Multiple Liner Regression (2)

Summaries

Dummy Variables – independent variables with binary features

1. Independent variables represent a complete set of classification
2. Y^ = b0 + sum(bi*Xi^)
3. b0 represents the average Y due to the last classification not specified. (this last classification is not specified to prevent linear dependency between the dummy variables as all information are contained in Y and Xi)
4. bi represent the different between the effect of Xi and the last classification
5. DOF = n (data point) – (k+1) (number of classification, k is the number of independent variable)

Heteroskedasticity: error term variance is not constant across the observations

1. Unconditional Heteroskedasticity: does not depend on the independent variable. Spread is random. Does not cause much problem
2. Conditional Heteroskedasticity: e.g. variance increases as the value of the independent variable increases => cause big problem

Problem: standard error is too small, since the expected value is unchanged => increases type I error (reject what should not be rejected) (Power = 1- Type II error)

Breusch-Pagan Test for conditional heteroskedasticity:

Chi-test with nR² with DOF = k (# of independent variable), n is the # of sample

R² is obtained by regressing the 1^st regression squared residual against the independent variable

Correction: Use White-corrected standard error if there is heteroskedasticity