Multiple Linear Regression

Equation for Multiple Linear Regression

Ŷ=b₀+b₁x+b₂x…bmxm

where m = the number of prediction variables

what is b₀

y intercept

what is b_i

the i’th regression coefficient indicating how strongly predictor variable x₁ can be used to predict Y with the model

what is R²

coefficient of determination

proportion of variance of x shared with y

two ways to calculate R²

1. SSm/SSt

2. (1-SSr)/SSt

What is R

multiple correlation coefficient

correlation between predicted values Ŷ and observed values Y

how to calculate R

square root of R²

dfm

number of predictor variables

dfr

N-(m+1) OR N-m-1

where N = number of observations and

m = number of B coefficients

What is the measure of effect size and how is it calculated?

Cohen’s f²

R² / 1- R²

What is multicolinearity and how do we test for it?

High similarity between 2 or more predictor variables (usually r>0.9)

Check using Tolerance - 1-R², where R² is the goodness of fit of one predictor variable with all the others

Tolerance should be above 0.1

What is singularity and how do we test for it?

Look for high multivariate correlations, and low tolerances