Question 1

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, there is not enough evidence to conclude that LawnSize makes a significant contribution to the model in the presence of Income at a 0.05 level of significance.

Accepted Answer

The p-value for LawnSize is 0.748, which is greater than the level of significance of 0.05. Therefore, we fail to reject the null hypothesis and conclude that there is not enough evidence to suggest that LawnSize makes a significant contribution to the model in the presence of Income.

Question 2

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, what is the p-value of the test statistic when testing whether the model is a good-fitting model?

Accepted Answer

The answer of SCENARIO 14-19 The marketing manager for a...

Question 3

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, what is the p-value of the test statistic when testing whether LawnSize makes a significant contribution to the model in the presence of Income?

Accepted Answer

The answer of SCENARIO 14-19 The marketing manager for a...

Question 4

The following two statements are equivalent in meaning: A.The test of significance for a specific regression coefficient in a multiple regression model is a test of significance for adding that variable into the model given the other variable is included. B.The t test for a regression coefficient is actually a test for the contribution of that independent variable.

Accepted Answer

Both statements essentially mean that the significance test for a regression coefficient is testing the importance or contribution of a specific independent variable in the model while controlling for the other variables already included. Therefore, the two statements are equivalent in meaning. The two statements are equivalent and both refer to the test of significance for a specific regression coefficient in a multiple regression model, which assesses whether adding that variable into the model provides a significant contribution to the prediction of the dependent variable, given that the other variables are already included. The t test for the coefficient is used to determine whether the estimated coefficient is significantly different from zero, indicating that the corresponding independent variable has a significant effect on the dependent variable. Therefore, statement A and B convey the same meaning.

Question 5

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, what is the estimated probability that a home owner with a family income of $100,000 and a lawn size of 2,000 square feet will purchase a lawn service?

Accepted Answer

The answer of SCENARIO 14-19 The marketing manager for a...

Question 6

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, there is not enough evidence to conclude that Income makes a significant contribution to the model in the presence of LawnSize at a 0.05 level of significance.

Accepted Answer

The answer of SCENARIO 14-19 The marketing manager for a...

Question 7

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, which of the following is the correct interpretation for the Lawn Size slope coefficient?
A)Holding constant the effect of income, the estimated number of lawn services purchased increases by 1.2804 for each increase of one thousand square feet in lawn
Size.
B)Holding constant the effect of income, the estimated average number of lawn services purchased increases by 1.2804 for each increase of one thousand square feet in lawn
Size.
C)Holding constant the effect of income, the estimated probability of purchasing a lawn service increases by 1.2804 for each increase of one thousand square feet in lawn
Size.
D)Holding constant the effect of income, the estimated natural logarithm of the odds ratio of purchasing a lawn service increases by 1.2804 for each increase of one
Thousand square feet in lawn size.

Accepted Answer

The answer of SCENARIO 14-19 The marketing manager for a...

Question 8

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, there is not enough evidence to conclude that the model is not a good-fitting model at a 0.05 level of significance.

Accepted Answer

The PHStat output does not show any significant lack of fit, meaning that the model is a good fit for the data. Therefore, there is not enough evidence to conclude that the model is not a good-fitting model at a 0.05 level of significance. The PHStat output given does not provide any information about the goodness of fit of the model. Therefore, the statement in the scenario cannot be evaluated based on the given information.

Question 9

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, which of the following is the correct interpretation for the Income slope coefficient?
A)Holding constant the effect of lawn size, the estimated number of lawn services purchased increases by 0.0304 for each increase of one thousand dollars in family
Income.
B)Holding constant the effect of lawn size, the estimated average number of lawn services purchased increases by 0.0304 for each increase of one thousand dollars in
Family income.
C)Holding constant the effect of lawn size, the estimated probability of purchasing a lawn service increases by 0.0304 for each increase of one thousand dollars in family
Income.
D)Holding constant the effect of lawn size, the estimated natural logarithm of the odds ratio of purchasing a lawn service increases by 0.0304 for each increase of one
Thousand dollars in family income.

Accepted Answer

The answer of SCENARIO 14-19 The marketing manager for a...

Question 10

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, what should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether Income makes a significant contribution to the model in the presence of LawnSize at a 0.05 level of significance?

Accepted Answer

The answer of SCENARIO 14-19 The marketing manager for a...

Question 11

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, what is the estimated odds ratio for a home owner with a family income of $100,000 and a lawn size of 2,000 square feet?

Accepted Answer

The answer of SCENARIO 14-19 The marketing manager for a...

Question 12

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, what should be the decision ('reject' or 'do not reject')on the null hypothesis when testing whether LawnSize makes a significant contribution to the model in the presence of Income at a 0.05 level of significance?

Accepted Answer

The answer of SCENARIO 14-19 The marketing manager for a...

Question 13

To properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term.

Accepted Answer

Interaction terms are used to examine if the effect of one independent variable on the dependent variable changes across the levels of another independent variable. To properly examine the effect of a categorical independent variable in a multiple linear regression model, we typically use dummy coding (or one-hot encoding) to convert the categorical variable into numerical form, not necessarily an interaction term.

Question 14

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, what are the degrees of freedom for the chi-square distribution when testing whether the model is a good-fitting model?

Accepted Answer

The answer of SCENARIO 14-19 The marketing manager for a...

Question 15

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, what is the p-value of the test statistic when testing whether Income makes a significant contribution to the model in the presence of LawnSize?

Accepted Answer

The answer of SCENARIO 14-19 The marketing manager for a...

Question 16

SCENARIO 14-19 The marketing manager for a nationally franchised lawn service company would like to study the characteristics that differentiate home owners who do and do not have a lawn service.A random sample of 30 home owners located in a suburban area near a large city was selected; 11 did not have a lawn service (code 0)and 19 had a lawn service (code 1).Additional information available concerning these 30 home owners includes family income (Income, in thousands of dollars)and lawn size (Lawn Size, in thousands of square feet). The PHStat output is given below: 
-Referring to Scenario 14-19, the null hypothesis that the model is a good- fitting model cannot be rejected when allowing for a 5% probability of making a type I error.

Accepted Answer

This conclusion can be drawn from the "Model Summary" table, where the p-value for the "Adjusted R Square" is greater than 0.05 (0.257). This indicates that the model is not a significant improvement over a simple mean model, and therefore the null hypothesis (that the model is a good-fitting model) cannot be rejected at a significance level of 5%. The PHStat output does not provide a p-value for the goodness-of-fit test, but it does provide the chi-square test statistic and the degrees of freedom. If the chi-square test statistic does not exceed the critical value from the chi-square distribution with the appropriate degrees of freedom at the chosen significance level, then we cannot reject the null hypothesis that the model is a good-fitting model. Therefore, if the marketing manager chose a significance level of 0.05 (which is common), and the chi-square test statistic is less than the critical value from the chi-square distribution with 2 degrees of freedom (which is 5.99 at 0.05), then the null hypothesis cannot be rejected.

Quiz 14: Introduction to Multiple Regression

To properly examine the effect of a categorical independent variable in a multiple linear regression model we use an interaction term.