8). Graduation Rates and Admission Rates at Public Colleges (25 points) The data from this regression came from the top 100 public colleges in the United States. The Y variable is graduation rate (a variable ranging from a possible 0% to 100%). The X variable is admission rate (a variable with a possible range from 0% to 100%). The regression is an attempt to explain the variation in graduation rates across the top 100 public colleges by the admission rate (meaning how selective they are). For example, a 20% admission rate would be much more selective than an 80% admission rate. a). Explain the most important findings of this regression analysis. (10 points) b). Make a prediction of the graduation rate at a college where the admission rate is 25%. (5 points) c). What other X variables might you like to have to improve the R squared of this model? (5 points) d). Do you think that admission rate would prove to be a confounding variable once other X variables are added to the model? Agree or disagree and make a brief argument. (5 points) SUMMARY OUTPUT Regression Statistics Multiple R 0.435848 R Square 0.189964 Adjusted R Square 0.181698 Standard Error 0.099466 Observations 100 ANOVA Significance df SS MS F F Regression 0.227373 0.227373 22.98224 5.83E-06 Residual 98 0.969558 0.009893 Total 99 1. 196931 Standard Jpper Lower Upper Coefficients Error t Stat P-value Lower 95% 95% 95.0% 95.0% Intercept 0.836349 0.042898 19.49612 1.69E-35 0.751219 0.921479 0.751219 0.9214 Admission Rate -0.30663 0.063963 -4.79398 5.83E-06 -0.43357 -0.1797 -0.43357 -0.17