An air travel service samples domestic airline flights to explore the relationsh
ID: 3266403 • Letter: A
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: 0; H1: > 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 $140 Baltimore, MD Sacramento, CA 2,395 292 Las Vegas, NV Philadelphia, PA 2,176 303 Sacramento, CA Seattle, WA 605 267 Atlanta, GA Orlando, FL 403 239 Boston, MA Miami, FL 1,258 220 Chicago, IL Covington, KY 264 151 Columbus, OH Minneapolis, MN 627 205 Fort Lauderdale, FL Los Angeles, CA 2,342 180 Chicago, IL Indianapolis, IN 177 275 Philadelphia, PA San Francisco, CA 2,521 225 Houston, TX Raleigh/Durham, NC 1,050 333 Houston, TX Midland/Odessa, TX 441 170 Cleveland, OH Dallas/Ft.Worth, TX 1,021 119 Baltimore, MD Columbus, OH 336 190 Boston, MA Covington, KY 752 100 Kansas City, MO San Diego, CA 1,333 132 Milwaukee, WI Phoenix, AZ 1,460 255 Portland, OR Washington, DC 2,350 161 Phoenix, AZ San Jose, CA 621 120 Baltimore, MD St. Louis, MO 737 331 Houston, TX Orlando, FL 853 278 Houston, TX Seattle, WA 1,894 183 Burbank, CA New York, NY 2,465 343 Atlanta, GA San Diego, CA 1,891 287 Minneapolis, MN New York, NY 1,028 127 Atlanta, GA West Palm Beach, FL 545 141 Kansas City, MO Seattle, WA 1,489 256 Baltimore, MD Portland, ME 452 146 New Orleans, LA Washington, DC 969 127Explanation / Answer
First i am pasting the Excel regression output
b1. Correlation r between Fare and distance = 0.314
b2. Here tcritical = 2.0484 so it should be greater than t.
b3. Test Statistic t = 1.748
b4. At the 0.05 significance level, is it reasonable to conclude that the correlation coefficient is greater than zero?
No, as t < tcritical so, it is not reasonable to conclude that the correlation coefficent is not greater than zero.
We shall not reject the null hypothesis.
C. As R2 = 0.0984
so 9.84% of the variation in Fare is accounted for by Distance of a flight.
D1 . The regression equation is
Fare = 173.8052 + 0.030 * Distance.
D2. Each additional mile add $ 0.03 to the fare.
D3. the fare for a 2,000-mile flight.
2000 mile flight fare = 173.8052 + 0.03 * 2000 = $233.8052
SUMMARY OUTPUT Regression Statistics Multiple R 0.313659 R Square 0.098382 Adjusted R Square 0.066181 Standard Error 71.2833 Observations 30 ANOVA df SS MS F Significance F Regression 1 15524.82 15524.82 3.05528 0.091434 Residual 28 142276.6 5081.309 Total 29 157801.5 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 173.8052 24.39283 7.12526 9.41E-08 123.8388 223.7717 123.8388 223.7717 Distance 0.03083 0.017638 1.747936 0.091434 -0.0053 0.066959 -0.0053 0.066959Related Questions
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