5. Suppose you want to investigate the impact of reality TV shows on a college student's decision to undergo cosmetic surgery. 170 college students answered questions about their impressions of reality TV shows featuring cosmetic surgery. Several variables were measured as follows: Desire (y): scale ranging from 5 to 25, where the higher the value, the greater the interest in having cosmetic surgery, Gender (x1): 1 if male, 0 if female Impression (x2): scale ranging from 1 to 7, where the higher the value, the better impression of reality TV show. We hypothesize a model here: y =BO+B1X1+B2x2+B3x1x2 +E, and fit to the data. The computer output is reported below. (Scientific notation example: 3.45E11 3.45×10¹¹) (a). Please find the least squares equation based on the printout. (2 pts) (b). Overall, is the model useful for predicting y? Please test using a = 0.05. (5 pts) (c). Please find the predicted level of desire (y) for a male college student with an impression-of-reality-TV-scale score of 5. (3 pts) (d). Conduct a test (at a = 0.05) to determine if gender and impression of reality show interact in the prediction of level of desire for cosmetic surgery. (5 pts) (e). The positive effect of impression of reality show on the desire for cosmetic surgery is stronger for female students than for male students. Please test this theory using a = 0.05. (5 pts) Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations ANOVA Regression Residual Total 0.67005692 0.44897628 0.43901802 2.35006637 df 170 SS MS F 3 747.001456 249.000485 45.0858166 166 916.786779 5.52281192 169 1663.78824 Standard Significance F 2.2926E-21 Coefficients Error P-value Upper 95% Intercept 13.1089031 t Stat Lower 95% 11.7789068 0.67363488 17.4855952 1.7187E-39 10.4489105 -4.3004293 0.35596268 -1.9722333 1.17921687 -1.6724941 0.09631061 Impression (X2) 0.58461808 0.16162928 3.61703087 0.00039508 0.26550406 -1.0984364 -0.0081626 -2.0039208 0.04670494 Interact(XIX2) -0.5532995 0.27610846 Gender (X1) 0.9037321