Rather than use a dummy variable (D, coded as 1 for men and 0 for women) as the explanatory variable in a regression of responses of men and women, a model included an explanatory variable X coded as +1 for men and -1 for women. (This type of indicator variable is sometimes used rather than a dummy variable.)
(a) What is the difference between the scatterplot of Y on X and the scatterplot of Y on D?
(b) Does the regression of Y on D have the same R2 as the regression of Y on X?
(c) In the regression of Y on X, what is the fitted value for men? For women?
(d) Compare b0 and b1 in the regression of Y on D to b0 and b1 in the regression of Y on X.