1. Ch12.1 Simple Linear Regression
The Simple Linear Regression Model
There exists parameters such that for any fixed value of x, the dependent variable is related to x through the model equation
ε is a random variable (called the random deviation) with
E(ε) = 0 and V(ε) = σ2
One can see how a dependent variable is related to an independent variable with a scatter plot.
Ch12.1

2. Ch12.1 Estimating Model Parameters
Principle of Least Squares
The vertical deviation of the point (xi,yi) from the line y = b0 + b1x is yi – (b0 + b1xi)
The sum of squared vertical deviations from the points
to the line is:
Ch12.2

3. The error sum of squares, denoted SSE, is
and the estimate of σ2 is
A computational formula for the SSE, is
The total sum of squares, denoted SST, is
The coefficient of determination, denoted by r2, is given by
Ch12.2

4. The least-squares (regression) line for the data is given by where
and
The fitted (predicted) values are obtained by substituting into the equation of the estimated regression line: The residuals are the vertical deviations
from the estimated line.
Ch12.2