Lecture 10 - Multiple Regression

Question 1

What is regression analysis?

Answer 1

Techniques that allow us to asses the relationship between one dependent variable and several independent variables

Question 2

What does regression allows us to do?

Answer 2

Predict using multiple independent predictors (IV), the effect that each IV (predictor) has on the DV

Question 3

What can we not assume about regression analysis?

Answer 3

Causality

Question 4

What is multiple linear regression?

Answer 4

It’s an extension of simple linear regression and has similar underlying assumptions

Question 5

What does the standard error of estimate do?

Answer 5

Provides an index of the general error that you are making with you predictions

Question 6

Is it or is it not possible to calculate confidence intervals around your prediction?

Answer 6

It is

Question 7

What is the standard error of estimate?

Answer 7

For every point on the regression line you can calculate the residual error - the standard error of estimate is the standard deviation of the errors of estimate

Question 8

Why is SEE useful?

Answer 8

Indicates the amount of error to expect, on average, in your predictions
Gets a sense of accuracy of your predictive model
Assumes random error

Question 9

What does the residual mean in the residual analysis?

Answer 9

It’s the part of the data that cannot be explained by the statistical model

Question 10

What does it mean if there is a pattern in the residual error?

Answer 10

If there’s a pattern in the residual then it is the action of a systematic error?

Question 11

What does homoscedascity mean?

Answer 11

The same spread of data

Question 12

What are the different variables in multiple linear regression?

Answer 12

Predictor variables, criteria variables, predictor variable

Question 13

Multiple Linear Regression retains what squares approach?

Answer 13

The least squares - using the line that has the lowest sum of squared residuals

Question 14

What are some limitations and assumptions of regression analysis?

Answer 14

Ratio of cases to predictor - the cases to predictor must be high enough to make the regression model stable and useful

Outliers among the predictors and criteria variables - the least squares approach means that the residuals can have a large impact

Question 15

What are limiting factors for MLR?

Answer 15

Multicollinearity (high correlations between variables r

Question 16

Example of MLR equation

Answer 16

Six variables - overall quality of the lectures, teaching skills of the lecturer, quality of the tests and exams, lecturers perceived knowledge of subject, students expected grade, the enrolment of the course
Equation - overall =b1(teach) + b2(exam) + b3(knowledge) + b4(grade) + b5(enroll) + a

Question 17

What are the selection methods in multiple linear regression?

Answer 17

Enter - all variables entered together 
All subjects regression
Backwards elimination
Stepwise regression (forward selection)
The model is not reality (Steven jay Gould’s sin of reification)
CANNOT IMPLY A CAUSAL RELATIONSHIP

Question 18

Summarise MLR

Answer 18

Regression analysis are techniques that allow us to asses the relationship between one dependent variable and several independent variables

Question 19

What does regression allows us to do?

Answer 19

To predict using multiple independent predictors (IV)

Understand the effect that each IV (predictor) has on the DV

Question 20

Can we assume casuality?

Answer 20

No - the same as correlation analysis

Question 21

Why do we do residual analysis?

Answer 21

We need to understand how good the analysis is and is it systematic or random error