TravelAir.com samples domestic airline flights to explore the relationship between airfare and distance. The service would like to know if there is a correlation between airfare and flight distance. If there is a correlation, what percentage of the variation in airfare is accounted for by distance? How much does each additional mile add to the fare? The data follow. a. Draw a scatter diagram with Distance as the independent variable and Fare as the dependent variable. Is the relationship direct or indirect? b. Compute the correlation coefficient . At the .05 significance level, is it reasonable to conclude that the correlation coefficient is greater than zero? c. What percentage of the variation in Fare is accounted for by Distance of a flight? d. Determine the regression equation. How much does each additional mile add to the fare? Estimate the fare for a 1,500-mile flight. e. A traveler is planning to fly from Atlanta to London Heathrow. The distance is 4,218 miles. She wants to use the regression equation to estimate the fare. Explain why it would not be a good idea to estimate the fare for this international flight with the regression equation.

Question

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Answer 1

Textbook Question

Chapter 13, Problem 61CE

TravelAir.com samples domestic airline flights to explore the relationship between airfare and distance. The service would like to know if there is a correlation between airfare and flight distance. If there is a correlation, what percentage of the variation in airfare is accounted for by distance? How much does each additional mile add to the fare? The data follow.

Chapter 13, Problem 61CE, TravelAir.com samples domestic airline flights to explore the relationship between airfare and

a. Draw a scatter diagram with Distance as the independent variable and Fare as the dependent variable. Is the relationship direct or indirect?
b. Compute the correlation coefficient. At the .05 significance level, is it reasonable to conclude that the correlation coefficient is greater than zero?
c. What percentage of the variation in Fare is accounted for by Distance of a flight?
d. Determine the regression equation. How much does each additional mile add to the fare? Estimate the fare for a 1,500-mile flight.
e. A traveler is planning to fly from Atlanta to London Heathrow. The distance is 4,218 miles. She wants to use the regression equation to estimate the fare. Explain why it would not be a good idea to estimate the fare for this international flight with the regression equation.

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.

a.

Expert Solution

To determine

Construct a scatter diagram with Distance as the independent variable and Fare as the dependent variable.

Explain the relationship between the variables.

Answer to Problem 61CE

The scatter diagram of the data is as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 1

Explanation of Solution

Step-by-step procedure to obtain the scatterplot using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Scatterplot.
Enter horizontal axis as Sheet6!$X$1:$X$31 and vertical axis as Sheet6!$Y$1:$Y$31.
Click on OK.

From the scatterplot of the data indicates an increasing trend. It shows that as the distance increases, the fare also increases. Therefore, there is a positive association between distance and fare.

Thus, the relationship is direct.

b.

Expert Solution

To determine

Find the correlation coefficient.

Check whether the correlation coefficient is greater than zero.

Answer to Problem 61CE

The correlation coefficient is 0.656.

There is enough evidence to infer that the population correlation is positive.

Explanation of Solution

Step-by-step procedure to obtain the correlation coefficient using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Correlation matrix.
Enter Input Range as Sheet6!$X$1:$Y$31.
Click on OK.

Output obtained using MegaStat is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 2

The correlation coefficient is 0.656.

Denote the population correlation as ρ.

The hypotheses are given below:

Null hypothesis:

H0:ρ≤0

That is, the correlation in the population is less than or equal to zero.

Alternative hypothesis:

H1:ρ>0

That is, the correlation in the population is positive.

Test statistic:

The test statistic is as follows:

t=rn−21−r2

Here, the sample size is 30 and the correlation coefficient is 0.656.

The test statistic is as follows:

t=0.65630−21−0.6562=0.656×280.56964=4.599

Degrees of freedom:

df=n−2=30−2=28

The level of significance is 0.05. Therefore, 1−α=0.95.

Critical value:

Step-by-step software procedure to obtain the critical value using EXCEL software:

Open an EXCEL file.
In cell A1, enter the formula “=T.INV (0.95, 28)”.

Output obtained using the EXCEL is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 3

Decision rule:

Reject the null hypothesis H₀, if t-calculated> t-critical value.

Otherwise, fail to reject H₀.

Conclusion:

The value of test statistic is 4.599 and the critical value is 1.701.

Here, t-calculated(=4.599)> t-critical value(=1.701).

