Identify the p -value that indicates predictor significance at α = 0.05 .

Question

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Answer 1

Question

Compare Compare Correlation is the measure of the degree of the relationship between the variables. In regression, the relationship between the variables to predict one by another is assessed. In correlation there is no cause and effect between the variables, whereas in regression there is a cause and effect between the variables. By using correlation, we cannot predict anything, but regression is a predictive tool. Coefficients are symmetrical in correlation but in regression they are asymmetrical. Correlation is independent of change in origin and scale, but regression is not independent of change in scale.

Chapter 13, Problem 32CE

(a)

To determine

Identify the p-value that indicates predictor significance at α=0.05.

(a)

Expert Solution

Answer to Problem 32CE

The p-value for ‘% with Bachelor's Degree’ indicates predictor significance at α=0.05.

Explanation of Solution

Calculation:

The given information is that, the dataset of ‘Noodles & Company Sales, Seating, and Demographic data’ contains n=74 observations. The response variable is ‘annual sales per square foot’, there are k=5 predictor variables ‘Interior Seat Count, Patio Seat Count, Median HH Income, Median Age of Population, % with Bachelor's Degree’.

Software procedure:

Step by step procedure to obtain p-value for predictor using MegaStat software is given as,

• Choose MegaStat >Correlation/Regression>Regression Analysis.
• SelectInput ranges, enter the variable range for ‘Seats-Inside, Seats-Patio, MedIncome, MedAge, BachDeg%’ as the column of X, Independent variable(s)
• Enter the variable range for ‘Sales/SqFt’ as the column of Y, Dependent variable.
• Click OK.

Output using MegaStatsoftware is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 13, Problem 32CE

The p-value for predictor seats-inside is 0.0733.

The p-value for predictor seats-patio is 0.2350.

The p-value for predictor MedIncome is 0.0589.

The p-value for predictor MedAge is 0.9972.

The p-value for predictor BachDeg% is 0.0015.

For seats-inside:

Let β1 is the parameter for the predictor seats-inside.

Null hypothesis:

H0:β1=0.

The predictor variable seats-inside is not related to annual sales.

Alternative hypothesis:

H1:β1≠0.

The predictor variable seats-inside is related to annual sales.

Rejection rules:

• If p-value is less than the level of significance then the null hypothesis is rejected. The predictor is significant.
• If p-value is greater than the level of significance then the null hypothesis is not rejected. The predictor is not significant.

Conclusion:

The p-value for predictor seats-inside is 0.0733.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0733)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-inside is not related to annual sales.

The predictor seats-inside is not significant.

For seats-Patio:

Let β2 is the parameter for the predictor seats-Patio.

Null hypothesis:

H0:β2=0

The predictor variable seats-Patio is not related to annual sales.

Alternative hypothesis:

H1:β2≠0

The predictor variable seats-Patio is related to annual sales.

Conclusion:

The p-value for predictor seats-patio is 0.2350.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.2350)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-patio is not related to annual sales.

The predictor seats-patio is not significant.

For Median Income:

Let β3 is the parameter for the predictor median income.

Null hypothesis:

H0:β3=0

The predictor variable median income is not related to annual sales.

Alternative hypothesis:

H1:β3≠0

The predictor variable median income is related to annual sales.

Conclusion:

The p-value for predictor median income is 0.0589.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0589)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median income is not related to annual sales.

The predictor median income is not significant.

For Median Age of population:

Let β4 is the parameter for the predictor median age of population.

Null hypothesis:

H0:β4=0

The predictor variable median age of population is not related to annual sales.

Alternative hypothesis:

H1:β4≠0

The predictor variable median age of population is related to annual sales.

Conclusion:

The p-value for predictor median age of population is 0.9972.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.9972)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median age of population is not related to annual sales.

The predictor median age of population is not significant.

For % with Bachelor's Degree:

Let β5 is the parameter for the predictor % with Bachelor's Degree.

Null hypothesis:

H0:β5=0

The predictor variable % with Bachelor's Degree is not related to annual sales.

Alternative hypothesis:

H1:β5≠0

The predictor variable % with Bachelor's Degree is related to annual sales.

Conclusion:

The p-value for predictor ‘% with Bachelor's Degree’ is 0.0015.

The level of significance is 0.05.

The p-value is less than the level of significance.

That is, p-value(=0.0015)<α(=0.05).

The null hypothesis is rejected.

The predictor variable ‘% with Bachelor's Degree’ is related to annual sales.

The predictor ‘% with Bachelor's Degree’of population is significant.

(b)

To determine

Explain whether p-values support the conclusions reached from the t tests.

(b)

Expert Solution

Answer to Problem 32CE

Yes, p-values support the conclusions reached from the t tests.

