Lecture 9_Categorical Predictors in MLR

Question 1

What does it mean that a variable has “Interval-level properties”?

Answer 1

Values of the variable are directly comparable.
3 - 2 = 1
larger # = more (etc.)

Question 2

What is a Nominal variable?

Answer 2

variables where numbers only indicate category or group membership (RACE: Hispanic = 1, Black = 2, etc.)

Question 3

In MLR, why do we need a coding strategy for nominal predictor variables?

Answer 3

MLR treats all IVs in equation as having interval-level properties (a regression coefficient tells the amount Y is expected to change when X changes by 1 unit)

Question 4

What are three different coding strategies?

Answer 4

Dummy coding (most frequent)
Effect coding
Orthogonal Contrast coding

Question 5

With a nominal variable, when do you NOT need to use a coding strategy?

Answer 5

when the variable only has two categories [simply code as 0 and 1 (note, using 0 is useful)]

Question 6

With a nominal variable (with 2 categories), what does the intercept from the regression table represent?

Answer 6

The mean of the outcome variable for the group coded 0.

Question 7

With a nominal variable (with 2 categories), what does the slope from the regression table represent?

Answer 7

the difference in group means (ie. the change in Outcome when Predictor changes by 1)

Question 8

Using a coding strategy for categorical variables in MLR will give the same results as what other type of statistical analysis?

Answer 8

Analysis of Variance (ANOVA) on group means

Question 9

Because multiple linear regression can include both a categorical IV (using a coding strategy) and a continuous IV, it can also be used to conduct what type of statistical analysis?

Answer 9

Analysis of Covariance (ANCOVA)

Question 10

How many dummy variables are needed to represent a categorical variable with (g) groups?

Answer 10

of new variables = (g - 1)

In the language of ANOVA:
the # of new variables = df (of the factor)

Question 11

How do you interpret the regression coefficients (a, b₁, and b₂) of a MLR using a categorical predictor with 3 groups?

Answer 11

The intercept (Constant) is the expected value of DV when all predictors [D₁ and D₂] = 0, (i.e., for the reference group, Whites.)

b₁ is the amount DV is expected to change when D₁ changes from 0 to 1, (i.e., the difference between Hispanics and Whites).

b₂ is the amount DV is expected to change when D₂ changes from 0 to 1, (i.e., the difference between Blacks and Whites).

Question 12

What is the advantage of “mean-centering” a continuous variable?

Answer 12

a value of 0 becomes meaningful as the average of the scores

Question 13

What does an ANCOVA analysis compare?

Answer 13

ANCOVA compares differences in group means after adjusting for differences on a continuous covariate

Question 14

What regression approach is used for analyzing a Categorical Predictor and a Continuous Predictor (ANCOVA)?

Answer 14

Sequential Approach required to get F-test and ΔR²
for the Race variable (as represented by two
dummy variables).
• Step 1: enter Age (mean-centered)
• Step 2: enter D₁ & D₂ (representing Race)
• Examine F-test for ΔR² with df = 2.

Question 15

What happens to the SD and Variance of a mean-centered variable?

Answer 15

they are unchanged

Question 16

How do you interpret the regression coefficients when analyzing a Categorical Predictor and a Continuous Predictor (ANCOVA)?

Answer 16

In Model 2 the coefficients may be interpreted as before, but are now adjusted for the covariate, AGEc.

The intercept is now the expected value of PD for Whites of average age.

D₁ is the amount PD is expected to change when D₁ changes from 0 to 1, (i.e., the difference between Hispanics and Whites, both of average age).

D₂ is the amount PD is expected to change when D₂ changes from 0 to 1, (i.e., the difference between Blacks and Whites, both of average age).

Question 17

Compare and contrast using MLR for ANOVA and ANCOVA analyses.

Answer 17

Dummy variables are entered as a block to obtain the F-test and ΔR² value for the original categorical variable.
• The resulting regression coefficients for the dummy variables represent differences in the group means relative to the reference group (ANOVA).
• When other continuous variables are included in the model, these coefficients represent differences in adjusted group means (ANCOVA).