Homework SourseFollowing the recent season the NFL performed an analysis in
Following the recent season, the NFL performed an analysis in which a simple linear regression model was developed with average home attendance used as the dependent variable and number of games won during the season as the independent variable.The staff is interested in determing whether games won could be used as a predictor for average attendance. Develop the simple linear regression model. The data is as follows:
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a. What percentage of total variation in average home attendance is explained by knowing the number of games the team won?
b. What is the standard error of the estimate for this regression model?
c Using Significance level of .05, test to determine whether the regression slope coefficient is significantly different from 0
d. After examining the regression analysis results, what should the NFL staff conclude about how the average attendance is related to the number of games the team won?
| TEAM | GMS | TOTAL | AVG | PCT | Wins | Points Scored | Points Allowed |
| Arizona | 7 | 297,568 | 42,509 | 57.8 | 5 | 311 | 387 |
| Atlanta | 8 | 565,106 | 70,638 | 99.2 | 8 | 351 | 341 |
| Baltimore | 8 | 563,076 | 70,384 | 102.1 | 6 | 265 | 299 |
| Buffalo | 8 | 575,248 | 71,906 | 89.9 | 5 | 271 | 367 |
| Carolina | 8 | 587,700 | 73,462 | 100.3 | 11 | 391 | 259 |
| Chicago | 8 | 496,965 | 62,120 | 92.8 | 11 | 260 | 202 |
| Cincinnati | 8 | 526,469 | 65,808 | 100.4 | 11 | 421 | 350 |
| Cleveland | 8 | 578,330 | 72,291 | 100.4 | 6 | 232 | 301 |
| Dallas | 8 | 505,258 | 63,157 | 95.9 | 9 | 325 | 308 |
| Denver | 8 | 608,790 | 76,098 | 100 | 13 | 395 | 258 |
| Detroit | 8 | 492,580 | 61,572 | 94.7 | 5 | 254 | 345 |
| Green Bay | 8 | 562,419 | 70,302 | 115.6 | 4 | 298 | 344 |
| Houston | 8 | 562,397 | 70,299 | 101.2 | 2 | 260 | 431 |
| Indianapolis | 8 | 457,373 | 57,171 | 94.9 | 14 | 439 | 247 |
| Jacksonville | 8 | 525,519 | 65,689 | 89 | 12 | 361 | 269 |
| Kansas City | 8 | 623,325 | 77,915 | 98.1 | 10 | 403 | 325 |
| Miami | 8 | 575,256 | 71,907 | 95.6 | 9 | 318 | 317 |
| Minnesota | 8 | 511,960 | 63,995 | 99.9 | 9 | 306 | 344 |
| New England | 8 | 550,048 | 68,756 | 101.1 | 10 | 379 | 338 |
| New Orleans | 8 | 417,270 | 52,158 | 65.4 | 3 | 235 | 398 |
| NY Giants | 8 | 628,519 | 78,564 | 99.8 | 11 | 422 | 314 |
| NY Jets | 8 | 619,958 | 77,494 | 98.4 | 4 | 240 | 355 |
| Oakland | 8 | 418,450 | 52,306 | 83 | 4 | 290 | 383 |
| Philadelphia | 8 | 541,393 | 67,674 | 102.5 | 6 | 310 | 388 |
| Pittsburgh | 8 | 507,434 | 63,429 | 97.6 | 11 | 389 | 258 |
| San Diego | 8 | 529,916 | 66,239 | 92.9 | 9 | 418 | 312 |
| San Francisco | 8 | 523,426 | 65,428 | 93.2 | 4 | 239 | 428 |
| Seattle | 8 | 532,954 | 66,619 | 99.4 | 13 | 452 | 271 |
| St. Louis | 8 | 523,685 | 65,460 | 100.2 | 6 | 363 | 429 |
| Tampa Bay | 8 | 521,741 | 65,217 | 99.3 | 11 | 300 | 274 |
| Tennessee | 8 | 553,192 | 69,149 | 103.2 | 4 | 299 | 421 |
| Washington | 8 | 716,999 | 89,624 | 111.9 | 10 | 359 | 293 |
Solution
(a)Adjusted R Square is 0.0074777
(b)3.37609
(c)0.0000771, it is zero
(d)We conclude that the average attendance is not related to the number of games the team won. because the P-value is greater than significance level 0.05.
0.000219094
The
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| Regression Statistics | ||||||||||
| Multiple R | 0.198732547 | |||||||||
| R Square | 0.039494625 | |||||||||
| Adjusted R Square | 0.007477779 | |||||||||
| Standard Error | 3.376091988 | |||||||||
| Observations | 32 | |||||||||
| ANOVA | ||||||||||
| df | SS | MS | F | Significance F | ||||||
| Regression | 1 | 14.06008657 | 14.06008657 | 1.233557653 | 0.275539149 | |||||
| Residual | 30 | 341.9399134 | 11.39799711 | |||||||
| Total | 31 | 356 | ||||||||
| Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 95.0% | Upper 95.0% | |||
| Intercept | 2.801684397 | 4.718296956 | 0.593791451 | 0.557102832 | -6.834363484 | 12.43773228 | -6.834363484 | 12.43773228 | ||
| X Variable 1 | 7.71786E-05 | 6.94892E-05 | 1.110656406 | 0.275539149 | -6.47372E-05 | 0.000219094 | -6.47372E-05 | 0.000219094 |
