Rather than use a dummy variable ( , 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  coded as...

Rather than use a dummy variable (, 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
 coded as
 for men and
 for women. (This type of indicator variable is sometimes used rather than a dummy variable.)

(a) What is the difference between the scatterplot of
 on
 and the scatterplot of
 on
?

(b) Does the regression of
 on
 have the same
 as the regression of
 on
?

(c) In the regression of
 on
, what is the fitted value for men? For women?

(d) Compare
 and
 in the regression of
 on
 to
 and
 in the regression of
 on
.