Multiple Liner Regression

Summaries

In multiple liner regression, the slopes are called partial slope coefficients.

When one more variable is added, the coefficient will change unless the new variable is independent (no correlation) from the previous one.

The p-value is the smallest level of significant that the null hypothesis won’t be rejected.

Confidence intervals of coefficients

= b^+/- t*sigma_b

Assumptions:

1)      There is linear relationship between the dependent and independent variables

2)      E(error) = 0 conditional on independent variable

3)      All errors are independent, with equal variance, mean=0 and Gaussian

4)      There are no linear relationships between the independent variables.

F-test:

F=MSR/MSE = RSS/k / SSE/(n-k-1)

*** Even the null hypothesis is “=”, it is still one-sided test and using F-test

Adjusted R² = 1- ((n-1)/(n-k-1)*(1-R²))

-          adding more variables will increase R² but may reduce Adjusted R²