Interpret your estimated coefficient on WEIGHT. (That is, in words, what does the value tell you?) Does the sign of this coefficient match your expectations? What happened to the adjusted R2 when WEIGHT was added to this regression? What does this tell you?
| OBS | MAKE | MODEL | TIME | SPEED | WEIGHT | HP | HP | TIME | |
| 1 | Audi | TT Roadster | 8.9 | 133 | 1335 | 150 | 150 | 8.9 | |
| 2 | Mini | Cooper S | 7.4 | 134 | 1240 | 168 | 168 | 7.4 | |
| 3 | Volvo | C70 T5 Sport | 7.4 | 150 | 1711 | 220 | 220 | 7.4 | |
| 4 | Saab | Nine-Three | 7.9 | 149 | 1680 | 247 | 247 | 7.9 | |
| 5 | Mercedes-Benz | SL350 | 6.6 | 155 | 1825 | 268 | 268 | 6.6 | |
| 6 | Jaguar | XK8 | 6.7 | 154 | 1703 | 290 | 290 | 6.7 | |
| 7 | Bugatti | Veyron 16.4 | 2.4 | 253 | 1950 | 1000 | 1000 | 2.4 | |
| 8 | Lotus | Exige | 4.9 | 147 | 875 | 189 | 189 | 4.9 | |
| 9 | BMW | M3 (E30) | 6.7 | 144 | 1257 | 220 | 220 | 6.7 | |
| 10 | BMW | 330i Sport | 5.9 | 155 | 1510 | 231 | 231 | 5.9 | |
| 11 | Porsche | Cayman S | 5.3 | 171 | 1350 | 291 | 291 | 5.3 | |
| 12 | Nissan | Skyline GT-R (R34) | 4.7 | 165 | 1560 | 276 | 276 | 4.7 | |
| 13 | Porsche | 911 RS | 4.7 | 172 | 1270 | 300 | 300 | 4.7 | |
| 14 | Ford | Shelby GT | 5 | 150 | 1584 | 319 | 319 | 5 | |
| 15 | Mitsubishi | Evo VII RS Sprint | 4.4 | 150 | 1260 | 320 | 320 | 4.4 | |
| 16 | Aston Martin | V8 Vantage | 5.2 | 175 | 1630 | 380 | 380 | 5.2 | |
| 17 | Mercedes-Benz | SLK55 AMG | 4.8 | 155 | 1540 | 355 | 355 | 4.8 | |
| 18 | Maserati | Quattroporte Sport GT | 5.1 | 171 | 1930 | 394 | 394 | 5.1 | |
| 19 | Spyker | C8 | 4.5 | 187 | 1275 | 400 | 400 | 4.5 | |
| 20 | Ferrari | 288GTO | 4.9 | 189 | 1161 | 400 | 400 | 4.9 | |
| 21 | Mosler | MT900 | 3.9 | 190 | 1130 | 435 | 435 | 3.9 | |
| 22 | Lamborghini | Countach QV | 4.9 | 180 | 1447 | 455 | 455 | 4.9 | |
| 23 | Chrysler | Viper GTS-R | 4 | 190 | 1290 | 460 | 460 | 4 | |
| 24 | Bentley | Arnage T | 5.2 | 179 | 2585 | 500 | 500 | 5.2 | |
| 25 | Ferrari | 430 Scuderia | 3.5 | 198 | 1350 | 503 | 503 | 3.5 | |
| 26 | Saleen | S7 | 3.3 | 240 | 1247 | 550 | 550 | 3.3 | |
| 27 | Lamborghini | Murcielago | 4 | 205 | 1650 | 570 | 570 | 4 | |
| 28 | Pagani | Zonda F | 3.6 | 214 | 1230 | 602 | 602 | 3.6 | |
| 29 | McLaren | F1 | 3.2 | 240 | 1140 | 627 | 627 | 3.2 | |
| 30 | Koenigsegg | CCR | 3.2 | 242 | 1180 | 806 | 806 | 3.2 |
The TIME output corresponding to HP can be found as follows:
|
SUMMARY OUTPUT |
|
|
|
|
|
Regression Statistics |
|
|
Multiple R |
0.797539769 |
|
R Square |
0.636069683 |
|
Adjusted R Square |
0.623072172 |
|
Standard Error |
0.945077588 |
|
Observations |
30 |
|
|
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
|
Intercept |
7.630122482 |
0.40417 |
18.87848641 |
1.83E-17 |
6.802217 |
8.458028 |
|
HP |
-0.00643163 |
0.000919 |
-6.99555614 |
1.32E-07 |
-0.00831 |
-0.00455 |
The fitted regression equation is:
TIMEi=7.6301-0.0064 x HPi + ei
Estimate the regression TIMEi = β0 + β1HPi + β2WEIGHTi + ε
|
|
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
|
|
Intercept |
3.936870335 |
1.29084 |
3.049851421 |
0.004964 |
1.292704 |
6.581036 |
|
WEIGHT |
0.000776715 |
0.000861 |
0.902190335 |
0.374652 |
-0.00099 |
0.00254 |
The fitted regression equation is:
TIME= 3.9369-0.00078 x WEIGHTi - ei
1. Interpret your estimated coefficient on WEIGHT. (That is, in words, what does the value tell you?) Does the sign of this coefficient match your expectations? What happened to the adjusted R2 when WEIGHT was added to this regression? What does this tell you?
Given information:
The data represents the values of the variables time, weight, Hp and etc.
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