Question - 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
• Afterwatching the video, try this extra credit assignment:
• Prompt:
• Answer Part 1, Part 2,andPart 3. Given the following coefficients from a logit analysis, and the sample data values given for two respondents, calculate the probability of a person likinga dark-colored imported car over a light-colored imported car. Your answers are probabilities.
• 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
• Age0.101
• Gender0.34
• EducLevel-5.1
• Income0.000142
• Constant3.22
• 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(Yi=yi).
• 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.