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.

• Afterwatching 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.