Page 134 - Applied Statistics with R
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134 CHAPTER 8. INFERENCE FOR SIMPLE LINEAR REGRESSION
3.04
Empirical Mean of β 0 3.00 2.98
^ 3.02
2.96
0 2000 4000 6000 8000 10000
Number of Simulations
8.3 Standard Errors
So now we believe the two distributional results,
2
̄
̂
2
∼ ( , ( 1 + ))
0
0
2
̂
∼ ( , ) .
1
1
Then by standardizing these results we find that
̂
− 0 ∼ (0, 1)
0
̂
SD[ ]
0
and
̂
− 1 ∼ (0, 1)
1
̂
SD[ ]
1
where
