10. EXAMPLE
• Example of simple
linear regression which
has one independent
variable.
11.
12.
13.
14.
15. Least Squares Estimation of b0, b1
• b0 Mean response when x=0 (y-intercept)
• b1 Change in mean response when x increases
by 1 unit (slope)
• b0, b1 are unknown parameters (like m)
• b0+b1x Mean response when explanatory
variable takes on the value x
• Goal: Choose values (estimates) that minimize
the sum of squared errors (SSE) of observed
values to the straight-line:
2
n
2
^ ^ ^
^
^ ^
y b 0 b1 x SSE i 1 yi y i i 1 yi b 0 b 1 xi
n
16. The least squares estimate of the slope
coefficient β1 of true regression line is
β1= Σ(Xi-X’)(Yi-Y’)
Σ (Xi-X’)2
The least squares estimate of the intercept
β0 of true regression line is
β0 = Y’ – β1x’