By the rejection rule, reject the null hypothesis.

Thus, there is enough evidence to infer that the population correlation is positive.

c.

Expert Solution

To determine

Explain what percentage of the variation in ‘Fare’ is accounted for by ‘Distance’ of a flight.

Explanation of Solution

The coefficient of determination is the square of correlation coefficient.

From part (b), the correlation coefficient is 0.656.

Thus, the coefficient of determination is 0.43(=0.6562).

Thus, about 43% of the variation in fares is explained by the variation in distance.

d.

Expert Solution

To determine

Find the regression equation.

Explain how much does each additional mile add to the fare.

Find the fare for a 1,500 mile flight.

Answer to Problem 61CE

The regression equation is Fare=147.08+0.0527Distance.

The fare for a 1,500 mile flight is $226.1.

Explanation of Solution

Step-by-step procedure to obtain the ‘Regression equation’ using the MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Regression Analysis.
Select input range as ‘Sheet6!$Y$1:$Y$31’ under Y/Dependent variable.
Select input range ‘Sheet6!$X$1:$X$31’ under X/Independent variables.
Click on OK.

Output using the Mega Stat software is given below:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 4

From the output, the regression equation is, Fare=147.08+0.0527Distance

Thus, for each additional mile $0.0527 is added to the fare.

Substitute the value ‘1,500’ for ‘distance’ in the regression equation.

Fare=147.08+0.0527Distance=147.08+0.0527(1500)=226.1

Thus, fare for a 1,500 mile flight is $226.1.

e.

Expert Solution

To determine

Explain why it is not suitable to estimate the fare for the international flight with the regression equation.

Explanation of Solution

It is given that the distance is 4,218 miles. This flight is far away from the range of the sampled data. Thus, using the regression equation may not be suitable to estimate the fare for the flight.

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Answer 2

Textbook Question

Chapter 13, Problem 61CE

TravelAir.com samples domestic airline flights to explore the relationship between airfare and distance. The service would like to know if there is a correlation between airfare and flight distance. If there is a correlation, what percentage of the variation in airfare is accounted for by distance? How much does each additional mile add to the fare? The data follow.

Chapter 13, Problem 61CE, TravelAir.com samples domestic airline flights to explore the relationship between airfare and

a. Draw a scatter diagram with Distance as the independent variable and Fare as the dependent variable. Is the relationship direct or indirect?
b. Compute the correlation coefficient. At the .05 significance level, is it reasonable to conclude that the correlation coefficient is greater than zero?
c. What percentage of the variation in Fare is accounted for by Distance of a flight?
d. Determine the regression equation. How much does each additional mile add to the fare? Estimate the fare for a 1,500-mile flight.
e. A traveler is planning to fly from Atlanta to London Heathrow. The distance is 4,218 miles. She wants to use the regression equation to estimate the fare. Explain why it would not be a good idea to estimate the fare for this international flight with the regression equation.

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.

a.

Expert Solution

To determine

Construct a scatter diagram with Distance as the independent variable and Fare as the dependent variable.

Explain the relationship between the variables.

Answer to Problem 61CE

The scatter diagram of the data is as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 1

Explanation of Solution

Step-by-step procedure to obtain the scatterplot using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Scatterplot.
Enter horizontal axis as Sheet6!$X$1:$X$31 and vertical axis as Sheet6!$Y$1:$Y$31.
Click on OK.

From the scatterplot of the data indicates an increasing trend. It shows that as the distance increases, the fare also increases. Therefore, there is a positive association between distance and fare.

Thus, the relationship is direct.

b.

Expert Solution

To determine

Find the correlation coefficient.

Check whether the correlation coefficient is greater than zero.

Answer to Problem 61CE

The correlation coefficient is 0.656.

There is enough evidence to infer that the population correlation is positive.

Explanation of Solution

Step-by-step procedure to obtain the correlation coefficient using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Correlation matrix.
Enter Input Range as Sheet6!$X$1:$Y$31.
Click on OK.

Output obtained using MegaStat is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 2

The correlation coefficient is 0.656.

Denote the population correlation as ρ.

The hypotheses are given below:

Null hypothesis:

H0:ρ≤0

That is, the correlation in the population is less than or equal to zero.

Alternative hypothesis:

H1:ρ>0

That is, the correlation in the population is positive.

