Multiple Regression and Prediction

Question 1

What are the two types of covariates?

Answer 1

Continuous and Factor

Question 2

Describe continuous covarites?

Answer 2

Each slope coefficient relates to the expected change in density for a one unit increase in the covariates
The intercept coefficient relates to the expected density when all covariates are equal to zero

Question 3

Describe factor covarites?

Answer 3

Fitting variables as factors permits the response to vary with the covarities in a non-linear way
Typically fitted using treatment constraints, one level of the factor variable forms the baseline and the remaining levels of the factor has corresponding coefficients

Question 4

What are the degrees of freedom for confidence intervals?

Answer 4

N-P-1 where P is the number of explanatory variables fitted in the model, N is the total number of observations

Question 5

Adjusted Square Formula

Answer 5

1 - ((N-1)(1-R^2)/N-P-1)

Question 6

What does an adjusted R^2 closer to 1 indicate?

Answer 6

Better Predictive Power

Question 7

What is extrapolation?

Answer 7

Predicting for combinations of covariates that did not actually occur in the data