Answer Happy

For part vi and vii, look at the equations below.
13. Let y be any response variable and x a binary explanatory variable. Let {(tiBi): i = 1, ..., n} be a sample of size n. Let no be the number of observations with t; = 0 and 7; the number of observations with 2; = 1. Let y, be the average of the yi with xx = 0 and 7, the average of the y; with 2: = 1. i. Explain why we can write n no = (1 – , ni = X i=1 i=1 Show that 7 = n/n and (1 - 1) = 10/n.. How do you interpret z? ii. Argue that 7. = no (1 – ti]yi, T1 = ni? DAY: i=1 iii. Show that the average of y, in the entire sample, y, can be written as a weighted average: y = (1 – 77, + xy [Hint: Write y = (1 - *;+:] iv. Show that when x; is binary, 12 «?- (T) = 7(1 – 7). [Hint: When a, is binary, a = 2:.] v. Show that 72 72 Xiyi - Ty = [(1 - 7) (71 - T.). i=1 vi. Use parts (iv) and (v) to obtain (2.74). vii. Derive equation (2.73).

80 = 7o [2.73] Bo = 7ı - To [2.74]