5. Regression

Question 1

What is correlation?

Answer 1

Standardised covariance between two variables.

Question 2

Why is the least squares solution so named?

Answer 2

It attempts to minimise the residual SS - so least squares.

Question 3

What are degrees of freedom for residual?

Answer 3

Total sample size, minus number of predictors, minus 1

Question 4

What are degrees of freedom for regression?

Answer 4

Number of predictors.

Question 5

If more predictors added to equation, what happens to R square?

Answer 5

It gets bigger.

Question 6

What can happen to the bs if IVs are highly intercorrelated?

Answer 6

R square might be significant, but none of the bs will be.

Question 7

Why is b called the partial regression coefficient?

Answer 7

Because b represents the expected change in DV (units) while controlling for other IVs.

Question 8

When should b, the unstandardised regression coefficient, be used?

Answer 8

1. When variables are in a meaningful metric
2. To explore policy implications
3. To compare results across samples or studies

Question 9

When should β, the standardised regression coefficient, be used?

Answer 9

1. When variables are not in meaningful metric

2. To compare relative effects of different IVs in the same study.

Question 10

When is missing data considered a concern?

Answer 10

Usually only when it’s over 5%

Question 11

When can sizes of b be used to compare relative importance of predictors in same sample?

Answer 11

When they are in the same metric, e.g. hours or centimetres.

Question 12

Should common causes be included in regression model?

Answer 12

Hell yeah! They must be included in order to interpret regression coefficients as effects validly.

Question 13

Do mediating variables have to be included to interpret regression coefficients as effects?

Answer 13

No. They’re just variables lying in between the cause and the effect – there could be any number of them, really, but they don’t reduce causality.

Question 14

Is a high R square more important for explanation or prediction?

Answer 14

For prediction.

Question 15

If you want to make statements about the effects of one variable on another, your interest is ____________

Answer 15

If you want to make statements about the effects of one variable on another, your interest is EXPLANATION.

E.g., Conservatism predicts life satisfaction. But doesn’t explain it. Conservatives more likely to be married, religious, etc. –these variables also account for some of the variance in life satisfaction

Question 16

What kind of effect does simultaneous regression estimate?

Answer 16

Direct effects.

Question 17

Regression weights in simultaneous regression change depending on ____________________

Answer 17

Regression weights in simultaneous regression change depending on the variables entered.

Question 18

In sequential regression, tests of the bs are affected by ____________.

Answer 18

In sequential regression, tests of the bs are effected by order of entry.

Question 19

What does a test of b reflect in sequential regression?

Answer 19

A test of b reflects the proportion of variance, say, VarX1 accounts for in VarY when it is entered in the analysis last. I.e. over and above the variables entered before it.

Question 20

What test statistic does t square for the b coefficient correspond to in sequential regression?

Answer 20

The F statistic for the test of delta R square (R square change)

Question 21

Sequential MR estimates the variance due to __________ effects

Answer 21

Sequential MR estimates the variance due to total effects. 18/10

Question 22

Does the order of entry in sequential regression change the overall R square?

Answer 22

No, but the order of entry will affect what portion of variance is explained by each variable.

Question 23

What is the formula for semipartial (part) correlation?

Answer 23

Square root of delta R square.

Question 24

What is the semipartial (part) correlation?

Answer 24

The correlation of Y with X1, when the effects of X2, X3 etc. are removed from X1 (not DV). So the effect over and above all other effects.

Question 25

How can you determine the unique effect/variance of a variable?

Answer 25

Square the semipartial (part) correlation.

Question 26

What’s the long way of getting semipartial (part) correlations?

Answer 26

Do several sequential regressions, entering each variable last.

Question 27

How do you calculate the total variance in the DV explained by a variable?

Answer 27

By squaring the zero-order correlation with the DV..

Question 28

How do you calculate the unique variance in the DV explained by a variable?

Answer 28

By squaring the PART correlation with the DV.

Question 29

How do you calculate the shared variance between variables?

Answer 29

By taking R square and subtracting the unique variance of each variable from it.

Question 30

In simple bivariate regression, r is equal to what regression coefficient?

Answer 30

Beta, the standardised regression coefficient

Question 31

In simple bivariate regression, from which other values can R square be derived?

Answer 31

By squaring r or Beta.