Test statistic:

The test statistic is as follows:

t=rn−21−r2

Here, the sample size is 30 and the correlation coefficient is 0.656.

The test statistic is as follows:

t=0.65630−21−0.6562=0.656×280.56964=4.599

Degrees of freedom:

df=n−2=30−2=28

The level of significance is 0.05. Therefore, 1−α=0.95.

Critical value:

Step-by-step software procedure to obtain the critical value using EXCEL software:

Open an EXCEL file.
In cell A1, enter the formula “=T.INV (0.95, 28)”.

Output obtained using the EXCEL is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 3

Decision rule:

Reject the null hypothesis H₀, if t-calculated> t-critical value.

Otherwise, fail to reject H₀.

Conclusion:

The value of test statistic is 4.599 and the critical value is 1.701.

Here, t-calculated(=4.599)> t-critical value(=1.701).

By the rejection rule, reject the null hypothesis.

Thus, there is enough evidence to infer that the population correlation is positive.

c.

Expert Solution

To determine

Explain what percentage of the variation in ‘Fare’ is accounted for by ‘Distance’ of a flight.

Explanation of Solution

The coefficient of determination is the square of correlation coefficient.

From part (b), the correlation coefficient is 0.656.

Thus, the coefficient of determination is 0.43(=0.6562).

Thus, about 43% of the variation in fares is explained by the variation in distance.

d.

Expert Solution

To determine

Find the regression equation.

Explain how much does each additional mile add to the fare.

Find the fare for a 1,500 mile flight.

Answer to Problem 61CE

The regression equation is Fare=147.08+0.0527Distance.

The fare for a 1,500 mile flight is $226.1.

Explanation of Solution

Step-by-step procedure to obtain the ‘Regression equation’ using the MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Regression Analysis.
Select input range as ‘Sheet6!$Y$1:$Y$31’ under Y/Dependent variable.
Select input range ‘Sheet6!$X$1:$X$31’ under X/Independent variables.
Click on OK.

Output using the Mega Stat software is given below:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 4

From the output, the regression equation is, Fare=147.08+0.0527Distance

Thus, for each additional mile $0.0527 is added to the fare.

Substitute the value ‘1,500’ for ‘distance’ in the regression equation.

Fare=147.08+0.0527Distance=147.08+0.0527(1500)=226.1

Thus, fare for a 1,500 mile flight is $226.1.

e.

Expert Solution

To determine

Explain why it is not suitable to estimate the fare for the international flight with the regression equation.

Explanation of Solution

It is given that the distance is 4,218 miles. This flight is far away from the range of the sampled data. Thus, using the regression equation may not be suitable to estimate the fare for the flight.

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

Answer 3

Textbook Question

Chapter 13, Problem 61CE

TravelAir.com samples domestic airline flights to explore the relationship between airfare and distance. The service would like to know if there is a correlation between airfare and flight distance. If there is a correlation, what percentage of the variation in airfare is accounted for by distance? How much does each additional mile add to the fare? The data follow.

Chapter 13, Problem 61CE, TravelAir.com samples domestic airline flights to explore the relationship between airfare and

a. Draw a scatter diagram with Distance as the independent variable and Fare as the dependent variable. Is the relationship direct or indirect?
b. Compute the correlation coefficient. At the .05 significance level, is it reasonable to conclude that the correlation coefficient is greater than zero?
c. What percentage of the variation in Fare is accounted for by Distance of a flight?
d. Determine the regression equation. How much does each additional mile add to the fare? Estimate the fare for a 1,500-mile flight.
e. A traveler is planning to fly from Atlanta to London Heathrow. The distance is 4,218 miles. She wants to use the regression equation to estimate the fare. Explain why it would not be a good idea to estimate the fare for this international flight with the regression equation.

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.

a.

Expert Solution

To determine

Construct a scatter diagram with Distance as the independent variable and Fare as the dependent variable.

Explain the relationship between the variables.

Answer to Problem 61CE

The scatter diagram of the data is as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 1

Explanation of Solution

Step-by-step procedure to obtain the scatterplot using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Scatterplot.
Enter horizontal axis as Sheet6!$X$1:$X$31 and vertical axis as Sheet6!$Y$1:$Y$31.
Click on OK.

