Using the mtcars dataset, answer the following questions:
Fill in the following table:
Variable | Correlation with mpg |
cyl | -0.85216 |
disp | -0.84755 |
hp | -0.77617 |
drat | 0.681172 |
wt | -0.86766 |
qsec | 0.418684 |
vs | 0.664039 |
am | 0.599832 |
gear | 0.480285 |
carb | -0.55093 |
| mpg | cyl | disp | hp | drat | wt | qsec | vs | am | gear | carb | |
| Mazda RX4 | 21 | 6 | 160 | 110 | 3.9 | 2.62 | 16.46 | 0 | 1 | 4 | 4 | |
| Mazda RX4 Wag | 21 | 6 | 160 | 110 | 3.9 | 2.875 | 17.02 | 0 | 1 | 4 | 4 | |
| Datsun 710 | 22.8 | 4 | 108 | 93 | 3.85 | 2.32 | 18.61 | 1 | 1 | 4 | 1 | |
| Hornet 4 Drive | 21.4 | 6 | 258 | 110 | 3.08 | 3.215 | 19.44 | 1 | 0 | 3 | 1 | |
| Hornet Sportabout | 18.7 | 8 | 360 | 175 | 3.15 | 3.44 | 17.02 | 0 | 0 | 3 | 2 | |
| Valiant | 18.1 | 6 | 225 | 105 | 2.76 | 3.46 | 20.22 | 1 | 0 | 3 | 1 | |
| Duster 360 | 14.3 | 8 | 360 | 245 | 3.21 | 3.57 | 15.84 | 0 | 0 | 3 | 4 | |
| Merc 240D | 24.4 | 4 | 146.7 | 62 | 3.69 | 3.19 | 20 | 1 | 0 | 4 | 2 | |
| Merc 230 | 22.8 | 4 | 140.8 | 95 | 3.92 | 3.15 | 22.9 | 1 | 0 | 4 | 2 | |
| Merc 280 | 19.2 | 6 | 167.6 | 123 | 3.92 | 3.44 | 18.3 | 1 | 0 | 4 | 4 | |
| Merc 280C | 17.8 | 6 | 167.6 | 123 | 3.92 | 3.44 | 18.9 | 1 | 0 | 4 | 4 | |
| Merc 450SE | 16.4 | 8 | 275.8 | 180 | 3.07 | 4.07 | 17.4 | 0 | 0 | 3 | 3 | |
| Merc 450SL | 17.3 | 8 | 275.8 | 180 | 3.07 | 3.73 | 17.6 | 0 | 0 | 3 | 3 | |
| Merc 450SLC | 15.2 | 8 | 275.8 | 180 | 3.07 | 3.78 | 18 | 0 | 0 | 3 | 3 | |
| Cadillac Fleetwood | 10.4 | 8 | 472 | 205 | 2.93 | 5.25 | 17.98 | 0 | 0 | 3 | 4 | |
| Lincoln Continental | 10.4 | 8 | 460 | 215 | 3 | 5.424 | 17.82 | 0 | 0 | 3 | 4 | |
| Chrysler Imperial | 14.7 | 8 | 440 | 230 | 3.23 | 5.345 | 17.42 | 0 | 0 | 3 | 4 | |
| Fiat 128 | 32.4 | 4 | 78.7 | 66 | 4.08 | 2.2 | 19.47 | 1 | 1 | 4 | 1 | |
| Honda Civic | 30.4 | 4 | 75.7 | 52 | 4.93 | 1.615 | 18.52 | 1 | 1 | 4 | 2 | |
| Toyota Corolla | 33.9 | 4 | 71.1 | 65 | 4.22 | 1.835 | 19.9 | 1 | 1 | 4 | 1 | |
| Toyota Corona | 21.5 | 4 | 120.1 | 97 | 3.7 | 2.465 | 20.01 | 1 | 0 | 3 | 1 | |
| Dodge Challenger | 15.5 | 8 | 318 | 150 | 2.76 | 3.52 | 16.87 | 0 | 0 | 3 | 2 | |
| AMC Javelin | 15.2 | 8 | 304 | 150 | 3.15 | 3.435 | 17.3 | 0 | 0 | 3 | 2 | |
| Camaro Z28 | 13.3 | 8 | 350 | 245 | 3.73 | 3.84 | 15.41 | 0 | 0 | 3 | 4 | |
| Pontiac Firebird | 19.2 | 8 | 400 | 175 | 3.08 | 3.845 | 17.05 | 0 | 0 | 3 | 2 | |
| Fiat X1-9 | 27.3 | 4 | 79 | 66 | 4.08 | 1.935 | 18.9 | 1 | 1 | 4 | 1 | |
| Porsche 914-2 | 26 | 4 | 120.3 | 91 | 4.43 | 2.14 | 16.7 | 0 | 1 | 5 | 2 | |
| Lotus Europa | 30.4 | 4 | 95.1 | 113 | 3.77 | 1.513 | 16.9 | 1 | 1 | 5 | 2 | |
| Ford Pantera L | 15.8 | 8 | 351 | 264 | 4.22 | 3.17 | 14.5 | 0 | 1 | 5 | 4 | |
| Ferrari Dino | 19.7 | 6 | 145 | 175 | 3.62 | 2.77 | 15.5 | 0 | 1 | 5 | 6 | |
| Maserati Bora | 15 | 8 | 301 | 335 | 3.54 | 3.57 | 14.6 | 0 | 1 | 5 | 8 | |
| Volvo 142E | 21.4 | 4 | 121 | 109 | 4.11 | 2.78 | 18.6 | 1 | 1 | 4 | 2 | |
| | | | | | | | | | | | |
| correlation | -0.85216 | | -0.84755 | -0.77617 | 0.681172 | -0.86766 | 0.418684 | 0.664039 | 0.599832 | 0.480285 | -0.55093 | |
Which of the variables is the best predictor of mpg? Justifyyour answer using the correlation coefficient and ascatterplot.
Fit a regression model based on your answer to question 2. Writeyour model below.
Is the slope significant? Justify your answer.
Interpret the slope of your regression model.
Interpret the r2 value.
Do you believe your model is a good model for predicting mpg?Justify your answer.
