by Albert Major
REGRESSION RECAP
• A correlation alone is incomplete. You need the p value and the confidence interval before you draw conclusions.
• A correlation near zero is weak. You cannot decide if a relationship exists without significance testing.
• In a regression equation, b0 is the intercept. It is the expected value of Y when X is zero.
• b1 is the slope. It tells you the expected change in Y for each unit change in X.
• Regression does not always produce a straight line. Polynomial terms create curved fits, but simple linear regression assumes linearity between predictor and outcome.
• A slope can be positive, negative, zero, or undefined. A zero slope is a flat line. An undefined slope is vertical.
• R squared shows the proportion of variance in the outcome explained by the model. It reflects how much of the outcome you can account for with your predictor.
CATEGORICAL PREDICTORS AND DUMMY CODING
• To put a categorical predictor into a regression model, you convert it into numeric form.
• Dummy coding uses 0 and 1.
• The group coded 0 is the reference group.
• The intercept becomes the mean of the reference group.
• The slope becomes the difference between the reference group and the other group.
• Example: gender coded as female 0 and male 1.
– Intercept = average of females
– Slope = (male mean) minus (female mean)