From the scatterplot of the data indicates an increasing trend. It shows that as the distance increases, the fare also increases. Therefore, there is a positive association between distance and fare.

Thus, the relationship is direct.

b.

Expert Solution

To determine

Find the correlation coefficient.

Check whether the correlation coefficient is greater than zero.

Answer to Problem 61CE

The correlation coefficient is 0.656.

There is enough evidence to infer that the population correlation is positive.

Explanation of Solution

Step-by-step procedure to obtain the correlation coefficient using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Correlation matrix.
Enter Input Range as Sheet6!$X$1:$Y$31.
Click on OK.

Output obtained using MegaStat is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 2

The correlation coefficient is 0.656.

Denote the population correlation as ρ.

The hypotheses are given below:

Null hypothesis:

H0:ρ≤0

That is, the correlation in the population is less than or equal to zero.

Alternative hypothesis:

H1:ρ>0

That is, the correlation in the population is positive.

Test statistic:

The test statistic is as follows:

t=rn−21−r2

Here, the sample size is 30 and the correlation coefficient is 0.656.

The test statistic is as follows:

t=0.65630−21−0.6562=0.656×280.56964=4.599

Degrees of freedom:

df=n−2=30−2=28

The level of significance is 0.05. Therefore, 1−α=0.95.

Critical value:

Step-by-step software procedure to obtain the critical value using EXCEL software:

Open an EXCEL file.
In cell A1, enter the formula “=T.INV (0.95, 28)”.

Output obtained using the EXCEL is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 3

Decision rule:

Reject the null hypothesis H₀, if t-calculated> t-critical value.

Otherwise, fail to reject H₀.

Conclusion:

The value of test statistic is 4.599 and the critical value is 1.701.

Here, t-calculated(=4.599)> t-critical value(=1.701).

By the rejection rule, reject the null hypothesis.

Thus, there is enough evidence to infer that the population correlation is positive.

c.

Expert Solution

To determine

Explain what percentage of the variation in ‘Fare’ is accounted for by ‘Distance’ of a flight.

Explanation of Solution

The coefficient of determination is the square of correlation coefficient.

From part (b), the correlation coefficient is 0.656.

Thus, the coefficient of determination is 0.43(=0.6562).

Thus, about 43% of the variation in fares is explained by the variation in distance.

d.

Expert Solution

To determine

Find the regression equation.

Explain how much does each additional mile add to the fare.

Find the fare for a 1,500 mile flight.

Answer to Problem 61CE

The regression equation is Fare=147.08+0.0527Distance.

The fare for a 1,500 mile flight is $226.1.

Explanation of Solution

Step-by-step procedure to obtain the ‘Regression equation’ using the MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Regression Analysis.
Select input range as ‘Sheet6!$Y$1:$Y$31’ under Y/Dependent variable.
Select input range ‘Sheet6!$X$1:$X$31’ under X/Independent variables.
Click on OK.

Output using the Mega Stat software is given below:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 4

From the output, the regression equation is, Fare=147.08+0.0527Distance

Thus, for each additional mile $0.0527 is added to the fare.

Substitute the value ‘1,500’ for ‘distance’ in the regression equation.

Fare=147.08+0.0527Distance=147.08+0.0527(1500)=226.1

Thus, fare for a 1,500 mile flight is $226.1.

e.

Expert Solution

To determine

Explain why it is not suitable to estimate the fare for the international flight with the regression equation.

Explanation of Solution

It is given that the distance is 4,218 miles. This flight is far away from the range of the sampled data. Thus, using the regression equation may not be suitable to estimate the fare for the flight.

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

Answer 4

Textbook Question

Chapter 13, Problem 61CE

TravelAir.com samples domestic airline flights to explore the relationship between airfare and distance. The service would like to know if there is a correlation between airfare and flight distance. If there is a correlation, what percentage of the variation in airfare is accounted for by distance? How much does each additional mile add to the fare? The data follow.

Chapter 13, Problem 61CE, TravelAir.com samples domestic airline flights to explore the relationship between airfare and

a. Draw a scatter diagram with Distance as the independent variable and Fare as the dependent variable. Is the relationship direct or indirect?
b. Compute the correlation coefficient. At the .05 significance level, is it reasonable to conclude that the correlation coefficient is greater than zero?
c. What percentage of the variation in Fare is accounted for by Distance of a flight?
d. Determine the regression equation. How much does each additional mile add to the fare? Estimate the fare for a 1,500-mile flight.
e. A traveler is planning to fly from Atlanta to London Heathrow. The distance is 4,218 miles. She wants to use the regression equation to estimate the fare. Explain why it would not be a good idea to estimate the fare for this international flight with the regression equation.