Explanation of Solution

Justification: The conclusion reached from the t test is that the predictor variable ‘% with Bachelor's Degree’ is significant predictor and the predictor variables ‘seats-inside, seats-patio, median income, median age of population, ‘% with Bachelor's Degree’’ are not significant predictors. The conclusions for the predictor variables with the p-values at α=0.05, level of significance are same as the t tests.

Hence, p-values support the conclusions reached from the t tests.

(c)

To determine

Explain whether the t test or the p-value approach is preferred.

(c)

Expert Solution

Answer to Problem 32CE

The p-value approach is preferred because it determines the strength of the significance for the predictor.

Explanation of Solution

Justification: The conclusion using the t test and p-value approach are same, but in most of the tests p-value is preferred because the strength of the significance for the predictor is better determined using the p-value when compared with the t test statistic. Hence, the p-value approach is preferred in tests.

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Answer 2

Question

Compare Compare Correlation is the measure of the degree of the relationship between the variables. In regression, the relationship between the variables to predict one by another is assessed. In correlation there is no cause and effect between the variables, whereas in regression there is a cause and effect between the variables. By using correlation, we cannot predict anything, but regression is a predictive tool. Coefficients are symmetrical in correlation but in regression they are asymmetrical. Correlation is independent of change in origin and scale, but regression is not independent of change in scale.

Chapter 13, Problem 32CE

(a)

To determine

Identify the p-value that indicates predictor significance at α=0.05.

(a)

Expert Solution

Answer to Problem 32CE

The p-value for ‘% with Bachelor's Degree’ indicates predictor significance at α=0.05.

Explanation of Solution

Calculation:

The given information is that, the dataset of ‘Noodles & Company Sales, Seating, and Demographic data’ contains n=74 observations. The response variable is ‘annual sales per square foot’, there are k=5 predictor variables ‘Interior Seat Count, Patio Seat Count, Median HH Income, Median Age of Population, % with Bachelor's Degree’.

Software procedure:

Step by step procedure to obtain p-value for predictor using MegaStat software is given as,

• Choose MegaStat >Correlation/Regression>Regression Analysis.
• SelectInput ranges, enter the variable range for ‘Seats-Inside, Seats-Patio, MedIncome, MedAge, BachDeg%’ as the column of X, Independent variable(s)
• Enter the variable range for ‘Sales/SqFt’ as the column of Y, Dependent variable.
• Click OK.

Output using MegaStatsoftware is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 13, Problem 32CE

The p-value for predictor seats-inside is 0.0733.

The p-value for predictor seats-patio is 0.2350.

The p-value for predictor MedIncome is 0.0589.

The p-value for predictor MedAge is 0.9972.

The p-value for predictor BachDeg% is 0.0015.

For seats-inside:

Let β1 is the parameter for the predictor seats-inside.

Null hypothesis:

H0:β1=0.

The predictor variable seats-inside is not related to annual sales.

Alternative hypothesis:

H1:β1≠0.

The predictor variable seats-inside is related to annual sales.

Rejection rules:

• If p-value is less than the level of significance then the null hypothesis is rejected. The predictor is significant.
• If p-value is greater than the level of significance then the null hypothesis is not rejected. The predictor is not significant.

Conclusion:

The p-value for predictor seats-inside is 0.0733.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0733)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-inside is not related to annual sales.

The predictor seats-inside is not significant.

For seats-Patio:

Let β2 is the parameter for the predictor seats-Patio.

Null hypothesis:

H0:β2=0

The predictor variable seats-Patio is not related to annual sales.

Alternative hypothesis:

H1:β2≠0

The predictor variable seats-Patio is related to annual sales.

Conclusion:

The p-value for predictor seats-patio is 0.2350.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.2350)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-patio is not related to annual sales.

The predictor seats-patio is not significant.

For Median Income:

Let β3 is the parameter for the predictor median income.

Null hypothesis:

H0:β3=0

The predictor variable median income is not related to annual sales.

Alternative hypothesis:

H1:β3≠0

The predictor variable median income is related to annual sales.

Conclusion:

The p-value for predictor median income is 0.0589.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0589)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median income is not related to annual sales.

The predictor median income is not significant.

For Median Age of population:

Let β4 is the parameter for the predictor median age of population.

Null hypothesis:

H0:β4=0

The predictor variable median age of population is not related to annual sales.

Alternative hypothesis:

H1:β4≠0

The predictor variable median age of population is related to annual sales.

Conclusion:

The p-value for predictor median age of population is 0.9972.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.9972)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median age of population is not related to annual sales.

The predictor median age of population is not significant.

For % with Bachelor's Degree:

Let β5 is the parameter for the predictor % with Bachelor's Degree.

Null hypothesis:

H0:β5=0

The predictor variable % with Bachelor's Degree is not related to annual sales.

