Lecture 7_MR with 3+ variables

Question 1

A partial regression coefficient (b) for a particular predictor (IV)…

Answer 1

simultaneously controls for (or adjusts for) the influence of all the other IVs in the model.

Question 2

To minimize bias in the estimate of a key IV’s regression coefficient, what should we try to include?

Answer 2

it is important to include common causes (if not included it will attribute too much influence to the DV)

Question 3

How do we interpret the regression coefficient (b) for a particular predictor (IV) in MR with 2+ variables?

Answer 3

The influence of IV on the DV, “holding all other predictors constant”

Question 4

The standardized coefficients (β) provide a measure of …

Answer 4

the relative importance of the IV’s

Question 5

What must we do to the semipartial (part) correlations to obtain their unique contribution to the variance explained?

Answer 5

square it (sr²)

Question 6

How do we determine if one standardized coefficient (β) is significantly different than another?

Answer 6

1. calculate the standard error of the difference between two β coefficients (Note that this involves working with the inverse of the correlation matrix among the IVs.)
2. conduct a t-test on the difference in their β coefficients (able to because they are on the same metric) t = (β₁ - β₂)/SE₁-₂

Question 7

What is T.Z. Keith’s “trick” to get the standard error of the difference between two β coefficients without having to use the inverse matrix?

Answer 7

1. Use the DESCRIPTIVES command with the /SAVE option to create standardized versions of the two predictors that we wish to compare.
2. Form two new terms from these variables as SUM2 = (ZX1 + ZX2) DIF2 = (ZX1 – ZX2)
3. Substitute these into the regression equation in place of X1 and X2 and examine the test of significance on the difference term.

Question 8

When using MR solely for the purpose of prediction, what is our goal for R²?

Answer 8

maximize R² (Any variable that increases its value is a candidate for entry into our model)

Question 9

When using MR in explanatory work (theory testing), what is our goal for R²?

Answer 9

maximizing R² is less important.
– start with a set of variables that we theorize to be related to the DV, put these into our model and see how large the resulting R² value is.

Question 10

What tool is useful for displaying our causal thinking regarding a set of variables?

Answer 10

Path diagram

Question 11

What are the criteria for a proper table?

Answer 11

double spaced
no vertical lines
note at bottom (with R², F, df, and p values)
Table title with description at top