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.

a.

Expert Solution

To determine

Construct a scatter diagram with Distance as the independent variable and Fare as the dependent variable.

Explain the relationship between the variables.

Answer to Problem 61CE

The scatter diagram of the data is as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 1

Explanation of Solution

Step-by-step procedure to obtain the scatterplot using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Scatterplot.
Enter horizontal axis as Sheet6!$X$1:$X$31 and vertical axis as Sheet6!$Y$1:$Y$31.
Click on OK.

From the scatterplot of the data indicates an increasing trend. It shows that as the distance increases, the fare also increases. Therefore, there is a positive association between distance and fare.

Thus, the relationship is direct.

b.

Expert Solution

To determine

Find the correlation coefficient.

Check whether the correlation coefficient is greater than zero.

Answer to Problem 61CE

The correlation coefficient is 0.656.

There is enough evidence to infer that the population correlation is positive.

Explanation of Solution

Step-by-step procedure to obtain the correlation coefficient using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Correlation matrix.
Enter Input Range as Sheet6!$X$1:$Y$31.
Click on OK.

Output obtained using MegaStat is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 2

The correlation coefficient is 0.656.

Denote the population correlation as ρ.

The hypotheses are given below:

Null hypothesis:

H0:ρ≤0

That is, the correlation in the population is less than or equal to zero.

Alternative hypothesis:

H1:ρ>0

That is, the correlation in the population is positive.

Test statistic:

The test statistic is as follows:

t=rn−21−r2

Here, the sample size is 30 and the correlation coefficient is 0.656.

The test statistic is as follows:

t=0.65630−21−0.6562=0.656×280.56964=4.599

Degrees of freedom:

df=n−2=30−2=28

The level of significance is 0.05. Therefore, 1−α=0.95.

Critical value:

Step-by-step software procedure to obtain the critical value using EXCEL software:

Open an EXCEL file.
In cell A1, enter the formula “=T.INV (0.95, 28)”.

Output obtained using the EXCEL is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 3

Decision rule:

Reject the null hypothesis H₀, if t-calculated> t-critical value.

Otherwise, fail to reject H₀.

Conclusion:

The value of test statistic is 4.599 and the critical value is 1.701.

Here, t-calculated(=4.599)> t-critical value(=1.701).

By the rejection rule, reject the null hypothesis.

Thus, there is enough evidence to infer that the population correlation is positive.

c.

Expert Solution

To determine

Explain what percentage of the variation in ‘Fare’ is accounted for by ‘Distance’ of a flight.

Explanation of Solution

The coefficient of determination is the square of correlation coefficient.

From part (b), the correlation coefficient is 0.656.

Thus, the coefficient of determination is 0.43(=0.6562).

Thus, about 43% of the variation in fares is explained by the variation in distance.

d.

Expert Solution

To determine

Find the regression equation.

Explain how much does each additional mile add to the fare.

Find the fare for a 1,500 mile flight.

Answer to Problem 61CE

The regression equation is Fare=147.08+0.0527Distance.

The fare for a 1,500 mile flight is $226.1.

Explanation of Solution

Step-by-step procedure to obtain the ‘Regression equation’ using the MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Regression Analysis.
Select input range as ‘Sheet6!$Y$1:$Y$31’ under Y/Dependent variable.
Select input range ‘Sheet6!$X$1:$X$31’ under X/Independent variables.
Click on OK.

Output using the Mega Stat software is given below:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 4

From the output, the regression equation is, Fare=147.08+0.0527Distance

Thus, for each additional mile $0.0527 is added to the fare.

Substitute the value ‘1,500’ for ‘distance’ in the regression equation.

Fare=147.08+0.0527Distance=147.08+0.0527(1500)=226.1

Thus, fare for a 1,500 mile flight is $226.1.

e.

Expert Solution

To determine

Explain why it is not suitable to estimate the fare for the international flight with the regression equation.

