Question

The NFL data in Table B.1 is attached.

10.2 Consider the National Football League data in Table B.1. Restricting your attention to regressors x (rushing yards), x2 (passing yards), x (field goal percentage), x7 (percent rushing), xs (opponents' rushing yards), and x, (opponents' passing yards), apply the all-possible-regressions procedure. Evaluate R2, Cp, and MSRes for each model. Which subset of regressors do you recommend? x1 x3 10 2113 1985 38.9 64.7 4 868 59.7 2205 1917 615 55.0 2096 1575 11 2003 2855 38.8 61.3 3 11 2957 1737 401 60.0 14 914 6S6 M, 2175 13 2285 2905 416 45.3 4957 614 1903 2476 10 2971 166639.2 3.8 15 836 66.1 1457 1866 786 610 1848 2339 11 2309 2927 39.7 74.18 10 2528 2341 381 654 12 754 66.1 1564 2092 11 2147 2737 370 78.3 1 761 58.0 1821 1909 4 1689 1414 42.1 47.6 3 714 57.0 2577 2001 2566 1838 42.3 542 1 797 58.9 2476 2254 48 19 984 67.5 1984 2217 1480 10 2109 2191 39.5 51.9 2363 37.3 2229 374 53.6 5 1037 58.8 1761 2032 2204 5.1 714 986 58.6 1709 2025 2140 38.8 58.3 6 819 59.2 1901 1686 366 52.6 19 791 54A 2288 1835 353 59.3 5 776 49.6 2072 1914 41.1 553 10 789 54.3 2861 2496 38.2 69.6 6 582 58.7 2411 2670 5 1722 1730 52.6 5 1498 2072 353 59.3 1873 2929 4 1775 1983 39.3 78.3 7 901 3 1904 1792 39.7 38.1 3 1929 1606 397 688 4 2080 1492 35.5 68.8 8 7 10 2301 2835 35.3 74.1 2 683 59.7 51.7 2289 2202 9 734 61.9 2203 1988 21 627 52.7 2592 2324 722 578 2053 2550 576 54.9 20482628 0 2416 38.7 50.056 9 2048 2020 1416 2649 1503 1503 39.3 47.0 9 875 53.5 2560 2241

Answer 1

ca11: 1m(formula y~ xl + x2 + X4 + x7 + x8) Residuals 1Q Median 3Q Max 2.6762 -0.8558 -0.1853 0.9785 3.6185 Mi n Coeff1c1ents: Estimate std. Error t value Pr(tl) (Intercept) -2.7937956 9.3051869 -0.300 0.766812 0.0007467 0.0017119 0.436 0.666958 0.0034566 0.0007449 4.641 0.000126 0.0164967 0.0355743 0.464 0.647401 0.1623914 0.13633991.191 0.246316 X4 0.0045469 0.0013760 3.304 0.003228 ** signif. codes: 0 ‘ , 0.001 ‘**, 0.01 ‘*' 0.05 ‘.' 0.1 ‘ ' 1 Residual standard error: 1.762 on 22 degrees of freedom Multiple R-squared: 0.7911, F-statistic: 16.66 on 5 and 22 DF, p-value: 7.746e-07 Adjusted R-squared: 0.7436 Ana lVsis of variance Tahle

As decreasing the number of independent variables the value of adjusted R2 decreases. Therefore the first model is the best model

Call: 1m(formula - y ~ xl + x2 + X4 + x7 + x8 + x9) Residuals: 1Q Median 3Q Max 2.9118 -0.5572 -0.1314 0.8105 3.0991 Mi n coefficients: Estimate Std. Error t value PrĢt!) (Intercept) -3.0261572 9.0713478 -0.334 0.7420 0.0011301 0.0016890 0.669 0.5107 0.0036547 0.0007385 4.949 6.76e-05 0.0222446 0.0348954 0.637 0.5307 0.1713689 0.1330341 1.288 0.2117 x2 x4 x8 x9 -0.0035015 0.0015185 -2.306 0.0314 * 0.0019116 0.0013019 -1.468 0.1568

Residual standard error: 1.717 on 21 degrees of freedom Multiple R-squared 0.8106, Adjusted R-squared: 0.7564 F-statistic: 14.98 on 6 and 21 DF, p-value: 1.274e-06 Analysis of Variance Table Response: y Df Sum Sq Mean Sq F valuePr(>F) x1 x2 x4 x7 1 115.068 115.068 39.0117 3.399e-06 ** 1 83.343 83.343 28.2559 2.856e-05 ** 1 1.444 1.444 0.4896 0.491780 1 24.909 24.909 8.4449 0.008449 ** 1 33.900 33.900 11.4931 0.002761** 1 6.359 6.359 2.1559 0.156845 x9 Residuals 21 61.9412.950

ik Estimated rdf infl 1.0; not estimating variance vari Cp 29.75395 28.00000 28.00000 28.00000 87.50789