Question

Consider the following data for a dependent variable y and two independent variables, 31 and 22. 108 113 178 94 176 170 118 142 211 Round your all answers to two decimal places. Enter negative values as negative numbers, if necessary. a. Develop an estimated regression equation relating y to Xi. Predict y if Xı = 35. y = b. Develop an estimated regression equation relating y to 22. ĝ= + x2 Predict y if x2 = 15. ŷ = c. Develop an estimated regression equation relating y to X1 and 22. ŷ = Predict y if 21 = 35 and 22 = 15. y =

Answer 1

a) Let the neguessicu equation of you Xile: whene, ß = Gov (X,Y) - 1.8622] 2 = 7 - 8. . x = (19,2521) :. The neguession aan of you x, is : y = At x1 = 35; Ø = 114.429 6) Ler the regression equation of you xz be: = 22 + B₂ X2 whore, &r = Cox (X217) = 1, 5912) 3, * P.* (4.1314 The regression ear of you X2 is a Y = 79.4374+ 4.6912721 AT X2 = 15; ĝ = 24-4374 A her the nequessin equation as you X, and X2 be? 7= 8 + 8 x1 + V2 X 2 voliene, ?. = Eyizi (2121) – (sy: azi) (22 izi) 11.9591 (32)(Sai) – (E21127)? 22 = (Eyrazi) (2x) - (Syian (Zari dzi) = 5.1891 (Sure) bázt) – (36112,02 | 5- - - - X = - 24.5 11 | 2. The negression eqn of you x, aw X2 is: y = - 24.5047 + 1959 X, + 5.189X2 Arx1 = 35 and X2 = 15 ; 7 = 121.8953

COMPUTATIONAL TABLE:

Observation	Y	X1	X2	yix1i	yix2i	yi2	x1i2	x2i2	x1ix2i
1	95	29	13
2	108	47	11
3	113	24	17
4	178	51	17
5	94	40	6
6	176	52	19
7	170	75	8
8	118	36	13
9	142	59	13
10	211	77	16
Sum	1405	490	133	5311	697.5	15060.5	2852	154.1	-53

NOTE:

1) The lowercase letters indicate deviation from their mean. [y_i² = Σ(Y_{i -} ȳ)²]

2) Some of the calculations I have not done as it can be done easily.