## Regression

Regression is a procedure for predicting the value of one metric (continuous) variable based on the value of another.

A regression equation involves a predictor variable (indepdent variable) and a criterion variable (dependent variable).

A regression line can be drawn which minimizes deviation (this is the least squares criterion).

This line has a slope ("b") and a point where it cross the y axis (the y intercept "a").

Regression equation: Y = bX + a (+ error)

Y = predicted score on criterion variable

X = score on predictor variable

## Multiple regression

Multiple regression uses multiple independent (predictor) variables to predict one dependent (criterion) variable

It yields a multiple correlation coefficient (multiple R)

• Multiple R is highest (the prediction is better) when the predictor variables have low correlation with each other, but high correlations with the criterion.
• If predictors are highly correlated with each other, combining them yields no new information. Predictor overlap is called multicolinearity.
• Multiple R is never lower than the highest simple correlation between an individual predictor and the criterion.
• Multiple R can be squared to indicate the proportion of variance accounted for by all the predictor variables together.

R-square = coefficient of determination

An F value can be calculated:

F = SS regression (df)/SS average (df)