for the given model is 1.23.

In the F-statistic, the numerator is divided by fewer degrees of freedom and the denominator is divided by more degrees of freedom.

The variable that explains little variation than other variables is dropped out as it is an insignificant variable. Hence, if an insignificant variable is dropped out, it causes the F-statistic to increase.

If the F-statistics is increased after removing the insignificant variable, then removing that variable is good idea. Otherwise, it is a bad idea.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 3

Question

Chapter 10.3, Problem 58E

a.

To determine

Identify the variable that can be eliminated first to possibly improve the given model.

a.

Expert Solution

Answer to Problem 58E

The variable that can be eliminated first to possibly improve the given model is X2.

Explanation of Solution

In order to improve a regression model, the most insignificant independent variable in the model should be eliminated first. The high p-value indicates that the variable is insignificant.

From the multiple regression model, it is clear that the variable X2 has the highest p-value. Hence, one should try to eliminate the variable X2 to possibly improve the given model.

b.

To determine

Describe about the R2 of the model.

Explain whether the change in R2 represents that removing the variable chosen in Part (a) is a good or bad idea.

b.

Expert Solution

Answer to Problem 58E

The coefficient of determination R2 is 15.0%.

Explanation of Solution

The larger value of R2 indicates that the model is better. From the multiple regression output, it is clear that the coefficient of determination R2 is 15.0%.

Generally, even eliminating an insignificant variable tends to decrease the value of R2. However, if R2 is not decreased by any substantial amount, it indicates that removing X2 is a good idea. If there is a substantial decrease in R2, it is an indication that removing X2 is a bad idea.

c.

To determine

Obtain the p-value of ANOVA for the original 3-predictor model.

Explain whether the type of change in the p-value for ANOVA represents that removing the variable chosen in Part (a) is a good or bad idea.

c.

Expert Solution

Answer to Problem 58E

The p-value of ANOVA for the original 3-predictor model is 0.322.

Explanation of Solution

From the multiple regression output, it is clear that the p-value of ANOVA for the original 3-predictor model is 0.322.

In common, removing an insignificant variable tends to improve the model. Thus, it causes the p-value of ANOVA to decrease.

Thus, if the p-value decreases after removing X2, it is an indication that removing X2 is a good idea. If the p-value increases after removing X2, it is an indication that removing X2 is a bad idea.

d.

To determine

Obtain the F-statistic from ANOVA for the given model.

Explain whether there is a change in F-statistic for ANOVA when removing an insignificant variable.

d.

Expert Solution

Answer to Problem 58E

The F-statistic of ANOVA for the given model is 1.23.

Explanation of Solution

From the multiple regression output, it is clear that the F-statistic of ANOVA for the given model is 1.23.

In the F-statistic, the numerator is divided by fewer degrees of freedom and the denominator is divided by more degrees of freedom.

The variable that explains little variation than other variables is dropped out as it is an insignificant variable. Hence, if an insignificant variable is dropped out, it causes the F-statistic to increase.

If the F-statistics is increased after removing the insignificant variable, then removing that variable is good idea. Otherwise, it is a bad idea.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 4

Question

Chapter 10.3, Problem 58E

a.

To determine

Identify the variable that can be eliminated first to possibly improve the given model.

a.

Expert Solution

Answer to Problem 58E

The variable that can be eliminated first to possibly improve the given model is X2.

Explanation of Solution

In order to improve a regression model, the most insignificant independent variable in the model should be eliminated first. The high p-value indicates that the variable is insignificant.

From the multiple regression model, it is clear that the variable X2 has the highest p-value. Hence, one should try to eliminate the variable X2 to possibly improve the given model.

b.

To determine

Describe about the R2 of the model.

Explain whether the change in R2 represents that removing the variable chosen in Part (a) is a good or bad idea.

b.

Expert Solution

Answer to Problem 58E

The coefficient of determination R2 is 15.0%.

Explanation of Solution

The larger value of R2 indicates that the model is better. From the multiple regression output, it is clear that the coefficient of determination R2 is 15.0%.

