ravelAir.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. Origin Destination Distance Fare Detroit, MI Myrtle Beach, SC 636 $ 109 Baltimore, MD Sacramento, CA 2,395 252 Las Vegas, NV Philadelphia, PA 2,176 221 Sacramento, CA Seattle, WA 605 151 Atlanta, GA Orlando, FL 403 138 Boston, MA Miami, FL 1,258 209 Chicago, IL Covington, KY 264 254 Columbus, OH Minneapolis, MN 627 259 Fort Lauderdale, FL Los Angeles, CA 2,342 215 Chicago, IL Indianapolis, IN 177 128 Philadelphia, PA San Francisco, CA 2,521 348 Houston, TX Raleigh/Durham, NC 1,050 224 Houston, TX Midland/Odessa, TX 441 175 Cleveland, OH Dallas/Ft.Worth, TX 1,021 256 Baltimore, MD Columbus, OH 336 121 Boston, MA Covington, KY 752 252 Kansas City, MO San Diego, CA 1,333 206 Milwaukee, WI Phoenix, AZ 1,460 167 Portland, OR Washington, DC 2,350 308 Phoenix, AZ San Jose, CA 621 152 Baltimore, MD St. Louis, MO 737 175 Houston, TX Orlando, FL 853 191 Houston, TX Seattle, WA 1,894 231 Burbank, CA New York, NY 2,465 251 Atlanta, GA San Diego, CA 1,891 291 Minneapolis, MN New York, NY 1,028 260 Atlanta, GA West Palm Beach, FL 545 123 Kansas City, MO Seattle, WA 1,489 211 Baltimore, MD Portland, ME 452 139 New Orleans, LA Washington, DC 969 243 b-2. State the decision rule for 0.05 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places. d-1. Determine the regression equation. (Round your answers to 5 decimal places.) d-2. How much does each additional mile add to the fare? (Round your answer to 5 decimal places.) d-3. Estimate the fare for a 1,500-mile flight. (Round your answer to 2 decimal places.)
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
ravelAir.com samples domestic airline flights to explore the relationship between airfare and distance. The service would like to know if there is a
| Origin | Destination | Distance | Fare | ||||||
| Detroit, MI | Myrtle Beach, SC | 636 | $ | 109 | |||||
| Baltimore, MD | Sacramento, CA | 2,395 | 252 | ||||||
| Las Vegas, NV | Philadelphia, PA | 2,176 | 221 | ||||||
| Sacramento, CA | Seattle, WA | 605 | 151 | ||||||
| Atlanta, GA | Orlando, FL | 403 | 138 | ||||||
| Boston, MA | Miami, FL | 1,258 | 209 | ||||||
| Chicago, IL | Covington, KY | 264 | 254 | ||||||
| Columbus, OH | Minneapolis, MN | 627 | 259 | ||||||
| Fort Lauderdale, FL | Los Angeles, CA | 2,342 | 215 | ||||||
| Chicago, IL | Indianapolis, IN | 177 | 128 | ||||||
| Philadelphia, PA | San Francisco, CA | 2,521 | 348 | ||||||
| Houston, TX | Raleigh/Durham, NC | 1,050 | 224 | ||||||
| Houston, TX | Midland/Odessa, TX | 441 | 175 | ||||||
| Cleveland, OH | Dallas/Ft.Worth, TX | 1,021 | 256 | ||||||
| Baltimore, MD | Columbus, OH | 336 | 121 | ||||||
| Boston, MA | Covington, KY | 752 | 252 | ||||||
| Kansas City, MO | San Diego, CA | 1,333 | 206 | ||||||
| Milwaukee, WI | Phoenix, AZ | 1,460 | 167 | ||||||
| Portland, OR | Washington, DC | 2,350 | 308 | ||||||
| Phoenix, AZ | San Jose, CA | 621 | 152 | ||||||
| Baltimore, MD | St. Louis, MO | 737 | 175 | ||||||
| Houston, TX | Orlando, FL | 853 | 191 | ||||||
| Houston, TX | Seattle, WA | 1,894 | 231 | ||||||
| Burbank, CA | New York, NY | 2,465 | 251 | ||||||
| Atlanta, GA | San Diego, CA | 1,891 | 291 | ||||||
| Minneapolis, MN | New York, NY | 1,028 | 260 | ||||||
| Atlanta, GA | West Palm Beach, FL | 545 | 123 | ||||||
| Kansas City, MO | Seattle, WA | 1,489 | 211 | ||||||
| Baltimore, MD | Portland, ME | 452 | 139 | ||||||
| New Orleans, LA | Washington, DC | 969 | 243 | ||||||
b-2. State the decision rule for 0.05 significance level: H0: ρ ≤ 0; H1: ρ > 0. (Round your answer to 3 decimal places.
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d-1. Determine the regression equation. (Round your answers to 5 decimal places.)
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d-2. How much does each additional mile add to the fare? (Round your answer to 5 decimal places.)
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d-3. Estimate the fare for a 1,500-mile flight. (Round your answer to 2 decimal places.)
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