Question

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.

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:
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:
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:
Which Respondent has a higher probability of preferring a dark-colored car?
This is quite straightforward if you have Parts 1 and 2 correct.

Answer 1

This ques belongs to Logistic Regression, As we have to predict a binary categorical outcome. Please find the answers in the below attachments.