Generally, even eliminating an insignificant variable tends to decrease the value of R2. However, if R2 is not decreased by any substantial amount, it indicates that removing X2 is a good idea. If there is a substantial decrease in R2, it is an indication that removing X2 is a bad idea.

c.

To determine

Obtain the p-value of ANOVA for the original 3-predictor model.

Explain whether the type of change in the p-value for ANOVA represents that removing the variable chosen in Part (a) is a good or bad idea.

c.

Expert Solution

Answer to Problem 58E

The p-value of ANOVA for the original 3-predictor model is 0.322.

Explanation of Solution

From the multiple regression output, it is clear that the p-value of ANOVA for the original 3-predictor model is 0.322.

In common, removing an insignificant variable tends to improve the model. Thus, it causes the p-value of ANOVA to decrease.

Thus, if the p-value decreases after removing X2, it is an indication that removing X2 is a good idea. If the p-value increases after removing X2, it is an indication that removing X2 is a bad idea.

d.

To determine

Obtain the F-statistic from ANOVA for the given model.

Explain whether there is a change in F-statistic for ANOVA when removing an insignificant variable.

d.

Expert Solution

Answer to Problem 58E

The F-statistic of ANOVA for the given model is 1.23.

Explanation of Solution

From the multiple regression output, it is clear that the F-statistic of ANOVA for the given model is 1.23.

In the F-statistic, the numerator is divided by fewer degrees of freedom and the denominator is divided by more degrees of freedom.

The variable that explains little variation than other variables is dropped out as it is an insignificant variable. Hence, if an insignificant variable is dropped out, it causes the F-statistic to increase.

If the F-statistics is increased after removing the insignificant variable, then removing that variable is good idea. Otherwise, it is a bad idea.

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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Answer 5

Chapter 10.3, Problem 58E

a.

To determine

Identify the variable that can be eliminated first to possibly improve the given model.

a.

Expert Solution

Answer to Problem 58E

The variable that can be eliminated first to possibly improve the given model is X2.

Explanation of Solution

In order to improve a regression model, the most insignificant independent variable in the model should be eliminated first. The high p-value indicates that the variable is insignificant.

From the multiple regression model, it is clear that the variable X2 has the highest p-value. Hence, one should try to eliminate the variable X2 to possibly improve the given model.

b.

To determine

Describe about the R2 of the model.

Explain whether the change in R2 represents that removing the variable chosen in Part (a) is a good or bad idea.

b.

Expert Solution

Answer to Problem 58E

The coefficient of determination R2 is 15.0%.

Explanation of Solution

The larger value of R2 indicates that the model is better. From the multiple regression output, it is clear that the coefficient of determination R2 is 15.0%.

Generally, even eliminating an insignificant variable tends to decrease the value of R2. However, if R2 is not decreased by any substantial amount, it indicates that removing X2 is a good idea. If there is a substantial decrease in R2, it is an indication that removing X2 is a bad idea.

c.

To determine

Obtain the p-value of ANOVA for the original 3-predictor model.

Explain whether the type of change in the p-value for ANOVA represents that removing the variable chosen in Part (a) is a good or bad idea.

c.

Expert Solution

Answer to Problem 58E

The p-value of ANOVA for the original 3-predictor model is 0.322.

Explanation of Solution

From the multiple regression output, it is clear that the p-value of ANOVA for the original 3-predictor model is 0.322.

In common, removing an insignificant variable tends to improve the model. Thus, it causes the p-value of ANOVA to decrease.

Thus, if the p-value decreases after removing X2, it is an indication that removing X2 is a good idea. If the p-value increases after removing X2, it is an indication that removing X2 is a bad idea.

d.

To determine

Obtain the F-statistic from ANOVA for the given model.

Explain whether there is a change in F-statistic for ANOVA when removing an insignificant variable.

d.

Expert Solution

Answer to Problem 58E

The F-statistic of ANOVA for the given model is 1.23.

Explanation of Solution

From the multiple regression output, it is clear that the F-statistic of ANOVA for the given model is 1.23.

