Question

Question 7 Solve the problem. Consider the data set shown below. Find the estimate of the y-intercept of the v 03 23 8 10 11 x -2 0 2 4 6 8 10 1.5 0.94643 0 1.49045 0.9003

Answer 1

By the method of least square we can fit a regression line forming normal equations.

To find the best predicted value , we put the given value of predictor in fitted line.

(1) The given data us o 1x F20 2 4 6 8 Now, the least square regression line Y = at bx - we have to estimate a. how, normal equations to are. Ey = hat beX - Exy = a 2x + b&x? - 3 from the table we get Ey = 37, EX= 28, 2*4= 254 Ex² = 224 putting there in 4 ③ 37=7a + 286 - @ 254 = 28 at 224 b multiply by 4 28¢ +112b = 148 28 at 224 b = 254 (subtracting) - 112b = -106 b = 0.94 643 putting bin za= 37-28% 0.94643

22- 37 -26.5 za = 10.5 a = 1.49045 @ The Rain fall Inche) geven data I Yield (Per aere Y is xy an 1x2. 80 10.5 8.8 13.4 12.5 18.8 10.3 70 15. 6 16.0 112.9 46 S0.5 5 30.95 110.95 46.2 406.56 77:44 58.8 787.92/17 9.56 59.0 737.5 156.25 82.4 1549. 12/353-44 49. 22 So6.76 106.og 3109 293. 349 7.6.0 1185.6 243.36 78.8 (1260.8 1256 532.8 7187.81 1531.397 Linear regression model is Y= at by normal equations {y = natbex Exy = aɛxt bEX² - 2 putting the values, we get $32.8 = ga+ 119.9 b -3 7187.81 = 119.99+ 1531,39 - 9

® Xg multiply by 1919 we get also 1016.Ya + 127 46 416 = 60183.12 10XB 1a +13782.51 6 = 64 690.29 • subtractio -10361b -U837.1? Th=4.379 x betting value of b in ③ we get [â= 4.267) then becomes - £313A 4 42 6 7 | e ③ aiven regression line is ŷ = 3.5X-5.4 -- we have to find ŷ at x = ~112 from 0, when x= -102 ŷ = 315X1-112) - 5.4 1 9 = -9.6] Đ Given regression live in 9 = 19.4 +0.93% - 0 we have to find i at x=44 from 9 = 19.4 +0.93 X44 17 = 60139]

0 Given regression line is ŷ = 3x - we have to find } at x = 4.6 from 0 ŷ = 3x4,6 ♡ = 13.8