Problem
Set 3

Part 1: Interpreting Regression Coefficients for
Categorical Variables

A researcher is using free- and reduced-price lunch
program (FRPL) status as a way to predict math test scores for students. Often,
FRPL is used as a proxy variable for low income or low socioeconomic status
(students from families that have low income or meet other criteria for
assistance receive vouchers for FRPL at school). For this section of the
problem set, consider a scenario where FRPL is a variable that is dummy coded
so that a student that is in the FRPL program gets coded as a 1 and a student
that is not in FRPL is coded as a 0. That is:

Student in FRPL
= 1 (In FRPL)

Student in FRPL
= 0 (Not in FRPL)

The researcher runs the proposed model in stats software.
Substituting in the software’s estimates of the model coefficients, the
resulting regression formula looks like this:

Where di represents the dummy variable for FRPL.

Questions:

1. What is the
mean test score for students in the FRPL program?

2. What is the
mean test score for students who are not in the FRPL program?

3. Name three
assumptions of this model and what you would do to check each of them.

Part II. Running analysis with One Categorical Predictor

Using the dataset in the HW folder (a revised version of the data also
used in lab), a researcher wants to see if a student’s perception of personal
math ability is predictive of their math scores. Seesmathrecode is a dummy
variable in which students were asked to respond if they agree to the statement
“I see myself as a math person.” Students selected either “agree” or
“disagree.”

1. Using
regression analysis, use the variable “seesmathrecode” as a predictor and X1MTSCOR
(standardized math score) as the dependent variable. Paste your output below.

2. What is the
mean standardized math score for students who agreed to the statement? For
students who disagreed?.

3. Interpret the
regression coefficient of seesmathrecode.

4. Bonus: If you were to create a scatter
plot of the model above (in fact, you can do this in SPSS), you get two columns
of data points. One column will line up with the x-value of 0 and one will line
up with the x-value of 1 (vertically). If you were to plot a regression line
for this data, the line would cross the two columns at particular points. What
would these points be?

Part III: Regression with a Categorical Predictor and a Continuous
Predictor

As usual, the researcher needs to make sure that what’s being measured by
math perception is not simply socioeconomic status (SES).

1. Write out the
equation for a model with the variable x1sestpos and seesmathrecode as
predictor variables and X1MTSCOR as a dependent variable.

α

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