In the F-statistic, the numerator is divided by fewer degrees of freedom and the denominator is divided by more degrees of freedom.

The variable that explains little variation than other variables is dropped out as it is an insignificant variable. Hence, if an insignificant variable is dropped out, it causes the F-statistic to increase.

If the F-statistics is increased after removing the insignificant variable, then removing that variable is good idea. Otherwise, it is a bad idea.

Answer 6

Chapter 10.3, Problem 58E

a.

To determine

Identify the variable that can be eliminated first to possibly improve the given model.

a.

Expert Solution

Answer to Problem 58E

The variable that can be eliminated first to possibly improve the given model is X2.

Explanation of Solution

In order to improve a regression model, the most insignificant independent variable in the model should be eliminated first. The high p-value indicates that the variable is insignificant.

From the multiple regression model, it is clear that the variable X2 has the highest p-value. Hence, one should try to eliminate the variable X2 to possibly improve the given model.

Answer 7

Chapter 10.3, Problem 58E

a.

To determine

Identify the variable that can be eliminated first to possibly improve the given model.

Answer 8

a.

Expert Solution

Answer to Problem 58E

The variable that can be eliminated first to possibly improve the given model is X2.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

In order to improve a regression model, the most insignificant independent variable in the model should be eliminated first. The high p-value indicates that the variable is insignificant.

From the multiple regression model, it is clear that the variable X2 has the highest p-value. Hence, one should try to eliminate the variable X2 to possibly improve the given model.

Answer 13

b.

To determine

Describe about the R2 of the model.

Explain whether the change in R2 represents that removing the variable chosen in Part (a) is a good or bad idea.

b.

Expert Solution

Answer to Problem 58E

The coefficient of determination R2 is 15.0%.

Explanation of Solution

The larger value of R2 indicates that the model is better. From the multiple regression output, it is clear that the coefficient of determination R2 is 15.0%.

Generally, even eliminating an insignificant variable tends to decrease the value of R2. However, if R2 is not decreased by any substantial amount, it indicates that removing X2 is a good idea. If there is a substantial decrease in R2, it is an indication that removing X2 is a bad idea.

Answer 14

b.

To determine

Describe about the R2 of the model.

Explain whether the change in R2 represents that removing the variable chosen in Part (a) is a good or bad idea.

Answer 15

b.

Expert Solution

Answer to Problem 58E

The coefficient of determination R2 is 15.0%.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

The larger value of R2 indicates that the model is better. From the multiple regression output, it is clear that the coefficient of determination R2 is 15.0%.

Generally, even eliminating an insignificant variable tends to decrease the value of R2. However, if R2 is not decreased by any substantial amount, it indicates that removing X2 is a good idea. If there is a substantial decrease in R2, it is an indication that removing X2 is a bad idea.

Answer 20

c.

To determine

Obtain the p-value of ANOVA for the original 3-predictor model.

Explain whether the type of change in the p-value for ANOVA represents that removing the variable chosen in Part (a) is a good or bad idea.

c.

Expert Solution

Answer to Problem 58E

The p-value of ANOVA for the original 3-predictor model is 0.322.

Explanation of Solution

From the multiple regression output, it is clear that the p-value of ANOVA for the original 3-predictor model is 0.322.

In common, removing an insignificant variable tends to improve the model. Thus, it causes the p-value of ANOVA to decrease.

Thus, if the p-value decreases after removing X2, it is an indication that removing X2 is a good idea. If the p-value increases after removing X2, it is an indication that removing X2 is a bad idea.

Answer 21

c.

To determine

Obtain the p-value of ANOVA for the original 3-predictor model.

Explain whether the type of change in the p-value for ANOVA represents that removing the variable chosen in Part (a) is a good or bad idea.

Answer 22

c.

Expert Solution

Answer to Problem 58E

The p-value of ANOVA for the original 3-predictor model is 0.322.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

From the multiple regression output, it is clear that the p-value of ANOVA for the original 3-predictor model is 0.322.