Alternative hypothesis:

H1:β5≠0

The predictor variable % with Bachelor's Degree is related to annual sales.

Conclusion:

The p-value for predictor ‘% with Bachelor's Degree’ is 0.0015.

The level of significance is 0.05.

The p-value is less than the level of significance.

That is, p-value(=0.0015)<α(=0.05).

The null hypothesis is rejected.

The predictor variable ‘% with Bachelor's Degree’ is related to annual sales.

The predictor ‘% with Bachelor's Degree’of population is significant.

(b)

To determine

Explain whether p-values support the conclusions reached from the t tests.

(b)

Expert Solution

Answer to Problem 32CE

Yes, p-values support the conclusions reached from the t tests.

Explanation of Solution

Justification: The conclusion reached from the t test is that the predictor variable ‘% with Bachelor's Degree’ is significant predictor and the predictor variables ‘seats-inside, seats-patio, median income, median age of population, ‘% with Bachelor's Degree’’ are not significant predictors. The conclusions for the predictor variables with the p-values at α=0.05, level of significance are same as the t tests.

Hence, p-values support the conclusions reached from the t tests.

(c)

To determine

Explain whether the t test or the p-value approach is preferred.

(c)

Expert Solution

Answer to Problem 32CE

The p-value approach is preferred because it determines the strength of the significance for the predictor.

Explanation of Solution

Justification: The conclusion using the t test and p-value approach are same, but in most of the tests p-value is preferred because the strength of the significance for the predictor is better determined using the p-value when compared with the t test statistic. Hence, the p-value approach is preferred in tests.

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Answer 3

Question

Compare Compare Correlation is the measure of the degree of the relationship between the variables. In regression, the relationship between the variables to predict one by another is assessed. In correlation there is no cause and effect between the variables, whereas in regression there is a cause and effect between the variables. By using correlation, we cannot predict anything, but regression is a predictive tool. Coefficients are symmetrical in correlation but in regression they are asymmetrical. Correlation is independent of change in origin and scale, but regression is not independent of change in scale.

Chapter 13, Problem 32CE

(a)

To determine

Identify the p-value that indicates predictor significance at α=0.05.

(a)

Expert Solution

Answer to Problem 32CE

The p-value for ‘% with Bachelor's Degree’ indicates predictor significance at α=0.05.

Explanation of Solution

Calculation:

The given information is that, the dataset of ‘Noodles & Company Sales, Seating, and Demographic data’ contains n=74 observations. The response variable is ‘annual sales per square foot’, there are k=5 predictor variables ‘Interior Seat Count, Patio Seat Count, Median HH Income, Median Age of Population, % with Bachelor's Degree’.

Software procedure:

Step by step procedure to obtain p-value for predictor using MegaStat software is given as,

• Choose MegaStat >Correlation/Regression>Regression Analysis.
• SelectInput ranges, enter the variable range for ‘Seats-Inside, Seats-Patio, MedIncome, MedAge, BachDeg%’ as the column of X, Independent variable(s)
• Enter the variable range for ‘Sales/SqFt’ as the column of Y, Dependent variable.
• Click OK.

Output using MegaStatsoftware is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 13, Problem 32CE

The p-value for predictor seats-inside is 0.0733.

The p-value for predictor seats-patio is 0.2350.

The p-value for predictor MedIncome is 0.0589.

The p-value for predictor MedAge is 0.9972.

The p-value for predictor BachDeg% is 0.0015.

For seats-inside:

Let β1 is the parameter for the predictor seats-inside.

Null hypothesis:

H0:β1=0.

The predictor variable seats-inside is not related to annual sales.

Alternative hypothesis:

H1:β1≠0.

The predictor variable seats-inside is related to annual sales.

Rejection rules:

• If p-value is less than the level of significance then the null hypothesis is rejected. The predictor is significant.
• If p-value is greater than the level of significance then the null hypothesis is not rejected. The predictor is not significant.

Conclusion:

The p-value for predictor seats-inside is 0.0733.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0733)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-inside is not related to annual sales.

The predictor seats-inside is not significant.

For seats-Patio:

Let β2 is the parameter for the predictor seats-Patio.

Null hypothesis:

H0:β2=0

The predictor variable seats-Patio is not related to annual sales.

Alternative hypothesis:

H1:β2≠0

The predictor variable seats-Patio is related to annual sales.

Conclusion:

The p-value for predictor seats-patio is 0.2350.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.2350)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-patio is not related to annual sales.

The predictor seats-patio is not significant.

For Median Income:

Let β3 is the parameter for the predictor median income.

Null hypothesis:

H0:β3=0

The predictor variable median income is not related to annual sales.

Alternative hypothesis:

H1:β3≠0

The predictor variable median income is related to annual sales.

