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2. We want to study how parent's heights affect children's height. Consider the regression model of Y=student's height (ft) on X1=mother's height (ft), X2=Gender Dummy variable. (female=0, male =1): Y = Bo + B1X1 + B2X2 (a) If the mother's height is 5.5 feet, what is your best prediction for the student's height, if the student is a male? What is the approximated 95% confidence interval for this prediction? Y = 3.4909 + 0.3517X, + 0.5048X2 D = 3.4909 + 0.3517 x 5.5 + 0.5048 x 1 = 5.93 D + 2se = (5.46, 6.40) (b) How to interpret the estimation of two coefficients B, and B2 in the following table? B1 : Keeping other factors unchanged, when mother's height increase by 1 unit, the children's height increase by 0.3517 unit. B2: Keeping other factors unchanged, on average male students are 0.5048 feet taller than female students. (c) What is the R-Square, R-adjusted and F-stat for this regression? R - Square = 0.57 Adjusted R Square = 0.56 (d) Do a 2-sided t-test on B, at the significance level of 0.05