28 Following the recent season, the NFL performed an analysis in which a simple

Question

28

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:

293

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

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Explanation / Answer

(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

(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.

The below is the output of Excel SUMMARY OUTPUT 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

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