Multiple Regression Analysis

1. Y and X must have a liner relationship.

2. X is not random and there is no multicollinearity among two or more of the independent variables.

3. The expected value of e is 0 (zero).

4. No heteroskedasticity, i.e., the error term’s variance is the same for all observations /does not exhibit a relationship with the independent variable.

5. No serial correlation, i.e. error terms are uncorrelated with one another across all observations.

6. The error term has a normal distribution.

Be sure to review and get comfortable with the standard form of a statistical software program’s output for a multiple variable regression analysis.

• Example multiple regression equation: Yi = b0 + b1X1i + b2X2i  + ei

• You will need to be able to:

• Use this equation to estimate a dependent variable (this becomes simple plug and chug once you are comfortable with the material)

• Test the overall validity of a multiple regression model (see Fcalc below)

• Perform tcalcs to test the validity of the y-intercept and individual slope coefficients.

• Determine confidence intervals for individual slope coefficients.

• Hypothesis testing to determine if a slope coefficient is statistically different from some specified value (maybe your colleague creating a similar model but deriving a different slope coefficient; this testing will determine if the difference is statistically significant).

• Determine the Standard Error of the Estimate (SEE)