Day 27
Assumptions for Linear Regression

EPSY 5261 : Introductory Statistical Methods

Learning Goals

At the end of this lesson, you should be able to …

• Check assumptions for a linear model.

Assumptions for a Linear Model

• L — Pattern is linear (plot your data)
• I — Observations are independent from each other (i.e., At a particular X value, one observation’s Y value does not affect observations’ Y values)
• N — The outcome variable is normally distributed
  • Some also add “no outliers”
• E — Equal variance
  • Variability in Y is constant at each X value (no fanning out of residuals on residual plot)

Linearity

Independence

• Consider all the coffee sales at a particular temperature
• Reasonable to assume that one day’s coffee sales does not affect another day’s sales

Normality

Equal Variance

• Should see that the range of residuals is constant (about the same) at each X value

A Residual Plot Showing Unequal Variance

Residual Plot to Evaluate Linearity

• Random pattern around the line residual = 0
• Means your model is not systematically over or under-predicting

A Residual Plot Showing Non-linearity

Assumptions for Linear Regression Activity

Summary

• For hypothesis test results for regression to be valid, we need to meet the following assumptions:
  • Linearity
  • Independence
  • Normality
  • Equal variances
• The mnemonic LINE can be used to hep remember the assumptions.