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Chapter 8
Inference for Simple Linear
Regression
“There are three types of lies: lies, damn lies, and statistics.”
— Benjamin Disraeli
After reading this chapter you will be able to:
• Understand the distributions of regression estimates.
• Create interval estimates for regression parameters, mean response, and
predictions.
• Test for significance of regression.
Last chapter we defined the simple linear regression model,
= + +
1
0
2
where ∼ (0, ). We then used observations ( , ), for = 1, 2, … , to
find values of and which minimized
0
1
2
( , ) = ∑( − ( + )) .
1
0
0
1
=1
̂
̂
We called these values and , which we found to be
0
1
∑ ( − ̄ )( − ̄)
̂
= = =1
1
∑ =1 ( − ̄ ) 2
̂
̂
= ̄ − . ̄
1
0
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