Question 1 (10 points) Four regression models are fitted to explore the effect of age on BMI. Use the results (see below) to answer the following questions. Model 1: regress bmi age Source | SS df MS Number of obs = 1285 .." F( 1, 1283) = 27.53 Model | 565.735749 1 565.735749 Prob > F = 0.0000 Residual | 26365.083 1283 20.5495581 R-squared = 0.0210 .*. Adj R-squared = 0.0202 Total | 26930.8188 1284 20.9741579 Root MSE = 4.5332 bmi | Coef. Std. Err. t P>|t) [95% Conf. Interval] age | -.0779364.0148537 -5.25 0.000 -.1070766 -.0487962 cons | 32.52028.9915627 32.80 0.000 30.57502 34.46554 Model 2: regress bmi gender Source | SS df MS Number of obs = 1285 F( 1, 1283) = 11.35 Model | 236.116065 1 236.116065 Prob > F =0.0008 Residual | 26694.7027 1283 20.8064713 R-squared = 0.0088 eww.. Adj R-squared = 0.0080 Total | 26930.8188 1284 20.9741579 Root MSE = 4.5614 bmi | Coef. Std. Err. t P>|t] [95% Conf. Interval] gender | .9167072.2721242 3.37 0.001 .38285 1.450564 cons | 26.73945 .2239109 119.42 0.000 26.30018 27.17872 Model 3: regress bmi age gender Source | SS of MS Number of obs = 1285 .... F( 2, 1282) = 20.01 Model | 815.142202 2 407.571101 Prob > F =0.0000 Residual | 26115.6766 1282 20.3710426 R-squared = 0.0303 -. Adj R-squared = 0.0288 Total | 26930.8188 1284 20.9741579 Root MSE = 4.5134 bmi | Coef. Std. Err. t P>|t) [95% Conf. Interval] age | - 0788591 .0147914-5.33 0.000 -1078771 -.0498411 gender | .9423034.2693045 3.50 0.000.4139776 1.470629 cons | 31.94339 1.000919 31.91 0.000 29.97977 33.90701 Model 4 regress bmi age gender agegender Source | SS df MS Number of obs = 1285 .=.. F( 3, 1281) = 15.60 Model | 949.005478 3 316.335159 Prob > F = 0.0000 Residual | 25981.8133 1281 20.282446 R-squared = 0.0352 wwwww Adj R-squared = 0.0330 Total | 26930.8188 1284 20.9741579 Root MSE = 4.5036 bmi | Coef. Std. Err. t P>|t) [95% Conf. Interval] age | -.0264662.0251744 -1.05 0.293 -.0758537.0229213 gender | 6.219454 2.071637 3.00 0.003 2.15528 10.28363 agegender | -.0798335.0310753-2.57 0.010 -.1407975 -.0188695 cons | 28.48597 1.67591 17.00 0.000 25.19814 31.7738 (a) Describe the age effect on BMI? (b) Describe the gender effect on BMI? (c) Is there a significant interaction effect between age and gender on BMI? If yes, please explain. (d) From the output, which measure will you use to select a better model? Based on the selected measure, which model will you choose? (e) How much variation of BMI is explained by the selected model