W12 - MULTIVARIATE STATISTICS

Question 1

Define multiple regression

Answer 1

Variation in X1 AND X2 explains variation in Y

Question 2

What linear combination of x1 and x2 explain variance in Y?

Answer 2

Partial regression coefficients are different to zero

Question 3

How much of the variance in Y is explained by variation in x1 and x2?

Answer 3

adjusted Rsqr

Question 4

What is a partial regression coefficient

Answer 4

the amount of change in Y as a consequence of a unit change in X1, after correcting for the variation in X2 that is shared (covaries) with X1.

Question 5

What happens when the covariance between two variables is zero

Answer 5

simple and multiple (partial) regression coefficients are the same

Question 6

How do you convert R^2 to percentage

Answer 6

(R^2)^2
Eg. Rsq = 0.7
Then - 0.7^2 = 0.49 = 49%

Question 7

What is a masking variable

Answer 7

A variable that displays no correlation when computed alone
It needs the variation from the variable it is correlated to for it to become apparent

Question 8

What is the combined explanatory power of using multiple variables?

Answer 8

R^2 gives the % variation in Y explained by the p (here, = 2) X
variables.
* 67% of the variation in Y is explained by variation in the two X variables, EVEN THOUGH when considered individually:
* X1 explains only 34% of the variation in Y
* X2 explains 0%

Question 9

In what 2 ways would a multiple regression result be surprising

Answer 9

1. Can’t always see which variables are important for explaining variance in Y just by looking at individual X variable relationships with Y
   * Need to know the relationship among the X variables.
2. Including multiple variables can improve how much variance in y can be explained
   * This again depends on the relationship among the x variables – as well as their association with Y.