Multiple linear regression

Question 1

What is the equation for multiple linear regression and what does it mean?

Answer 1

𝐘̂=𝐛_𝟎+𝐛_𝟏 𝑿_𝟏+𝐛_𝟐 𝑿_𝟐+𝐛_𝟑 𝑿_𝟑+𝐛_𝟒 𝑿_𝟒

Ŷ (Y hat) = The predicted outcome based on the regression model

X1, X2, X3, X4 = The predictor variables (the factors influencing Y)

𝑏_0 “(beta−zero)” = The intercept, representing the predicted value of Y when all predictors are 0

𝑏_1 (beta-one), 𝑏_2 (beta-two), 𝑏_3 (beta-three), 𝑏_4 (beta-four) represent the change in the predicted Y for each 1-unit increase in each predictor

Question 2

all the assumptions for multiple linear regression are the same, however there is one new one. What is that?

Answer 2

No multicollinearity
Multicollinearity = when predictor variables are strongly correlated with one another, means they are measuring the same thing

Can have little or moderate multicollinearity, but not strong

Question 3

How can we assess or detect multicollinearity?

Answer 3

• High correlation coefficients
• High variance inflation factors (VIFS)

Question 4

What is the equation for VIF?

Answer 4

VIF = 1/(1 −𝑅𝑖2)

Where Ri2 is the R squared value obtained by regressing the ith predictor variable on the remaining predictor variables

Question 5

How do we calculate the VIF by hand?

Answer 5

we run a linear regression model for each of the predictors

Question 6

What are the key concepts?

Answer 6

R-squared
F-value
Regression coefficient

Question 7

What does R-squared measure?

Answer 7

The proportion of variance in the outcome variable that is predictable from the predictor variable
- ranges between 0 and 1

Question 8

What is adjusted R-squared?

Answer 8

adjusts R-squared for the number of predictors in the model
- provides a more accurate measure of the goodness of fit/tells us more about model accuracy when more than one predictor variable is used
- always less than or equal to R squared

Question 9

What is Cohen’s f2 (f squared)

Answer 9

The effect size

Question 10

How to interpret the effect size?

Answer 10

small = 0.02
medium = 0.15
large = 0.35