In common, removing an insignificant variable tends to improve the model. Thus, it causes the p-value of ANOVA to decrease.

Thus, if the p-value decreases after removing X2, it is an indication that removing X2 is a good idea. If the p-value increases after removing X2, it is an indication that removing X2 is a bad idea.

Answer 27

d.

To determine

Obtain the F-statistic from ANOVA for the given model.

Explain whether there is a change in F-statistic for ANOVA when removing an insignificant variable.

d.

Expert Solution

Answer to Problem 58E

The F-statistic of ANOVA for the given model is 1.23.

Explanation of Solution

From the multiple regression output, it is clear that the F-statistic of ANOVA for the given model is 1.23.

In the F-statistic, the numerator is divided by fewer degrees of freedom and the denominator is divided by more degrees of freedom.

The variable that explains little variation than other variables is dropped out as it is an insignificant variable. Hence, if an insignificant variable is dropped out, it causes the F-statistic to increase.

If the F-statistics is increased after removing the insignificant variable, then removing that variable is good idea. Otherwise, it is a bad idea.

Answer 28

d.

To determine

Obtain the F-statistic from ANOVA for the given model.

Explain whether there is a change in F-statistic for ANOVA when removing an insignificant variable.

Answer 29

d.

Expert Solution

Answer to Problem 58E

The F-statistic of ANOVA for the given model is 1.23.

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

Explanation of Solution

From the multiple regression output, it is clear that the F-statistic of ANOVA for the given model is 1.23.

In the F-statistic, the numerator is divided by fewer degrees of freedom and the denominator is divided by more degrees of freedom.

The variable that explains little variation than other variables is dropped out as it is an insignificant variable. Hence, if an insignificant variable is dropped out, it causes the F-statistic to increase.

If the F-statistics is increased after removing the insignificant variable, then removing that variable is good idea. Otherwise, it is a bad idea.

Answer 34

Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - Prob. 7E Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

Identify the variable that can be eliminated first to possibly improve the given model.

Concept explainers

Videos

Identify the variable that can be eliminated first to possibly improve the given model.

Answer to Problem 58E

Explanation of Solution

Describe about the R2 of the model.

Explain whether the change in R2 represents that removing the variable chosen in Part (a) is a good or bad idea.

Answer to Problem 58E

Explanation of Solution

Obtain the p-value of ANOVA for the original 3-predictor model.

Explain whether the type of change in the p-value for ANOVA represents that removing the variable chosen in Part (a) is a good or bad idea.

Answer to Problem 58E

Explanation of Solution

Obtain the F-statistic from ANOVA for the given model.

Explain whether there is a change in F-statistic for ANOVA when removing an insignificant variable.

Answer to Problem 58E

Explanation of Solution

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Chapter 10 Solutions

Identify the variable that can be eliminated first to possibly improve the given model.

Concept explainers

Videos

Identify the variable that can be eliminated first to possibly improve the given model.

Answer to Problem 58E

Explanation of Solution

Describe about the R2 of the model. Explain whether the change in R2 represents that removing the variable chosen in Part (a) is a good or bad idea.

Answer to Problem 58E

Explanation of Solution

Obtain the p-value of ANOVA for the original 3-predictor model. Explain whether the type of change in the p-value for ANOVA represents that removing the variable chosen in Part (a) is a good or bad idea.

Answer to Problem 58E

Explanation of Solution

Obtain the F-statistic from ANOVA for the given model. Explain whether there is a change in F-statistic for ANOVA when removing an insignificant variable.

Answer to Problem 58E

Explanation of Solution

Want to see more full solutions like this?

Chapter 10 Solutions

Describe about the R2 of the model.

Explain whether the change in R2 represents that removing the variable chosen in Part (a) is a good or bad idea.

Obtain the p-value of ANOVA for the original 3-predictor model.

Explain whether the type of change in the p-value for ANOVA represents that removing the variable chosen in Part (a) is a good or bad idea.

Obtain the F-statistic from ANOVA for the given model.

Explain whether there is a change in F-statistic for ANOVA when removing an insignificant variable.