LINEAR REGRESSIONS Flashcards
What is the interpretation of
a) b1 in linear reg?
b) b1 in logistic reg?
c) b1 in cox regression?
d) b1 in poisson regression?
a) Increase in Y
b) Increase in the log odds of Y
c) Increase in the log hazard of Y
d) Increase in the log rate of Y
and all: per unit increase in x1, adjusted for all other variables in the model
Does Pearson correlation coefficient (r) measure the strength of any association?
Apparently not
But b does
What’s a good method to fit a regression line that best fit the data?
Least-square methods (minimizes the sum of squared deviations from regression line; i.e., the residual sum of squares)
How does the interpretation change when we re-center?
Expected response at the average x value
What happens to the slope when we normalize the variables?
The interpretation of the coefficient doesn’t change, but we end up with slope = correlation
What is R2?
The proportion of variance explained by the model
it’s also r^2 (as in the correlation)
What is a balanced design
When, in a multiple linear regression, we have uncorrelated predictors
2 reasons why correlation amongst predictors cause problem
- Variance of all coefficients increases
2. Interpretation become hazardous (when x1 changes, everything changes)
What is adjusted R2
it’s R2, so the proportion of variance explained by the model, with a penalty term for high numbers of predictors
Difference between confidence and prediction bands?
Confidence: reflects uncertainty about regression line
Prediction: also includes the uncertainty about future observations
Collinearity
When two predictor variables are correlated with each other
- it complicates model estimation, brings nothing new, may create bias, unstable estimates
Occam’s razor
Among competing hypotheses, the one with the fewest assumptions should be selected
Assumptions of linear model
- Linear relation bw x and y
- Normal residuals
- Constant variability of residuals
- Independence of residuals
