Linear Regression

Distribution of Parameters Since, a and b are constants and xi is a constant for i, then

Distribution of Parameters

Distribution of Parameters

Distribution of Parameters

Distribution of a Linear combination of normals

Distribution of a

Summary

Residuals

Residuals

Sum of Squares

Sum of Squares

Statistical Inferences

Statistical Inferences

Sum of Squares

Sum of Squares

Statistical Inferences Recall,

Statistical Inferences

Sum of Squares

Sum of Squares

Inference on a Mean Response

Inference on a Mean Response

Inference on a Mean Response

Inference on a Mean Response Unfortunately, we do not know s2, but we do have an estimate for s2. Recall,

Inference on a Mean Response Unfortunately, we do not know s2, but we do have an estimate for s2. Recall,

Inference on a Mean Response

Sum of Squares Compute 95% C.I. for 170 temp

Inference of Future Response