I'm solving exercises as preparation for a statistics exam and I'm scratching my head on the following exercise. I'll start by giving the data I have to work with:
n = 10; x (average) = 14; y (average) = 130; Sxx = 2528; Sxy = 21040; Syy = 184730.
I have to get a confidence interval for E(Y0), considering X0 = 18, with a degree of confidence of 99%.
So first I have to get the equation y^ = â + ^bx, which is: y^ = 13.481 + 8.3228x. Then substituting x with 18 I get y^ = 163.3994.
Checking the t-student table I get a t-value of 3.355 with 8 degrees of freedom. The CI will be something like: ]163.3994 - S3.355(1/10 + (18 - 14)^2/2528)^0.5, 163.3994 + (...) [
I get s = (1/(8)(Syy - 8.3228Sxy))^0.5
The thing is, the result of this is very far from what my teacher told me it should be (]142.0079, 184.5744[). Can you please tell me where is my mistake?