Conclusion:

The p-value for predictor median income is 0.0589.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0589)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median income is not related to annual sales.

The predictor median income is not significant.

For Median Age of population:

Let β4 is the parameter for the predictor median age of population.

Null hypothesis:

H0:β4=0

The predictor variable median age of population is not related to annual sales.

Alternative hypothesis:

H1:β4≠0

The predictor variable median age of population is related to annual sales.

Conclusion:

The p-value for predictor median age of population is 0.9972.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.9972)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median age of population is not related to annual sales.

The predictor median age of population is not significant.

For % with Bachelor's Degree:

Let β5 is the parameter for the predictor % with Bachelor's Degree.

Null hypothesis:

H0:β5=0

The predictor variable % with Bachelor's Degree is not related to annual sales.

Alternative hypothesis:

H1:β5≠0

The predictor variable % with Bachelor's Degree is related to annual sales.

Conclusion:

The p-value for predictor ‘% with Bachelor's Degree’ is 0.0015.

The level of significance is 0.05.

The p-value is less than the level of significance.

That is, p-value(=0.0015)<α(=0.05).

The null hypothesis is rejected.

The predictor variable ‘% with Bachelor's Degree’ is related to annual sales.

The predictor ‘% with Bachelor's Degree’of population is significant.

(b)

To determine

Explain whether p-values support the conclusions reached from the t tests.

(b)

Expert Solution

Answer to Problem 32CE

Yes, p-values support the conclusions reached from the t tests.

Explanation of Solution

Justification: The conclusion reached from the t test is that the predictor variable ‘% with Bachelor's Degree’ is significant predictor and the predictor variables ‘seats-inside, seats-patio, median income, median age of population, ‘% with Bachelor's Degree’’ are not significant predictors. The conclusions for the predictor variables with the p-values at α=0.05, level of significance are same as the t tests.

Hence, p-values support the conclusions reached from the t tests.

(c)

To determine

Explain whether the t test or the p-value approach is preferred.

(c)

Expert Solution

Answer to Problem 32CE

The p-value approach is preferred because it determines the strength of the significance for the predictor.

Explanation of Solution

Justification: The conclusion using the t test and p-value approach are same, but in most of the tests p-value is preferred because the strength of the significance for the predictor is better determined using the p-value when compared with the t test statistic. Hence, the p-value approach is preferred in tests.

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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

Compare Compare Correlation is the measure of the degree of the relationship between the variables. In regression, the relationship between the variables to predict one by another is assessed. In correlation there is no cause and effect between the variables, whereas in regression there is a cause and effect between the variables. By using correlation, we cannot predict anything, but regression is a predictive tool. Coefficients are symmetrical in correlation but in regression they are asymmetrical. Correlation is independent of change in origin and scale, but regression is not independent of change in scale.

Chapter 13, Problem 32CE

(a)

To determine

Identify the p-value that indicates predictor significance at α=0.05.

(a)

Expert Solution

Answer to Problem 32CE

The p-value for ‘% with Bachelor's Degree’ indicates predictor significance at α=0.05.

Explanation of Solution

Calculation:

The given information is that, the dataset of ‘Noodles & Company Sales, Seating, and Demographic data’ contains n=74 observations. The response variable is ‘annual sales per square foot’, there are k=5 predictor variables ‘Interior Seat Count, Patio Seat Count, Median HH Income, Median Age of Population, % with Bachelor's Degree’.

Software procedure:

Step by step procedure to obtain p-value for predictor using MegaStat software is given as,

• Choose MegaStat >Correlation/Regression>Regression Analysis.
• SelectInput ranges, enter the variable range for ‘Seats-Inside, Seats-Patio, MedIncome, MedAge, BachDeg%’ as the column of X, Independent variable(s)
• Enter the variable range for ‘Sales/SqFt’ as the column of Y, Dependent variable.
• Click OK.

Output using MegaStatsoftware is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 13, Problem 32CE

The p-value for predictor seats-inside is 0.0733.

The p-value for predictor seats-patio is 0.2350.

The p-value for predictor MedIncome is 0.0589.

The p-value for predictor MedAge is 0.9972.

The p-value for predictor BachDeg% is 0.0015.

For seats-inside:

Let β1 is the parameter for the predictor seats-inside.

Null hypothesis:

H0:β1=0.

The predictor variable seats-inside is not related to annual sales.

Alternative hypothesis:

H1:β1≠0.

The predictor variable seats-inside is related to annual sales.

Rejection rules:

• If p-value is less than the level of significance then the null hypothesis is rejected. The predictor is significant.
• If p-value is greater than the level of significance then the null hypothesis is not rejected. The predictor is not significant.

Conclusion:

The p-value for predictor seats-inside is 0.0733.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0733)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-inside is not related to annual sales.

