## Categorical (Nominal) Dependent Variables – Logit (Logistic Regression)

- Here is an introductory/survey video of Logit Analysis, which allows us to analyze nominal dependent variables. Regression only allow us to work with continuous variables.

Video: Introduction to Logit Analysis:

https://youtu.be/ANi_PpkTSJA

Note: This Extra Credit Assignment is a bit tougher than the other ones, so it is worth a bonus of up to 10% of the final grade if you get everything right. The other assignments are worth 7% each.

__After__watching the video, try this extra credit assignment:

__Prompt:__

Answer Part 1, Part 2,__and__Part 3. Given the following coefficients from a logit analysis, and the sample data values given for two respondents, calculate the probability of a person liking a dark-colored imported car over a light-colored imported car. Your answers are probabilities. Show your work. Use Word or PDF format for submission to Turnitin.com (link below). You may need to hand-write the formula and show your work on paper, then photograph or scan it into a file. That’s OK, but typing it into Word is preferred, if you can figure it out.

__The Dependent Variable (DV) is “Prefers Dark colored imported car.” This measure is labeled”PrefDark” in the data__

= 0 if preference is for a light colored car,

= 1 if preference is for a dark-colored car.

__Here are the Independent Variables (IVs):__

__Age in years__(no intervals – labeled “Age” in the data)

__Gender (measure is labeled “Gender” in the data)__

= 0 if male,

= 1 if female.

__Education level (measure is labeled EducLevel in the data)__

= 0 if completed high school only

= 1 if completed Associate’s degree (Community College)

= 2 if completed Undergraduate degree (BA or BS)

= 3 if completed a Graduate degree

__Income per year__(in Euros, measure is labeled Income))

Consider, also, these coefficients for each measure (data point), calculated by running a Logit analysis on the data sample for the DV,

*PrefDark*:

__Coefficients and Constant__

Age 0.101

Gender 0.34

EducLevel –5.1

Income 0.000142

Constant 3.22

*Assume all coefficients and the constant are statistically significant (you can’t ignore them).*

__Part 1 (4 points):__Now consider this person, Respondent 1:

Age = 24

Gender = 1 (female)

EducLevel = 2 (Undergraduate degree)

Income/year = Euros 38000

__What is the probability this person prefers a dark-colored imported car?__

__Part 2 (4 points):__Additionally, consider this other person, Respondent 2:

54 year old male, with a graduate degree, earning Euros 58000 per year.

__What is the probability this person prefers a dark-colored imported car?____Hint: Use the formula given in the video for calculating P(Y__

_{i}__=y__

_{i}__).__

Show your work, please.

__Part 3 (2 points)__

__Which Respondent has a higher probability of preferring a dark-colored car?__

This is quite straightforward if you have Parts 1 and 2 correct.