WEEK 6

Question 1

Write a formal multiple linear regression statistical model

Answer 1

yi = b0 + b1xi1 + b2xi2 + … + ei

Question 2

Define multiple linear regression

Answer 2

Has a continuous response variable like a simple linear regression but it has more than one continuous predictor (x1, x2)

Question 3

What are the basic assumptions of a multiple linear regression?

Answer 3

Linearity, normally distributed, residuals have homogeneous variances and predictors should not be strongly correlated (no collinearity)

Question 4

How does the slope parameter differ between the linear and multiple regressions

Answer 4

MLR has 2 slopes.
The effect of the response on the predictor is controlled by the effect of the 2nd, 3rd … predictor
In another words, it explains the change in x2 per unit of Y holding x2 constant

Question 5

Describe an interaction in MLR

Answer 5

The effect of X1 on Y depends on the level of X2 (vice-versa)

Question 6

How do we account for interactions in MLR

Answer 6

We add an interaction coefficient to the model, a multiplicative effect
Eg. B3 (X1i * X2i)

Question 7

How do we detect collinearity

Answer 7

Brainstorm which predictor variables in your model are likely to be correlated before building the model
Plot each variable against each other to check for effects
Calculate the tolerance and VIF
Lower tolerance is not good, T > 0.1 is really bad
High VIF is bad, VIF > 10 is really bad (strong correlation)

Question 8

In SLR we call the slope a regression slope. What is it called in a MLR?

Answer 8

Partial regression slope.

Question 9

What problems would we face when interpreting a model that has correlated variables?

Answer 9

Correlated predictors increase uncertainty in the effects of the predictor on the response variable, diminishing the power of the model.