Question

Problem 7. Consider the simple linear regression model Y1 = Bo + BiX; +€; for i=1,2,...,n where the errors Eį are uncorrelated, have mean zero and common variance Varſei] = 02. Suppose that the Xį are in centimeters and we want to write the model in inches. If one centimeter = c inch with c known, we can write the above model as Yį = y +71 Zitki where Zi is Xi converted to inches. Can you obtain the least-squared estimates of yo and from those of Bo and B, ? Show that the value of R2 = 1 - SSE remains the same for both model.

Answer 1

following images have solution:

Yes we can obtain Voff from &,&ßo 0 least square estimate 5 ßo - P- Biz Now, Ñ - Î *2;-2) (9,-Y) i Zi 72 2 = c X; , vì + 1, , - h. 12

- 24.7 * -- + x)) - c - メ I = (cx )(ママ) cx.-) ・イメージしたり、 らい BY - F-SZ マー!!」とメ 19. F - Of x 40g

& %= % - % Ž = % -28, c. X 1.8 z - eß .shs) asta {{l;-})? , which are mains unchanged. sốE, LY - , , ) ( - - y, 2 - 3)) - , (7-5-of.c(;->)) = 2,0--81663-3 ja R? = 1-SSE- 1-SSER - SSE! SST 357 .