A statistician is developing a predictive model for the final league table places for eighteen teams participating in a professional football league. Data has been collected for the last twelve seasons, for the following variables: final league place, spending on new players (in millions), average distance travelled for away games (in miles) and average attendance (in number of spectators). The statistician has calculated correlation coefcients and simple regressions on each factor, which are summarised in the tables on the next two pages: a) Based on the correlation table, identify which of the explanatory variables you believe will lead to a better regression model to predict nal league place, and briefly explain why you made that choice (4 marks) b) Calculate the missing values on each of the three regression models below (2 marks each) c) In the regressions with the independent variables Attendance and Spend, the slope coefficients have values of 0.0001 and 0.07499, respectively. Explain the meaning of these values and how they relate to the way league tables are normally presented (7 marks) d) Using the appropriate regression model, calculate the league position for a team that: (1.5 marks each) Place Av. Distance Attendance Spend Place 1 Av. Distance -0.518 Attendance 0.713 0.091 1 Spend 0.450 -0.465 0.186 1 SUMMARY OUTPUT Regression Statistics Multiple R 0.5185 R Square 0.2688 Adjusted R Square 0.1957 Standard Error 3.2335 Observations 12 ANOVA df SS MS F Significance F Regression 1 38.4428 38.4428 3.6767 0.08416 Residual 10 104.5572 10.4557 Total 11 143 Upper Coefficients Standard Error t Stat P-value Lower 95% 95% Intercept 11.6079 2.8227 4.1124 0.0021 5.3186 17.8972 Av. Distance -0.0510 0.02657 -1.9175 -0.1102 0.0083 SUMMARY OUTPUT Regression Statistics Multiple R 0.7134 R Square 0.5090 Adjusted R Square 0.4598 Standard Error 2.6498 Observations 12 ANOVA df SS MS F Significance F Regression 1 72.7832 72.7832 10.3655 0.0092 Residual 10 70.2168 7.02168 Total 11 143Upper Coefficients Standard Error t Stat P-value Lower 95% 95% Intercept 0.9876 1.8758 0.5266 0.6099 3.1908 5.1660 Attendance 0.0001 4.26E-05 0.0092 4.23E-05 0.0002 UL21/1063 Page 7 of 13 SUMMARY OUTPUT Regression Statistics Multiple R 0.4505 R Square 0.2029 Adjusted R Square 0.1232 Standard Error 3.3761 Observations 12 ANOVA df SS MS F Significance F Regression 1 29.0199 29.0199 2.5461 0.1417 Residual 10 113.9801 11.3980 Total 11 143 Upper Coefficients Standard Error t Stat P-value Lower 95% 95% Intercept 4.3844 1.6455 2.6644 0.0237 0.7178 8.0509 Spend 0.0749 0.0469 1.5956 0.1417