Question

Consider the following set of ordered pairs shown below. Assuming that the regression equation is y with caret=1.601+0.788x and the SSE=5.15​, construct a​ 90% confidence interval for x=5.

x	55	00	44	33	44	11
y	66	22	66	44	33	22

Calculate the upper and lower limits of the confidence interval.

UCL	=
LCL	=

Answer 1

Sxx =Σ (Xi - X̅ )2 = 18.83333334
Syy = Σ( Yi - Y̅ )2 = 16.83333334
Sxy = Σ (Xi - X̅ ) * (Yi - Y̅) =  14.83333334

Estimated Error Variance (σ̂2) =
S2 = ( 16.8333 - 0.7876 * 14.8333 ) / 6 - 2
S = 1.1347

Confidence Interval of
Ŷ = 1.6018 + 0.7876 X
Ŷ = 5.5398

t(0.0985/2) = t(0.1/2) = 2.132
X̅ = (Xi / n ) = 17/6 = 2.8333


90% confidence interval is (3.9797 < < 7.0999 )