Applied regression analysis Exercise 5.2. \'Suppose that the means and standard

Question

Applied regression analysis Exercise 5.2. 'Suppose that the means and standard deviations of Y and X are the same: (a) Show that, under these circumstances, where Byx is the least-squares slope for the simple regression of Y on X, Bxy is the least-squares slope for the simple regression of X on Y, and rxy is the correlation between the two variables. Show that the intercepts are also the same, Ayx Axiy- why, if Arx = Axir and Brix = Bry, is the least-squares line for the regression of y (b) on X different from the line for the regression of X on Y (as long as

Explanation / Answer

(c) No, the fact that expected height of a son whose father is taller than average is also greater than average but to a smaller extent and expected height of a son whose father is shorter than average is also smaller than average but to a smaller extent, does not imply a contradiction as the correlation between father's height and son's height is not exactly 1 which means they are not perfectly linearly correlated. The extents to which the heights differ will not always be same and can offest each other still implying the fact that Sx=Sy and Xbar = Ybar

(e) Recruiting a group of children who are reading substantially below grade level and observing their performance after one year is a poor reseach design as there is no control group in this expt. A control group of children with normal reading levels should also be taken and the program tested on them as well and then the efficacy of the program should be compared and tested. Having a control group in any research design alsways enhances the dseign and makes the concusions more effective.

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