7 - Multiple Regression

Question 1

What is multiple regression?

Answer 1

A way of predicting a dependent variable from a set of independent variables

Question 2

How many regression coefficients (b’s) does a multiple linear regression have?

Answer 2

One per independent variable

Question 3

What are the assumptions of multiple regression?

Answer 3

1. Independence
2. Normality
3. Homoscedasticity
4. Linearity
5. Multicollinearity

Question 4

What is the assumption of multicollinearity?

Answer 4

Two predictors should not be too highly correlated (0.8 or 0.9)

Question 5

When will a multiple regression model have a high R^2?

Answer 5

When the regression model has variables that are statistically significant

Question 6

How can an F-Test be used to test R^2?

Answer 6

An F-Test can be used to test competing models by testing the difference between R^2s

Question 7

What test can be used to test each partial regression coefficient, and how?

Answer 7

A t-test FINISH THIS BECAUSE IDKK

Question 8

What are the 3 ways to build regression models?

Answer 8

1. Hierarchical
2. Simultaneous Forced Entry
3. Stepwise

Question 9

Describe the hierarchical approach to building regression models.

Answer 9

Independent variables are entered in stages (based on theory)

Question 10

Describe the simultaneous forced entry approach to building regression models.

Answer 10

All independent variables are entred together.

Question 11

Describe the stepwise approach to building regression models.

Answer 11

Independent variables are entered according to some order. This could be in order of size/ correlation with the dependent variable or in order of significance.

Question 12

What R function can you use to determine the confidence intervals on the estimates of a regression model?

Answer 12

confint()

Question 13

What R function can you use to determine the standardized Beta coefficients of a regression model?

Answer 13

lm.beta() from the QuantPsyc package

Question 14

What R function can you use to compare the fit of 2 regression models?

Answer 14

anova()

Question 15

What is the Akaike Information Criterion?

Answer 15

A method for evaluating how well a model fits the data it was generated from.

Question 16

What R function can be used to generate AIC?

Answer 16

extractAIC()

Question 17

What AIC values indicate a better model fit?

Answer 17

Smaller values

Question 18

What is the root mean square error?

Answer 18

It is the square root of the variance of the residuals. In other words, it measures how far the predicted values are from the observed values in a regression analysis. (How concentrated the data are from the line of best fit).

Question 19

In what cases is the root mean square error most useful?

Answer 19

In cases where the model’s aim is to predict values.

Question 20

What root mean square errors are preferred?

Answer 20

Smaller values (0 indicates perfect fit).

Question 21

What R function can be used to get the root mean square error?

Answer 21

performance() from performance package.