Explanation of Solution

It is given that the distance is 4,218 miles. This flight is far away from the range of the sampled data. Thus, using the regression equation may not be suitable to estimate the fare for the flight.

Want to see more full solutions like this?

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

Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

Construct a scatter diagram with Distance as the independent variable and Fare as the dependent variable.

Explain the relationship between the variables.

Answer to Problem 61CE

The scatter diagram of the data is as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 1

Explanation of Solution

Step-by-step procedure to obtain the scatterplot using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Scatterplot.
Enter horizontal axis as Sheet6!$X$1:$X$31 and vertical axis as Sheet6!$Y$1:$Y$31.
Click on OK.

From the scatterplot of the data indicates an increasing trend. It shows that as the distance increases, the fare also increases. Therefore, there is a positive association between distance and fare.

Thus, the relationship is direct.

b.

Expert Solution

To determine

Find the correlation coefficient.

Check whether the correlation coefficient is greater than zero.

Answer to Problem 61CE

The correlation coefficient is 0.656.

There is enough evidence to infer that the population correlation is positive.

Explanation of Solution

Step-by-step procedure to obtain the correlation coefficient using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Correlation matrix.
Enter Input Range as Sheet6!$X$1:$Y$31.
Click on OK.

Output obtained using MegaStat is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 2

The correlation coefficient is 0.656.

Denote the population correlation as ρ.

The hypotheses are given below:

Null hypothesis:

H0:ρ≤0

That is, the correlation in the population is less than or equal to zero.

Alternative hypothesis:

H1:ρ>0

That is, the correlation in the population is positive.

Test statistic:

The test statistic is as follows:

t=rn−21−r2

Here, the sample size is 30 and the correlation coefficient is 0.656.

The test statistic is as follows:

t=0.65630−21−0.6562=0.656×280.56964=4.599

Degrees of freedom:

df=n−2=30−2=28

The level of significance is 0.05. Therefore, 1−α=0.95.

Critical value:

Step-by-step software procedure to obtain the critical value using EXCEL software:

Open an EXCEL file.
In cell A1, enter the formula “=T.INV (0.95, 28)”.

Output obtained using the EXCEL is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 3

Decision rule:

Reject the null hypothesis H₀, if t-calculated> t-critical value.

Otherwise, fail to reject H₀.

Conclusion:

The value of test statistic is 4.599 and the critical value is 1.701.

Here, t-calculated(=4.599)> t-critical value(=1.701).

By the rejection rule, reject the null hypothesis.

Thus, there is enough evidence to infer that the population correlation is positive.

c.

Expert Solution

To determine

Explain what percentage of the variation in ‘Fare’ is accounted for by ‘Distance’ of a flight.

Explanation of Solution

The coefficient of determination is the square of correlation coefficient.

From part (b), the correlation coefficient is 0.656.

Thus, the coefficient of determination is 0.43(=0.6562).

Thus, about 43% of the variation in fares is explained by the variation in distance.

d.

Expert Solution

To determine

Find the regression equation.

Explain how much does each additional mile add to the fare.

Find the fare for a 1,500 mile flight.

Answer to Problem 61CE

The regression equation is Fare=147.08+0.0527Distance.

The fare for a 1,500 mile flight is $226.1.

Explanation of Solution

Step-by-step procedure to obtain the ‘Regression equation’ using the MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Regression Analysis.
Select input range as ‘Sheet6!$Y$1:$Y$31’ under Y/Dependent variable.
Select input range ‘Sheet6!$X$1:$X$31’ under X/Independent variables.
Click on OK.

Output using the Mega Stat software is given below:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 4

From the output, the regression equation is, Fare=147.08+0.0527Distance

Thus, for each additional mile $0.0527 is added to the fare.

Substitute the value ‘1,500’ for ‘distance’ in the regression equation.

Fare=147.08+0.0527Distance=147.08+0.0527(1500)=226.1

Thus, fare for a 1,500 mile flight is $226.1.

e.

Expert Solution

To determine

Explain why it is not suitable to estimate the fare for the international flight with the regression equation.

Explanation of Solution

It is given that the distance is 4,218 miles. This flight is far away from the range of the sampled data. Thus, using the regression equation may not be suitable to estimate the fare for the flight.

Answer 8

a.

Expert Solution

To determine

Construct a scatter diagram with Distance as the independent variable and Fare as the dependent variable.