The predictor seats-inside is not significant.

For seats-Patio:

Let β2 is the parameter for the predictor seats-Patio.

Null hypothesis:

H0:β2=0

The predictor variable seats-Patio is not related to annual sales.

Alternative hypothesis:

H1:β2≠0

The predictor variable seats-Patio is related to annual sales.

Conclusion:

The p-value for predictor seats-patio is 0.2350.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.2350)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-patio is not related to annual sales.

The predictor seats-patio is not significant.

For Median Income:

Let β3 is the parameter for the predictor median income.

Null hypothesis:

H0:β3=0

The predictor variable median income is not related to annual sales.

Alternative hypothesis:

H1:β3≠0

The predictor variable median income is related to annual sales.

Conclusion:

The p-value for predictor median income is 0.0589.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0589)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median income is not related to annual sales.

The predictor median income is not significant.

For Median Age of population:

Let β4 is the parameter for the predictor median age of population.

Null hypothesis:

H0:β4=0

The predictor variable median age of population is not related to annual sales.

Alternative hypothesis:

H1:β4≠0

The predictor variable median age of population is related to annual sales.

Conclusion:

The p-value for predictor median age of population is 0.9972.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.9972)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median age of population is not related to annual sales.

The predictor median age of population is not significant.

For % with Bachelor's Degree:

Let β5 is the parameter for the predictor % with Bachelor's Degree.

Null hypothesis:

H0:β5=0

The predictor variable % with Bachelor's Degree is not related to annual sales.

Alternative hypothesis:

H1:β5≠0

The predictor variable % with Bachelor's Degree is related to annual sales.

Conclusion:

The p-value for predictor ‘% with Bachelor's Degree’ is 0.0015.

The level of significance is 0.05.

The p-value is less than the level of significance.

That is, p-value(=0.0015)<α(=0.05).

The null hypothesis is rejected.

The predictor variable ‘% with Bachelor's Degree’ is related to annual sales.

The predictor ‘% with Bachelor's Degree’of population is significant.

(b)

To determine

Explain whether p-values support the conclusions reached from the t tests.

(b)

Expert Solution

Answer to Problem 32CE

Yes, p-values support the conclusions reached from the t tests.

Explanation of Solution

Justification: The conclusion reached from the t test is that the predictor variable ‘% with Bachelor's Degree’ is significant predictor and the predictor variables ‘seats-inside, seats-patio, median income, median age of population, ‘% with Bachelor's Degree’’ are not significant predictors. The conclusions for the predictor variables with the p-values at α=0.05, level of significance are same as the t tests.

Hence, p-values support the conclusions reached from the t tests.

(c)

To determine

Explain whether the t test or the p-value approach is preferred.

(c)

Expert Solution

Answer to Problem 32CE

The p-value approach is preferred because it determines the strength of the significance for the predictor.

Explanation of Solution

Justification: The conclusion using the t test and p-value approach are same, but in most of the tests p-value is preferred because the strength of the significance for the predictor is better determined using the p-value when compared with the t test statistic. Hence, the p-value approach is preferred in tests.

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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 13, Problem 32CE

(a)

To determine

Identify the p-value that indicates predictor significance at α=0.05.

(a)

Expert Solution

Answer to Problem 32CE

The p-value for ‘% with Bachelor's Degree’ indicates predictor significance at α=0.05.

Explanation of Solution

Calculation:

The given information is that, the dataset of ‘Noodles & Company Sales, Seating, and Demographic data’ contains n=74 observations. The response variable is ‘annual sales per square foot’, there are k=5 predictor variables ‘Interior Seat Count, Patio Seat Count, Median HH Income, Median Age of Population, % with Bachelor's Degree’.

Software procedure:

Step by step procedure to obtain p-value for predictor using MegaStat software is given as,

• Choose MegaStat >Correlation/Regression>Regression Analysis.
• SelectInput ranges, enter the variable range for ‘Seats-Inside, Seats-Patio, MedIncome, MedAge, BachDeg%’ as the column of X, Independent variable(s)
• Enter the variable range for ‘Sales/SqFt’ as the column of Y, Dependent variable.
• Click OK.

Output using MegaStatsoftware is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 13, Problem 32CE

The p-value for predictor seats-inside is 0.0733.

The p-value for predictor seats-patio is 0.2350.

The p-value for predictor MedIncome is 0.0589.

The p-value for predictor MedAge is 0.9972.

The p-value for predictor BachDeg% is 0.0015.

For seats-inside:

Let β1 is the parameter for the predictor seats-inside.

Null hypothesis:

H0:β1=0.

The predictor variable seats-inside is not related to annual sales.

Alternative hypothesis:

H1:β1≠0.

The predictor variable seats-inside is related to annual sales.

