Regression The Linear Model Flashcards
(53 cards)
What does a linear model with several predictors look like on a graph?
A 3d regression plane
SSr
Residual Sum of Squares. How well a linear model fits the data.
What is Cross validation of linear regression model
Ensures model accurately predicts samw outcome in a different group of people.
Methods of cross validation
Adjusted R squared
Steins method
data splitting
What does adjusted R squared do?
Tells how much variance in Y would be accounted for if the model had been derived from population.
What does Steins formula do?
Tells how well model cross validates
2 oversimplified common rules of thumb for sample size when using linear model?
10-15 cases per predictor
What is a good method of deciding desired sample size?
Desired effect size
Amount of power wanted for statistical significance
Size of sample for large effect
77 participants with up to 20 predictors
If medium effect expected use sample size of
55-150 (20 predictors)
If small effect expected use sample size of
1043 cases with 20 predictors
3 main stages in fitting a linear model
Initial data checks
Run initial regression
Check residuals
4 Steps in initial checks when fitting linear model
Check linearity and unusual cases
Graphs: scatter plots
If lack of linearity
Transform data
Fitting linear regression model: run initial regression
Save diagnostic statistics
Fitting linear regression model : check residuals
Use zpred and zresid graphs to check 3 things Linearity Homodasticity Independence Check normality with histogram
Fit general linear model: If glm assumptions met and no bias
Model can be generalized
Fit general linear model: If heteroscedasticity found.?use either
Weighted least squares regression
OR
Bootstrap and transform data
Fit general linear model: If no normality
Bootstrap and transform
OR
Use a multi level model
Fit general linear model: If data lacks independence
Use a multi level model
Glm : multicollinearity defn
Strong corellation between 2+ predictor variables
Is less than perfect collinearity avoidable?
No. It is virtually unavoidable
What does perfect collinearity mean?
One predictor variable has a perfect linear correlation
Glm: multicollinearity and untrustworthy b’s
As correlation between two predictor variables increases the standard error of b’s increases. This increases the chance b is unrepresentative of the population
Compare glm with one predictor: what does large value of r squared mean
Better fit of model
