The following model for mean weight in kg is estimated in R where male is an ind

Question

The following model for mean weight in kg is estimated in R where male is an indicator variable that the subject is male, height is the height of the subject in cm, and waist is their waist girth in cm, measured at the narrowest part of their torso. mu (weightheight, waist, male) = beta_0 + beta_1 male + beta_2 height + beta_3 weist + beta_4 male times weist (a) Which parameters capture the difference in the mean weight for a male compared to a female of the same weight and height? (b) Which parameter captures the difference in the relationship between mean weight and waist for a male compared to a female, keeping height constant? (c) The results from the fit are shown below. Construct a 95% confidence interval for beta_2 and interpret the result.. Call: lm(formula = weight " male + waist + height + waist:male, data = bdims) Residuals: Min 1Q Median 3Q Max -14.714 -2.848 -0.161 2.768 20.115 Coefficients: Estimate Std. Error t value Pr(>|t|) (Intercept) -96.5079 5.1890 -18.60

Explanation / Answer

Part-a The parameter 1 captures the difference in the mean weight for a male compared to female of the same height and weight

Part-b-The parameter 4 captures the difference in the relation between mean weight and waist for a male compared to female, keeping height constant

Part-c-critical t = t0.05/2(502)=1.96

So, 95% confidence itnevral for 2=0.5188±1.96*0.0289=(0.4622                                 0.5754)

This emans that we are 95% confident that corresponding to a 1 cm increase in height the weigh increase on an average from 0.46 pounds to 0.57 pounds

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