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Q2) An epidemiologist was interested in examining the effects of three factors on a person's cholesterol levels. Let ", i= 1, 2, 3, represent the effects of the three factors, respectively, and y be the total cholesterol. The following output was generated using statistical software. Regression Analysis Predictor Coef StDev T P Constant 225.19 65.70 3.43 0.019 Male vs female 12.725 3.570 3.56 0.016 Vegetarian vs Non-vegetarian -39.45 23.24 -1.70 0.150 Number of days with 2 60 min exercise -33.48 12.29 -2.73 0.042 S = 14.01 R-Sq =95.1% R-Sq(adj) = 92.1 Analysis of Variance Source DF SS MS F Regression 18,951.1 6,317.0 32.19 Residual Error 981.1 196.2 Total 19,932.2 2a. Does the regression model appear to be useful? State the null and alternative hypotheses of interest, the critical and calculated test statistic, and justify your answer. (Use @= 0.05.) (2 points) 2b. Interpret the coefficient and test statistic for the "exercise' factor in the model. (2 points) 2c. Determine whether a reduced model (below) after removing 'vegetarian vs non-vegetarian' is a better model than the full model presented earlier. Use alpha of 0.05. (3 points) Regression Analysis Predictor Coef StDev T Constant 230.21 70.25 3.27 Male vs female 14.31 3.724 3.84 Number of days with > 60 min exercise -39.23 11.34 -3.46 S = 12.92 R-Sq = 94.97% R-Sq(adj) = 92.9 Analysis of Variance Source DF SS MS F Regression 18,931.1 9465 56.73 Residual Error 1001.1 166.85 Total 8 19.932.2