multiple linear regression

multiple linear regression

allows us to make predictions with multiple independent variables

MLR is a model of

a hypothetical model of the relationship between the outcome variable and at least two predictor variable

R²

proportion of variability in y explained by all the 2+ predictions

How good is the line/the model?

how well is the criterion variable y predicted by the predictor variables; want small SS Error

R² is larger than

r²

R² increasing does not equal

explains significantly more variance

R² estimates the parameter

P²

R² is a biased estimator because

it inflates and overestimates P²

what is a better point estimate of P²

R² adjusted

How to test significance of R²

Omnibus F-stat; F = (SSR/dfR) / (SSE/dfE)

what does the slope covey

change in y with all other predictors being held constant

How good is each predictor?

how well does each predictor variable contribute to the model to help predict the criterion variable

how to test the significance of the slope

t-test; with df = N-k-1; b/sb

Is there a better model

compare “full" model” with all predictor variable of interest with a reduced model

significance test for the increase in explained variance, from the added variables

F-statistic; Fchange —> compare to Fcrti

assumption lack multicollinearity

should be no high inter correlations among two or more independent variable in a multiple regression mode