Simple linear regression

Question 1

What are the assumptions of simple linear regression?

Answer 1

• outcome variable is interval/ratio level (continuous) data
• predictor variable is interval/ratio or categorical (with 2 levels)
• each observation is independent of the others (or each score should come from a different ppts)
• Non-zero variance, predictor variable must vary, not al values should be same across ppts (can be checked using scatterplot)
• The relationship between 2 variables must be linear
• residuals should be normally distributes
• Variance of the residuals is constant along the values of outcome variables

Question 2

How do we check linearity?

Answer 2

when the red line is relatively flat, and a flat line does not show a strong curve or pattern (using models residuals)

Question 3

How do we check normality of residuals?

Answer 3

• most points fall close to the dash line on
• can run Shapiro Wilk test to double check

Question 4

How do we check homoscedasticity (variance)?

Answer 4

• red line is roughly flat and with no clear pattern
  (on residual models)
• an also double check by testing the hypothesis using the Breusch-Pagan test

Question 5

What are the key concepts for analyzing and interpreting simple linear regression results?

Answer 5

R-squared
F-value
Regression coefficient

Question 6

What is R-sqaured?

Answer 6

The coefficient of determination
Indicates a goodness of fit
- varies between 0 and 1
- 1 means perfection (predicted perfectly)
- doesn’t tell us significance
- F-test tells us about significance

Question 7

What is (unstandardised) regression coefficient?

Answer 7

• (b)
• explains the relationship
• positive one indicates predictor variable and outcome variable move in same direction
• neg says opposite

Question 8

what do effect size numbers mean?

Answer 8

small = 0.02
medium = 0.15
large = 0.35