Rejection rules:

• If p-value is less than the level of significance then the null hypothesis is rejected. The predictor is significant.
• If p-value is greater than the level of significance then the null hypothesis is not rejected. The predictor is not significant.

Conclusion:

The p-value for predictor seats-inside is 0.0733.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0733)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-inside is not related to annual sales.

The predictor seats-inside is not significant.

For seats-Patio:

Let β2 is the parameter for the predictor seats-Patio.

Null hypothesis:

H0:β2=0

The predictor variable seats-Patio is not related to annual sales.

Alternative hypothesis:

H1:β2≠0

The predictor variable seats-Patio is related to annual sales.

Conclusion:

The p-value for predictor seats-patio is 0.2350.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.2350)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-patio is not related to annual sales.

The predictor seats-patio is not significant.

For Median Income:

Let β3 is the parameter for the predictor median income.

Null hypothesis:

H0:β3=0

The predictor variable median income is not related to annual sales.

Alternative hypothesis:

H1:β3≠0

The predictor variable median income is related to annual sales.

Conclusion:

The p-value for predictor median income is 0.0589.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0589)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median income is not related to annual sales.

The predictor median income is not significant.

For Median Age of population:

Let β4 is the parameter for the predictor median age of population.

Null hypothesis:

H0:β4=0

The predictor variable median age of population is not related to annual sales.

Alternative hypothesis:

H1:β4≠0

The predictor variable median age of population is related to annual sales.

Conclusion:

The p-value for predictor median age of population is 0.9972.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.9972)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median age of population is not related to annual sales.

The predictor median age of population is not significant.

For % with Bachelor's Degree:

Let β5 is the parameter for the predictor % with Bachelor's Degree.

Null hypothesis:

H0:β5=0

The predictor variable % with Bachelor's Degree is not related to annual sales.

Alternative hypothesis:

H1:β5≠0

The predictor variable % with Bachelor's Degree is related to annual sales.

Conclusion:

The p-value for predictor ‘% with Bachelor's Degree’ is 0.0015.

The level of significance is 0.05.

The p-value is less than the level of significance.

That is, p-value(=0.0015)<α(=0.05).

The null hypothesis is rejected.

The predictor variable ‘% with Bachelor's Degree’ is related to annual sales.

The predictor ‘% with Bachelor's Degree’of population is significant.

(b)

To determine

Explain whether p-values support the conclusions reached from the t tests.

(b)

Expert Solution

Answer to Problem 32CE

Yes, p-values support the conclusions reached from the t tests.

Explanation of Solution

Justification: The conclusion reached from the t test is that the predictor variable ‘% with Bachelor's Degree’ is significant predictor and the predictor variables ‘seats-inside, seats-patio, median income, median age of population, ‘% with Bachelor's Degree’’ are not significant predictors. The conclusions for the predictor variables with the p-values at α=0.05, level of significance are same as the t tests.

Hence, p-values support the conclusions reached from the t tests.

(c)

To determine

Explain whether the t test or the p-value approach is preferred.

(c)

Expert Solution

Answer to Problem 32CE

The p-value approach is preferred because it determines the strength of the significance for the predictor.

Explanation of Solution

Justification: The conclusion using the t test and p-value approach are same, but in most of the tests p-value is preferred because the strength of the significance for the predictor is better determined using the p-value when compared with the t test statistic. Hence, the p-value approach is preferred in tests.

Answer 6

Chapter 13, Problem 32CE

(a)

To determine

Identify the p-value that indicates predictor significance at α=0.05.

(a)

Expert Solution

Answer to Problem 32CE

The p-value for ‘% with Bachelor's Degree’ indicates predictor significance at α=0.05.

Explanation of Solution

Calculation:

The given information is that, the dataset of ‘Noodles & Company Sales, Seating, and Demographic data’ contains n=74 observations. The response variable is ‘annual sales per square foot’, there are k=5 predictor variables ‘Interior Seat Count, Patio Seat Count, Median HH Income, Median Age of Population, % with Bachelor's Degree’.

Software procedure:

Step by step procedure to obtain p-value for predictor using MegaStat software is given as,

• Choose MegaStat >Correlation/Regression>Regression Analysis.
• SelectInput ranges, enter the variable range for ‘Seats-Inside, Seats-Patio, MedIncome, MedAge, BachDeg%’ as the column of X, Independent variable(s)
• Enter the variable range for ‘Sales/SqFt’ as the column of Y, Dependent variable.
• Click OK.

Output using MegaStatsoftware is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 13, Problem 32CE

The p-value for predictor seats-inside is 0.0733.

The p-value for predictor seats-patio is 0.2350.

The p-value for predictor MedIncome is 0.0589.

The p-value for predictor MedAge is 0.9972.

