Final session 12b

Question 1

If our multiple regression analysis yields several t-tests, should we be concerned about Type I errors?

Answer 1

It is possible that the overall model is NOT significant, but some regression coefficients are
It is recommended that the overall model is a significant predictor of the DV before you interpret the results of individual coefficients (i.e., F-test for the model is significant)
In this way, there is at least some protection against Type I errors

Question 2

Why/how is R2adj used for model selection?

Answer 2

R2 always increases if we add predictors
R2adj may decrease if new predictors don’t help predict the DV very much
R2adj will aid in picking a parsimonious model
Pick the model that has the highest R2adj

Question 3

Multiple regression can use what IVs

Answer 3

both continuous and categorical

ANOVA is a special case of multiple regression with categorical IVs With one categorical IV → one-way ANOVA
With two categorical IVs and their interaction → two-way ANOVA

Question 4

When categorical IVs are used in multiple regression what is then used

Answer 4

some categorical coding scheme is used

For a categorical IV with k levels, k − 1 variables must be used to represent the IV

Question 5

what are Some coding schemes

Answer 5

Deviation coding -

Dummy coding - mean Helmert coding -

Question 6

explain Deviation coding

Answer 6

compares group means to the grand mean

Question 7

explain Dummy coding

Answer 7

compares group means to a reference group’s

Question 8

explain Helmert coding

Answer 8

compares mean of a group to mean of later groups in coding scheme (requires the groups are in some kind of order)

Question 9

what will we focus o in this class for coding

Answer 9

dummy coding

Question 10

The k − 1 dummy codes have what to represent group membership

Answer 10

0’s and 1’s

Question 11

what is the Reference group in dummy coding

Answer 11

Has 0’s on all dummy codes
Often times a control group
The means of the other groups are compared to the reference group

Question 12

what are the Dummy coding steps

Answer 12

Step 1: Create k − 1 new variables
Step 2: Choose one of the groups to serve as the reference group
Step 3: Assign 0’s to the reference group for all dummy codes
Step4: For the jth dummy code (j=1,…,k−1), assigna 1 to the jth group. Assign all other groups 0 for the variable. And repeat Step 4 as necessary.

Question 13

explain Step 1 - create new variables

Answer 13

Group is original variable Suppose k = 3

k − 1 = 2 Dummy codes X1 and X2

Question 14

explain Step 2 and 3. Designate reference group and use 0’s for that group

Answer 14

Group is original variable Suppose k = 3

k − 1 = 2 Dummy codes X1 and X2

Group 1 is the reference group

Question 15

explain Step 4. Finish coding for X1.

Answer 15

Group is original variable
Suppose k = 3

k − 1 = 2 Dummy codes
X1 and X2

Group 1 is the reference group

Question 16

explain Step 4. Finish coding for X2.

Answer 16

group is original variable,
supposed k = 3

k-1 = 2 dummy codes
X1 and X2

Group 1 is reference grop

Question 17

The dummy codes are then used as what

Answer 17

predictors in multiple regression:

Yˆ =b0 +b1X1 +b2X2 +···+bk−1Xk−1

Question 18

(dummy coding interpretation) In our regression line. . .

Answer 18

The intercept (b0) represents the mean of the reference group
The other regression coefficients represent the difference between the mean of the reference group and the group that has a “1” for the corresponding dummy code