Week 2

Question 1

What are residuals?

Answer 1

Residuals are the portion of the score (case) which is not predicted by the regression. Since real world relationship is going to be perfect, there will always be some error and this is expected, however, large errors indicate that the regression model is not adequate, patterns in the residuals can indicate heteroscedasticity or non linearity or both and isolated cases with large residuals are likely to be outliers

Question 2

What does Mahalanobis distance show?

Answer 2

Mahalanobis distance provides a way to measure how similar some set os conditions is to a known set of conditions. It accounts for the covariance among variables

Question 3

What does linear regression plan to show?

Answer 3

linear regression looks to predict an outcome (DV) using predictor variables (IVs)

Question 4

Linear regression looks to predict a single quantitative DV from multiple quantitative and/or qualitative variables. Are relationships always linear? How can non linear IV’s be made to appear linear?

Answer 4

By transforming them using log functions and so forth

Question 5

what does the Pearson correlation measure?

Answer 5

Pearson correlation measures the strength of the linear relationship

Question 6

Does regression model imperfect relationships?

Answer 6

Yes

Question 7

In regression, do we predict y from X?

Answer 7

Yes

Question 8

What does the equation to predict Y from X look like?

Answer 8

Y’ = A + BX

Where ‘ indicates “predicted”

Question 9

The prediction of Y will not always be perfect. How is the error calculated?

Answer 9

Actual Y minus predicted Y

Y - Y’

Question 10

What does the sum of squares have to do with regression?

Answer 10

The sum of least squares is used to find the value of A and B that create the equation of the line of best fit

Question 11

Natural variation in Y indicate that the points of Y are dispersed in a scatter, how is this denoted?

Answer 11

SSY

Question 12

What is the total variation of Y separated into?

Answer 12

Total variation can be separated into “regression” and and “error”

Question 13

How is the total variance explained

Answer 13

R2 is equal to the Sum of Squares due to Regression divided by the Sum of Squares Total

Question 14

What is the R value

Answer 14

The R value is the correlation between the DV and the IV’s

Question 15

What is the R2 value?

Answer 15

The R2 value is the total amount of variation accounted for by the predictors

Question 16

What is the R2 adjusted?

Answer 16

Adjusted R2 represents the R2 after accounting for the number of predictors and the sample size

Question 17

What is the standard error of the estimate?

Answer 17

the deviation about the predicted values

Question 18

What are the regression coefficients?

Answer 18

Regression coefficients are the values of the B’s for the model.
The unstandardised values are in the units of the original measures
The standardised values are the z-scores and gives some indication of which variables have the biggest influence on outcome