Question

We have a dataset with n= 10 pairs of observations (2, yi), and n n Σ Ti = 683, Yi = 813, i=1 i=1 72 n n <* = 47,405, 1:4: = 56,089, 4 = 66,731. i=1 i=1 i=1 What is an approximate 99% confidence interval for the mean response at Io = 90?

Answer 1

And for n=10 paire of observations (xi, Y;) X; = 683, IY; 2013, [x;2-47405, Sri y; = 560@9 [4,2 = 66,731 The estimate of slope say b, of the line of best fit in bi n SX;y;-(5X; 154;). n 39;2-152,12 10 x 56004 *** 603x813 560290-555279 10x47405-(68372 474050-4 6 6 489 bi 0.7421 7561 The gs1. approximate confidence interval for slope is shoes 5611 bi t ten-2 ) V (1-2)5** 217.7.077 where shres- Syy- bisxy and Syy= y;2-n 52 = 66731- 10 X (13)? 2 634.1 Sxy = E(X;-)( YiG) = {xi yi - N 5cy =5608910x683 x 813 = 561.1 ond sxx= [(x,-1/2 = Exi?- n5? = 47405-10X(683)? = 47405-46648.9 = 756-1 on and intercept of the line of best fit is entit ģ- but = 81.3 - 50.68543 683 013 16 -0.7421 x 10 a = 30.6146 So the estimated regression equation is ŷ = a + b 2

where t( q n-21= 3.3554 Then the estimated value of mean response y at Xoc go is 9. = a +6X90 z 30.6146+0.7421 X 90 = 97.4036 So the gg.l confidence interval for mean response ad Xo = 90 in Sores Yo I tQ 12,1-2) I + + (Xo-x3 n-2 sxx for d=0.01, n-2=8 97.4036 + 3.3554 217.7077 (40-68.3) t 756.1 = {97.4036 † 3. 3554x 6.0471) = (97.40367 22.9748) - 674.4208, 120.3784)