please, help.

2. Consider the following regression model where X and W are both quantitative contin- uous variables. (Y|X,W) = Bu + 3x + 3,W + B3X X W (a) What is the change in the mean response Y when X increases in one unit and W is held constant? (b) What test would you conduct to evaluate whether the interaction should be kept in the model? You must specify the name of the test (t.e., t-test. ESS F-test, ANOVA-F-test), write down the null and alternative hypotheses, and determine the degrees of freedom associated with the test. (Assume you have a total of n observations). 3. Consider the model (weight|height, waist, male) = 3o + B,male + Spheight +Bzwaist + B male x waist where weight is the response variable of interest measured in kg, height is the height of the subject in cm, waist is the subject's waist girth in cm (measured at the narrowest part of their torso) and male is an indicator variable indicating that the subject is male. A total of 507 subjects considered in the study (a) Which parameters capture the difference in the mean weight for a male compared to a female of the same height and waist? (b) Which parameters capture the difference in the relationship between mean weight and waist for a male compared to a female, keeping height constant? (C) What is the interpretation of 3, in the model. () Fitting the model in R we obtain the partial output below. Obtain the estimated coefficients and determine which one are significant at level a = 0.05. Call: Im(formula - weight - male + waist + height + waist :male, data - bdins) Coefficients: Estimate Std. Error t value (Intercept) 5.1890 -18.60 male 3.7111 2.25 waist 0.0361 28.36 height 0.0289 17.92 male: waist 0.0481 -3.09 Residual standard error: 4.39 on 502 degrees of freedom Multiple R-squared: 0.892, Adjusted R-squared: 0.892 F-statistic: 1.04e+03 on 4 and 502 DF, p-value: