Residual Analysis

Question 1

What are four assumptions made for simple linear regression measures of variation?

(Hint: L, I, N, E)

Answer 1

Linearity
The relarionship between X and Y is linear

Independence of errors
The errors are independent of one another

*Normality of Error*
The errors (ε<sub>i</sub>) are normally distributed

Equal variance (aka Homoscedasticity)
The variance of the errors (ε_i) is constant

Question 2

What is residual analysis?

Answer 2

Residual analysis evaluates the assumptions for regression and determines whether the regression module/method is appropriate.

The residual is equal to the difference between the observed Y and the predicted Y: e_i = Y_i - Ŷ_i

Question 3

How is linearity evaluated for a regression model?

Answer 3

The residuals are plotted on the Y axis and the X values (independent variables) are plotted on the X axis. If the residual plot does not have any apparent pattern, the linear model is appropriate for the data.

Question 4

How is the independence of errors assessed?

Answer 4

To assess the independence of errors, you plot the residuals on the Y axis, and time on the X axis. If the plot shows a cyclical pattern, it violates the assumpation of independence.

Question 5

How is the normality of residuals assessed?

Answer 5

If the normal probability plot of the residuals in close to a straight line, you can determine that the normality assumption is met.

Question 6

How is the equal variance of residuals assessed?

Answer 6

If there are no obvious patterns in a residual plot, the equal variance condition is met.