Explain the relationship between the variables.

Answer to Problem 61CE

The scatter diagram of the data is as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 1

Explanation of Solution

Step-by-step procedure to obtain the scatterplot using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Scatterplot.
Enter horizontal axis as Sheet6!$X$1:$X$31 and vertical axis as Sheet6!$Y$1:$Y$31.
Click on OK.

From the scatterplot of the data indicates an increasing trend. It shows that as the distance increases, the fare also increases. Therefore, there is a positive association between distance and fare.

Thus, the relationship is direct.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Construct a scatter diagram with Distance as the independent variable and Fare as the dependent variable.

Explain the relationship between the variables.

Answer 13

Answer to Problem 61CE

The scatter diagram of the data is as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 1

Answer 14

Explanation of Solution

Step-by-step procedure to obtain the scatterplot using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Scatterplot.
Enter horizontal axis as Sheet6!$X$1:$X$31 and vertical axis as Sheet6!$Y$1:$Y$31.
Click on OK.

From the scatterplot of the data indicates an increasing trend. It shows that as the distance increases, the fare also increases. Therefore, there is a positive association between distance and fare.

Thus, the relationship is direct.

Answer 15

b.

Expert Solution

To determine

Find the correlation coefficient.

Check whether the correlation coefficient is greater than zero.

Answer to Problem 61CE

The correlation coefficient is 0.656.

There is enough evidence to infer that the population correlation is positive.

Explanation of Solution

Step-by-step procedure to obtain the correlation coefficient using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Correlation matrix.
Enter Input Range as Sheet6!$X$1:$Y$31.
Click on OK.

Output obtained using MegaStat is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 2

The correlation coefficient is 0.656.

Denote the population correlation as ρ.

The hypotheses are given below:

Null hypothesis:

H0:ρ≤0

That is, the correlation in the population is less than or equal to zero.

Alternative hypothesis:

H1:ρ>0

That is, the correlation in the population is positive.

Test statistic:

The test statistic is as follows:

t=rn−21−r2

Here, the sample size is 30 and the correlation coefficient is 0.656.

The test statistic is as follows:

t=0.65630−21−0.6562=0.656×280.56964=4.599

Degrees of freedom:

df=n−2=30−2=28

The level of significance is 0.05. Therefore, 1−α=0.95.

Critical value:

Step-by-step software procedure to obtain the critical value using EXCEL software:

Open an EXCEL file.
In cell A1, enter the formula “=T.INV (0.95, 28)”.

Output obtained using the EXCEL is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 3

Decision rule:

Reject the null hypothesis H₀, if t-calculated> t-critical value.

Otherwise, fail to reject H₀.

Conclusion:

The value of test statistic is 4.599 and the critical value is 1.701.

Here, t-calculated(=4.599)> t-critical value(=1.701).

By the rejection rule, reject the null hypothesis.

Thus, there is enough evidence to infer that the population correlation is positive.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Find the correlation coefficient.

Check whether the correlation coefficient is greater than zero.

Answer 20

Answer to Problem 61CE

The correlation coefficient is 0.656.

There is enough evidence to infer that the population correlation is positive.

Answer 21

Explanation of Solution

Step-by-step procedure to obtain the correlation coefficient using MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Correlation matrix.
Enter Input Range as Sheet6!$X$1:$Y$31.
Click on OK.

Output obtained using MegaStat is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 2

The correlation coefficient is 0.656.

Denote the population correlation as ρ.

The hypotheses are given below:

Null hypothesis:

H0:ρ≤0

That is, the correlation in the population is less than or equal to zero.

Alternative hypothesis:

H1:ρ>0

That is, the correlation in the population is positive.

Test statistic:

The test statistic is as follows:

t=rn−21−r2

Here, the sample size is 30 and the correlation coefficient is 0.656.

The test statistic is as follows:

t=0.65630−21−0.6562=0.656×280.56964=4.599

Degrees of freedom:

df=n−2=30−2=28

The level of significance is 0.05. Therefore, 1−α=0.95.

Critical value:

Step-by-step software procedure to obtain the critical value using EXCEL software:

Open an EXCEL file.
In cell A1, enter the formula “=T.INV (0.95, 28)”.

