1.1 Basics of Multiple regression and underlying assumptions

Question 1

What are the assumptions of multiple regression?

Answer 1

a) Linear relationship exists between the dependent and independent variable
b) Residuals are normally distributed
c) Variance of the error terms is constant for all observations (heteroskedasticity)
d) Residual for one observation is not correlated with that of another observation (serial correlation)
e) Independent variables are not random, and there is no exact linear relation between any 2 or more independent variables (multicollinearity)

Question 2

What are multiple regression models used for?

Answer 2

Multiple regression models are used to
a) Identify relationships between variables
b) Forecast variables
c) Test existing theories

Allows for considerations of multiple underlying influences on the dependent variable

Question 3

What does multiple regression do

Answer 3

Multiple regression methodology estimates the intercept and slope coefficients such that the sum of the squared error terms is minimized.

Question 4

What is the residual under multiple regression

Answer 4

The residual is the difference between the observed value and the predicted value

Question 5

What is the use of the p-value?

Answer 5

1. The idea is to use the p-value to evaluate the null hypothesis that a slope coefficient equals zero.
2. P-value is the smallest level of significance (ᵅ)for which the null hypothesis can be rejected
3. Significance of coefficients by comparing the p-value to the chosen significance level
4. If the p-value < significance level, then the null hypothesis can be rejected
5. If the p-value > significance level, then the null hypothesis can’t be rejected

Question 6

How to interpret multiple regression results

Answer 6

• Intercept term is the value of the dependent variable when the independent variables are equal to zero
• Each slope coefficient is the estimated change in the dependent variable for 1 unit change in the independent variable while holding the other independent variables constant
  o Slope coefficients in multiple regression are called partial slope coefficients