Team Rank based on several factors Regression Statistics Multiple R 0.894 R Square 0.799 Adjusted R Square 0.745 Standard Error 89.008 Observations 20 ANOVA df SS MS F Significance F Regression 4 471595.683 117898.921 14.882 4.19593E-05 Residual 15 118835.219 7922.348 Total 19 590430.902 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5381.214 2346.661 2.293 0.037 379.424 10383.004 379.424 10383.004 Winning Percentage 14.471 7.719 1.875 0.013 -1.982 30.925 -1.982 30.925 Total Yards 15.181 8.319 1.825 0.088 -2.55 32.911 -2.551 32.911 Allowed Points 8.545 6.53 1.309 0.021 -5.373 22.464 -5.373 22.464 Scored Points 0.352 5.765 0.052 0.959 -11.988 12.588 -11.988 12.588
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The p-value is a measure of the probability that an observed difference could have occurred just by random chance. The lower the p-value, the greater the statistical significance because it tells the investigator that the hypothesis under consideration may be Show more…
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The National Football League has developed a regression model to predict the number of wins during a season for a team using the following independent variables: * Average points per game during the season (PPG) * Average number of penalties committed per game during the season (PEN) * Turnover differential during the season (TO) Turnover differential is defined as the number of times the team took the ball away from their opponent with a turnover minus the number of times the team gave the ball away to their opponent with a turnover. For example, if TO = +5, the team had five more takeaways than giveaways. If TO = -7, the team had seven more giveaways than takeaways during the season. The following Excel output shows the partially completed regression output from a random season. SUMMARY OUTPUT Regression Statistics Multiple R: 0.8075 R Square Adjusted R Square Standard Error: 1.9338 Observations: 32 ANOVA df SS MS F Significance F Regression: 0.00 Residual: 104.71 Total: 31 300.97 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept: 1.5572 3.1208 0.6217 PEN: -0.2938 0.3438 0.4000 PPG: 0.3523 0.0903 0.0005 TO: 0.1371 0.0397 0.0018 The mean square regression for this model is ______. 196.26 3.74 17.49 65.42
Madhur L.
The National Football League has developed a regression model to predict the number of wins during a season for a team using the following independent variables: - Average points per game during the season (PPG) - Average number of penalties committed per game during the season (PEN) - Turnover differential during the season (TO) Regression statistics: Multiple R: 0.8075 R square: 0.6532 Adjusted R square: 0.6254 Standard Error: 1.9338 Observations: 32 ANOVA: df: 2 SS: 196.26 MS: 98.13 F: 49.06 sig. f: 0.0001 Regression Coefficients: Intercept: 1.5572 PEN: -0.2938 PPG: 0.3523 TO: 0.1371 Turnover differential is defined as the number of times the team took the ball away from their opponent with a turnover minus the number of times the team gave the ball away to their opponent with a turnover. For example, if TO = +5, the team had five more takeaways than giveaways. If TO = -7, the team had seven more giveaways than takeaways during the season. The following Excel output shows the partially completed regression output from a random season. A. Write down the regression equation. B. Calculate the missing goodness-of-fit statistics and interpret the results as well as the statistical significance of the model. Explain the Adjusted R Square value and the difference to the R square value. Show workings. C. Comment on any issues with the model, the input and output factors, and its applicability. Include the pitfalls of regression analysis.
Sri K.
The NFL keeps track of a large number of statistics during the football season. For 2009 the number of points scored per game and how it related to such variables as the number of passes attempted per game ( PassAtt/G), the total pass yards gained during the season ( PassYds), and the total rushing yards gained in the season ( RushYds) were studied.The following tables provide information on the least-squares fit of a multiple regression model for Pts/G on the three explanatory variables. Analysis of Variance Source DF Sum of Squares Mean Square F Ratio Model 3 639.69354 213.231 44.9160 Error 28 132.92521 4.747 P-value Total 31 772.61875 <.0001 Parameter Estimates Term Estimate Std Error t Ratio Prob>|t| Intercept -2.426084 8.820979 -0.28 0.7853 PassAtt/G -0.509434 0.239595 -2.13 0.0424 PassYds 0.0094097 0.001016 9.26 <.0001 RushYds 0.0049685 0.001892 2.63 0.0138 If a team were to attempt 30 passes per game, pass for a total of 3500 yards, and rush for 2000 yards, what would the fitted regression model predict for the points the team would score per game? O a. 25.2 O b. 44.9 O c. 27.6 O d. 58.2 O e. 18.8
Shyam P.
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