Simple Linear Regression Populations and Parameters

1
Simple Linear Regression Populations and
Parameters

• Chapter 11

2
Simple Regression

• Single independent variable
• Dependent variable y
• Linear function

3
Assumption of Linearity

• Assumption of Linearity the slope of the
  equation does not change as x changes
• Linearity is not always a reasonable assumption

4
Random Error Term

• Random Error Term
• The model
• When we assume that the s are constants, the
  only random portion of the model for is the
  random error term .

5
Formal Assumptions of Regression Analysis

• The relation is, in fact, linear, so that the
  errors all have expected value zero for
  all i.
• The errors all have the same varianceVar
  for all i.
• The errors are independent of each other
• The errors are all normally distributed is
  normally distributed for all i.

6
Figure 11.2 Theoretical Distribution of y in
Regression
7
Estimating Model Parameters

• Intercept
• Slope
• is another population paramater