Output obtained using the EXCEL is given as follows:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 3

Decision rule:

Reject the null hypothesis H₀, if t-calculated> t-critical value.

Otherwise, fail to reject H₀.

Conclusion:

The value of test statistic is 4.599 and the critical value is 1.701.

Here, t-calculated(=4.599)> t-critical value(=1.701).

By the rejection rule, reject the null hypothesis.

Thus, there is enough evidence to infer that the population correlation is positive.

Answer 22

c.

Expert Solution

To determine

Explain what percentage of the variation in ‘Fare’ is accounted for by ‘Distance’ of a flight.

Explanation of Solution

The coefficient of determination is the square of correlation coefficient.

From part (b), the correlation coefficient is 0.656.

Thus, the coefficient of determination is 0.43(=0.6562).

Thus, about 43% of the variation in fares is explained by the variation in distance.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Explain what percentage of the variation in ‘Fare’ is accounted for by ‘Distance’ of a flight.

Answer 27

Explanation of Solution

The coefficient of determination is the square of correlation coefficient.

From part (b), the correlation coefficient is 0.656.

Thus, the coefficient of determination is 0.43(=0.6562).

Thus, about 43% of the variation in fares is explained by the variation in distance.

Answer 28

d.

Expert Solution

To determine

Find the regression equation.

Explain how much does each additional mile add to the fare.

Find the fare for a 1,500 mile flight.

Answer to Problem 61CE

The regression equation is Fare=147.08+0.0527Distance.

The fare for a 1,500 mile flight is $226.1.

Explanation of Solution

Step-by-step procedure to obtain the ‘Regression equation’ using the MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Regression Analysis.
Select input range as ‘Sheet6!$Y$1:$Y$31’ under Y/Dependent variable.
Select input range ‘Sheet6!$X$1:$X$31’ under X/Independent variables.
Click on OK.

Output using the Mega Stat software is given below:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 4

From the output, the regression equation is, Fare=147.08+0.0527Distance

Thus, for each additional mile $0.0527 is added to the fare.

Substitute the value ‘1,500’ for ‘distance’ in the regression equation.

Fare=147.08+0.0527Distance=147.08+0.0527(1500)=226.1

Thus, fare for a 1,500 mile flight is $226.1.

Answer 29

d.

Expert Solution

Answer 30

d.

Expert Solution

Answer 31

Expert Solution

Answer 32

To determine

Find the regression equation.

Explain how much does each additional mile add to the fare.

Find the fare for a 1,500 mile flight.

Answer 33

Answer to Problem 61CE

The regression equation is Fare=147.08+0.0527Distance.

The fare for a 1,500 mile flight is $226.1.

Answer 34

Explanation of Solution

Step-by-step procedure to obtain the ‘Regression equation’ using the MegaStat software:

In an EXCEL sheet enter the data values of x and y.
Go to Add-Ins > MegaStat > Correlation/Regression > Regression Analysis.
Select input range as ‘Sheet6!$Y$1:$Y$31’ under Y/Dependent variable.
Select input range ‘Sheet6!$X$1:$X$31’ under X/Independent variables.
Click on OK.

Output using the Mega Stat software is given below:

Loose Leaf for Statistical Techniques in Business and Economics, Chapter 13, Problem 61CE , additional homework tip 4

From the output, the regression equation is, Fare=147.08+0.0527Distance

Thus, for each additional mile $0.0527 is added to the fare.

Substitute the value ‘1,500’ for ‘distance’ in the regression equation.

Fare=147.08+0.0527Distance=147.08+0.0527(1500)=226.1

Thus, fare for a 1,500 mile flight is $226.1.

Answer 35

e.

Expert Solution

To determine

Explain why it is not suitable to estimate the fare for the international flight with the regression equation.

Explanation of Solution

It is given that the distance is 4,218 miles. This flight is far away from the range of the sampled data. Thus, using the regression equation may not be suitable to estimate the fare for the flight.

Answer 36

e.

Expert Solution

Answer 37

e.

Expert Solution

Answer 38

Expert Solution

Answer 39

To determine

Explain why it is not suitable to estimate the fare for the international flight with the regression equation.

Answer 40

Explanation of Solution

It is given that the distance is 4,218 miles. This flight is far away from the range of the sampled data. Thus, using the regression equation may not be suitable to estimate the fare for the flight.