1. MULTIPLE REGRESSION ANALYSIS: THE PROBLEM OF ESTIMATION
CHAPTER 7.
MULTIPLE REGRESSION ANALYSIS: THE PROBLEM OF ESTIMATION

2. The Three Variable Model
Yi = 1 + 2X2i + 3X3i + ui
CLRM:
E(ui / X2i, X3i) = 0
Cov (ui, uj) = i  j
Var (ui) = 2
Cov (ui, X2i) = cov (ui, X3i) = 0
The Model is correctly specified
No exact linear relationship between X2 and X3
Zero mean value of ui
No serial correlation
Homoscedasticity
Zero covariance between ui and Xi
No Specification Bias
No Multicollinearity

3. Multicollinearity

4. Two Variable Multiple Regression Model
Yi = 1 + 2X2i + 3X3i + ui

5. Yi = 1 + 2X2i + 3X3i + .....+ nXni + ui
What about for more than two variables in Multiple Regression Analysis?
Yi = 1 + 2X2i + 3X3i nXni + ui

6. R2 and Adjusted R2 Example:
Comparing two R2 for two models, then selecting the model with higher R2. Here, two models contain the same dependent variable but different independent variables. This can be done readily if an alternative coefficient of determination is considered.

7. K: number of parameters in the model including the intercept
Adjusted R2
K: number of parameters in the model including the intercept