Question

We have a dataset with n = 10 pairs of observations (xi; yi), and
Xn
i=1
xi = 683;
Xn
i=1
yi = 813;
Xn
i=1
x2i
= 47; 405;
Xn
i=1
xiyi = 56; 089;
Xn
i=1
y2
i = 66; 731:
What is an approximate 95% prediction interval for the response y0 at x0 = 60?

We have a dataset with n= 10 pairs of observations (li, Yi), and n n Ii 683, Yi = 813, i=1 п n n m = 47, 405, Xiyi = 56,089, 4 = 66, 731. i=1 i=1 i=1 What is an approximate 95% prediction interval for the response yo at xo = 60?

Answer 1

Given E xi 683 x = n=10 813 81.3 47405468.3 )° x16 ssy = 2 SS x = {x, ² nx2 = Ssx=756.1 Ssy={y;2_ny2 66731 -10 ( 81.3) - 63 4.1 Ssxy = {(xl) - nx ý = Ssxy = 561.1 56111 B SSX 256.1 SSTotal - Ssy = 63 4.1 SSReg = ß, SsxY 561.1 x 0.742098 SSE - SsTotal - SSReg= 634.1-416,390967 = 217. 7090 33 56089 - 10 (68.3)(8), 3) & SSay - 0.742098 - 416.390967 -

Bo SSE re V n-2 27.2136291=5.21666 839 P = ï - B, F = 81.3-0.742098 (6803) 30.61 47066 ŷ = 30.6147 +0.7421 x at ý = 3016147 +0.1421 (60) Ý = 75.1407 t 0.025,8 = taginez Prediction interval is - 2.306 Itt + (% -0,2 + Ssx 7561 ŷ & tx/2n^2r (75.14075 24306 X 5.21666839 +(60-683) (751407 12.029637/1.19111229) (75.1407512-0296373x1609138091) (61.9826 is the g5 . for response to at to 260. 88.2988) predictions interval