The p-value for predictor BachDeg% is 0.0015.

For seats-inside:

Let β1 is the parameter for the predictor seats-inside.

Null hypothesis:

H0:β1=0.

The predictor variable seats-inside is not related to annual sales.

Alternative hypothesis:

H1:β1≠0.

The predictor variable seats-inside is related to annual sales.

Rejection rules:

• If p-value is less than the level of significance then the null hypothesis is rejected. The predictor is significant.
• If p-value is greater than the level of significance then the null hypothesis is not rejected. The predictor is not significant.

Conclusion:

The p-value for predictor seats-inside is 0.0733.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0733)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-inside is not related to annual sales.

The predictor seats-inside is not significant.

For seats-Patio:

Let β2 is the parameter for the predictor seats-Patio.

Null hypothesis:

H0:β2=0

The predictor variable seats-Patio is not related to annual sales.

Alternative hypothesis:

H1:β2≠0

The predictor variable seats-Patio is related to annual sales.

Conclusion:

The p-value for predictor seats-patio is 0.2350.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.2350)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-patio is not related to annual sales.

The predictor seats-patio is not significant.

For Median Income:

Let β3 is the parameter for the predictor median income.

Null hypothesis:

H0:β3=0

The predictor variable median income is not related to annual sales.

Alternative hypothesis:

H1:β3≠0

The predictor variable median income is related to annual sales.

Conclusion:

The p-value for predictor median income is 0.0589.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0589)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median income is not related to annual sales.

The predictor median income is not significant.

For Median Age of population:

Let β4 is the parameter for the predictor median age of population.

Null hypothesis:

H0:β4=0

The predictor variable median age of population is not related to annual sales.

Alternative hypothesis:

H1:β4≠0

The predictor variable median age of population is related to annual sales.

Conclusion:

The p-value for predictor median age of population is 0.9972.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.9972)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median age of population is not related to annual sales.

The predictor median age of population is not significant.

For % with Bachelor's Degree:

Let β5 is the parameter for the predictor % with Bachelor's Degree.

Null hypothesis:

H0:β5=0

The predictor variable % with Bachelor's Degree is not related to annual sales.

Alternative hypothesis:

H1:β5≠0

The predictor variable % with Bachelor's Degree is related to annual sales.

Conclusion:

The p-value for predictor ‘% with Bachelor's Degree’ is 0.0015.

The level of significance is 0.05.

The p-value is less than the level of significance.

That is, p-value(=0.0015)<α(=0.05).

The null hypothesis is rejected.

The predictor variable ‘% with Bachelor's Degree’ is related to annual sales.

The predictor ‘% with Bachelor's Degree’of population is significant.

Answer 7

Chapter 13, Problem 32CE

(a)

To determine

Identify the p-value that indicates predictor significance at α=0.05.

Answer 8

(a)

Expert Solution

Answer to Problem 32CE

The p-value for ‘% with Bachelor's Degree’ indicates predictor significance at α=0.05.

Answer 9

(a)

Expert Solution

Answer 10

(a)

Expert Solution

Answer 11

Expert Solution

Answer 12

Explanation of Solution

Calculation:

The given information is that, the dataset of ‘Noodles & Company Sales, Seating, and Demographic data’ contains n=74 observations. The response variable is ‘annual sales per square foot’, there are k=5 predictor variables ‘Interior Seat Count, Patio Seat Count, Median HH Income, Median Age of Population, % with Bachelor's Degree’.

Software procedure:

Step by step procedure to obtain p-value for predictor using MegaStat software is given as,

• Choose MegaStat >Correlation/Regression>Regression Analysis.
• SelectInput ranges, enter the variable range for ‘Seats-Inside, Seats-Patio, MedIncome, MedAge, BachDeg%’ as the column of X, Independent variable(s)
• Enter the variable range for ‘Sales/SqFt’ as the column of Y, Dependent variable.
• Click OK.

Output using MegaStatsoftware is given below:

Loose-leaf For Applied Statistics In Business And Economics, Chapter 13, Problem 32CE

The p-value for predictor seats-inside is 0.0733.

The p-value for predictor seats-patio is 0.2350.

The p-value for predictor MedIncome is 0.0589.

The p-value for predictor MedAge is 0.9972.

The p-value for predictor BachDeg% is 0.0015.

For seats-inside:

Let β1 is the parameter for the predictor seats-inside.

Null hypothesis:

H0:β1=0.

The predictor variable seats-inside is not related to annual sales.

Alternative hypothesis:

H1:β1≠0.

The predictor variable seats-inside is related to annual sales.

Rejection rules:

• If p-value is less than the level of significance then the null hypothesis is rejected. The predictor is significant.
• If p-value is greater than the level of significance then the null hypothesis is not rejected. The predictor is not significant.

