356 Chapter 9: Regression
Simple Linear Regression
Start
Quit
44
Sample size = 15
Add This Point To List
Remove Selected Point From List
Data Points
Clear List
49,12
52,14
38,9
55,16
32,8
57,18
54,14
44,12
x =
y = 12
a =
b =
−2.51
0.32
The least squares estimators are as follows:
Average x value =
Sum of squares of the x values =
46.13
33212.0
The estimated regression line is Y = −2.51 + 0.32x
S(x, Y)
S(x, x)
S(Y, Y)
SSR
=
=
=
=
416.2
1287.73
147.6
13.08
100
80
60
40
20
0
-20 50 100 150 200 250 300
FIGURE 9.3
we see that it is a linear combination of the independent normal random variablesYi,
i=1,...,nand so is itself normally distributed. Using Equation 9.3.1, the mean and
variance ofBare computed as follows:
E[B]=
∑
i
(xi−x)E[Yi]
∑
i
xi^2 −nx^2
=
∑
i
(xi−x)(α+βxi)
∑
i
x^2 i−nx^2