An air travel service samples domestic airline flights to explore the relationsh

Question

An air travel service 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.

Compute the correlation of distance and fare? (Round your answer to 3 decimal places.)

          

    

State the decision rule for 0.05 significance level: H0: r %u2264 0; H1: r > 0. (Round your answer to 2 decimal places.)

          

Compute the value of the test statistic. (Round your answer to 2 decimal places.)

          

At the 0.05 significance level, is it reasonable to conclude that the correlation coefficient is greater than zero?

           

What percentage of the variation in Fare is accounted for by Distance of a flight? (Round your answer to the nearest whole number.)

           

          

Determine the regression equation. (Round your answers to 5 decimal places.)

         

How much does each additional mile add to the fare? (Round your answer to 5 decimal places.)

          

         

Estimate the fare for a 2,000-mile flight. (Round your answer to 2 decimal places.)

           

Origin Destination Distance Fare   Detroit, MI   Myrtle Beach, SC 636         159           Baltimore, MD   Sacramento, CA 2,395         338          Las Vegas, NV   Philadelphia, PA 2,176         294         Sacramento, CA   Seattle, WA 605         318           Atlanta, GA   Orlando, FL 403         174           Boston, MA   Miami, FL 1,258         227           Chicago, IL   Covington, KY 264         167           Columbus, OH   Minneapolis, MN 627         162          Fort Lauderdale, FL   Los Angeles, CA 2,342         247          Chicago, IL   Indianapolis, IN 177         171          Philadelphia, PA   San Francisco, CA 2,521         338          Houston, TX   Raleigh/Durham, NC 1,050         163         Houston, TX   Midland/Odessa, TX 441         174           Cleveland, OH   Dallas/Ft.Worth, TX 1,021         245           Baltimore, MD   Columbus, OH 336         290           Boston, MA   Covington, KY 752         111     Kansas City, MO   San Diego, CA 1,333         258           Milwaukee, WI   Phoenix, AZ 1,460         111           Portland, OR   Washington, DC 2,350         299           Phoenix, AZ   San Jose, CA 621         327           Baltimore, MD   St. Louis, MO 737         332          Houston, TX   Orlando, FL 853         315           Houston, TX   Seattle, WA 1,894         316           Burbank, CA   New York, NY 2,465         280           Atlanta, GA   San Diego, CA 1,891         136           Minneapolis, MN   New York, NY 1,028         327           Atlanta, GA   West Palm Beach, FL 545         165           Kansas City, MO   Seattle, WA 1,489         312           Baltimore, MD   Portland, ME 452         307           New Orleans, LA   Washington, DC 969         292        An air travel service 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.

Explanation / Answer

(b-1) r=0.208

(b-2) Given a=0.05, the critical value is t(0.95, df=n-2=28) =1.701

Reject H0 if t >1.701

(b-3)test statistic

= r*sqrt((n-2)/(1-r^2))

=0.208*sqrt(28/(1-0.208^2))

=1.13

(b-4) Do not reject Ho. There is not enough evidence to conclude that a positve correlation exists.

(c) R^2= 4.34%

(d-1)
regression equation:

y=193.1705+0.0203*Distance

(d-2)No. of additional miles: 0.0203

(d-3)
y=193.1705+0.0203*1250=218.5455

Regression output


confidence interval variables coefficients std. error t (df=28) p-value 95% lower 95% upper Intercept 193.1705 24.9183 7.752 1.91E-08 142.1277 244.2134 Distance 0.0203 0.0180 1.128 .2691 -0.0166 0.0572

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