Conclusion:

The p-value for predictor seats-inside is 0.0733.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0733)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-inside is not related to annual sales.

The predictor seats-inside is not significant.

For seats-Patio:

Let β2 is the parameter for the predictor seats-Patio.

Null hypothesis:

H0:β2=0

The predictor variable seats-Patio is not related to annual sales.

Alternative hypothesis:

H1:β2≠0

The predictor variable seats-Patio is related to annual sales.

Conclusion:

The p-value for predictor seats-patio is 0.2350.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.2350)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable seats-patio is not related to annual sales.

The predictor seats-patio is not significant.

For Median Income:

Let β3 is the parameter for the predictor median income.

Null hypothesis:

H0:β3=0

The predictor variable median income is not related to annual sales.

Alternative hypothesis:

H1:β3≠0

The predictor variable median income is related to annual sales.

Conclusion:

The p-value for predictor median income is 0.0589.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.0589)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median income is not related to annual sales.

The predictor median income is not significant.

For Median Age of population:

Let β4 is the parameter for the predictor median age of population.

Null hypothesis:

H0:β4=0

The predictor variable median age of population is not related to annual sales.

Alternative hypothesis:

H1:β4≠0

The predictor variable median age of population is related to annual sales.

Conclusion:

The p-value for predictor median age of population is 0.9972.

The level of significance is 0.05.

The p-value is greater than the level of significance.

That is, p-value(=0.9972)>α(=0.05).

The null hypothesis is not rejected.

The predictor variable median age of population is not related to annual sales.

The predictor median age of population is not significant.

For % with Bachelor's Degree:

Let β5 is the parameter for the predictor % with Bachelor's Degree.

Null hypothesis:

H0:β5=0

The predictor variable % with Bachelor's Degree is not related to annual sales.

Alternative hypothesis:

H1:β5≠0

The predictor variable % with Bachelor's Degree is related to annual sales.

Conclusion:

The p-value for predictor ‘% with Bachelor's Degree’ is 0.0015.

The level of significance is 0.05.

The p-value is less than the level of significance.

That is, p-value(=0.0015)<α(=0.05).

The null hypothesis is rejected.

The predictor variable ‘% with Bachelor's Degree’ is related to annual sales.

The predictor ‘% with Bachelor's Degree’of population is significant.

Answer 13

(b)

To determine

Explain whether p-values support the conclusions reached from the t tests.

(b)

Expert Solution

Answer to Problem 32CE

Yes, p-values support the conclusions reached from the t tests.

Explanation of Solution

Justification: The conclusion reached from the t test is that the predictor variable ‘% with Bachelor's Degree’ is significant predictor and the predictor variables ‘seats-inside, seats-patio, median income, median age of population, ‘% with Bachelor's Degree’’ are not significant predictors. The conclusions for the predictor variables with the p-values at α=0.05, level of significance are same as the t tests.

Hence, p-values support the conclusions reached from the t tests.

Answer 14

(b)

To determine

Explain whether p-values support the conclusions reached from the t tests.

Answer 15

(b)

Expert Solution

Answer to Problem 32CE

Yes, p-values support the conclusions reached from the t tests.

Answer 16

(b)

Expert Solution

Answer 17

(b)

Expert Solution

Answer 18

Expert Solution

Answer 19

Explanation of Solution

Justification: The conclusion reached from the t test is that the predictor variable ‘% with Bachelor's Degree’ is significant predictor and the predictor variables ‘seats-inside, seats-patio, median income, median age of population, ‘% with Bachelor's Degree’’ are not significant predictors. The conclusions for the predictor variables with the p-values at α=0.05, level of significance are same as the t tests.

Hence, p-values support the conclusions reached from the t tests.

Answer 20

(c)

To determine

Explain whether the t test or the p-value approach is preferred.

(c)

Expert Solution

Answer to Problem 32CE

The p-value approach is preferred because it determines the strength of the significance for the predictor.

Explanation of Solution

Justification: The conclusion using the t test and p-value approach are same, but in most of the tests p-value is preferred because the strength of the significance for the predictor is better determined using the p-value when compared with the t test statistic. Hence, the p-value approach is preferred in tests.

Answer 21

(c)

To determine

Explain whether the t test or the p-value approach is preferred.

Answer 22

(c)

Expert Solution

Answer to Problem 32CE

The p-value approach is preferred because it determines the strength of the significance for the predictor.

Answer 23

(c)

Expert Solution

Answer 24

(c)

Expert Solution

Answer 25

Expert Solution

Answer 26

Explanation of Solution

Justification: The conclusion using the t test and p-value approach are same, but in most of the tests p-value is preferred because the strength of the significance for the predictor is better determined using the p-value when compared with the t test statistic. Hence, the p-value approach is preferred in tests.