Linear and Multiple Regression

Question 1

What are regression’s used for?

Answer 1

To predict an outcome from a predictor variable.

Question 2

What is the equation of a straight line?

Answer 2

y=mx+c

Question 3

What does b0 represent?

Answer 3

The intercept

Question 4

What does b1 represent?

Answer 4

The slope

Question 5

What does the regression line aim to do?

Answer 5

Ensure the line of best fit produces the smallest amount of residuals.

Question 6

What does the R^2 value tell us?

Answer 6

How good the model/regression is - the amount of variance explained by the model.

Question 7

What does the F ratio tell us about a linear regressionn model?

Answer 7

If it is significant.

Question 7

What does the F ratio tell us about a linear regression model?

Answer 7

If the regression predicts a significant amount of the variation.

Question 8

How do you find the difference between the observed and predicted Y scores? (SS residual)

Answer 8

Predicted Y scores using the equation minus the actual Y scores, then square the values to stop them cancelling each other out.
∑(Y’− Y)^2

Question 9

How do you find the total variance of Y scores in the data set? (SS Total)

Answer 9

Each data point minus the mean for all Y data points, added together.
∑(Y - M)2

Question 10

What does the SS Residual tell us?

Answer 10

An estimate of the amount of variation that is NOT predicted by our regression

Question 11

How do you work out the SS regression?

Answer 11

SS Total - SS Residual

Question 12

What does the SS Regression tell us?

Answer 12

An estimate of the amount of variance explained by the regression of the model.

Question 13

What affects the estimate of the SS regression?

Answer 13

Sample size and the amount of total variation in the sample.

Question 14

How do you work out the R^2 value using SS values?

Answer 14

SS regression divided by the SS total

Question 15

What is another representation of SS regression?

Answer 15

SS m

Question 16

What is the F Ratio?

Answer 16

The ratio between two variances (predicted and error)

Question 17

How to work out the F ratio?

Answer 17

SS regression is divided by the degrees of freedom.

Question 18

What does the p-value mean?

Answer 18

It tells us whether the result is significant so we know whether to accept or reject the null hypothesis.

Question 19

What assumptions have to be met for a simple regression? (6)

Answer 19

• Outcome must be continuous
• Predictors must not have zero variance
• All values of the outcome should come from a different person/item
• The relationship we model in reality must be linear
• Homoscedasticity
• Residuals must be normally distributed

Question 20

What are the 2 types of multiple regression?

Answer 20

• Forced Entry Regression

- Hierarchical Regression

Question 21

What is the adjusted R^2?

Answer 21

R^2 will be an overestimate of the real R^2 In the population so it is adjusted down to allow for the overestimation of R^2.

Question 22

What are the unstandardised (b) and standardised (beta) coefficients used for?

Answer 22

Unstandardised - used within any equation.

Standardised - allows us to make comparisons across the predictors.

Question 23

What is the difference between Forced Entry and Hierarchical regression?

Answer 23

In forced entry, all the predictors are entered into the analysis at once. In hierarchical regression, some variables are controlled for.

Question 24

How do we compare models in hierarchical regression?

Answer 24

We check to see if more variance is explained in the second model compared to the first.

Question 25

If the beta value is positive for a dummy variable, what does this mean?

Answer 25

The category coded as ‘1’ is higher (scores higher) than the category coded as ‘0’.

Question 26

What is multicollinearity?

Answer 26

When predictors are highly correlated with each other.

Question 27

What numbers cause alarm in the collinearity VIF column?

Answer 27

Anything close to 10. (Anything over 5 is quite problematic).

Question 28

How much of the sample is allowed to be over 2SD away from the mean?

Answer 28

About 5%.

Question 29

What should the Cook’s distance be?

Answer 29

All below 1.