Homework 3

Regression; Jupyter Notebook Blogging

Direction

• Please submit your Jupyter Notebook for Part 1 in Homework 3 to Brightspace with the name below:

  • danl-320-hw3-LASTNAME-FIRSTNAME.ipynb
    ( e.g., danl-320-hw3-choe-byeonghak.ipynb )

• The due is April 4, 2025, 11:59 P.M.

• Please send Byeong-Hak an email (bchoe@geneseo.edu) if you have any questions.

Part 1. Regression

Consider the homes DataFrame from the 2004 American Housing Survey, which includes data on home values, demographics, schools, income, finance, mortgages, sales, neighborhood characteristics, noise, smells, state geography, and urban classification.

homes = pd.read_csv(
  'https://bcdanl.github.io/data/american_housing_survey.csv'
)

Variable Description

Variable	Description
LPRICE	Purchase price of unit and land
VALUE	Current market value of unit
STATE	State code
METRO	Central city/suburban status
ZINC2	Household income
HHGRAD	Educational level of householder
BATHS	Number of full bathrooms in unit
BEDRMS	Number of bedrooms in unit
PER	Number of persons in household
ZADULT	Number of adults (18+) in household
NUNITS	Number of units in building
EAPTBL	Apartment buildings within 1/2 block of unit
ECOM1	Business/institutions within 1/2 block
ECOM2	Factories/other industry within 1/2 block
EGREEN	Open spaces within 1/2 block of unit
EJUNK	Trash/junk in streets/properties in 1/2 block
ELOW1	Single-family town/rowhouses in 1/2 block
ESFD	Single-family homes within 1/2 block
ETRANS	RR/airport/4-lane highway within 1/2 block
EABAN	Abandoned/vandalized buildings within 1/2 block
HOWH	Rating of unit as a place to live
HOWN	Rating of neighborhood as a place to live
ODORA	Neighborhood has bad smells
STRNA	Neighborhood has heavy street noise/traffic
FRSTHO	First home
AMMORT	Amount of 1st mortgage when acquired
INTW	Interest rate of 1st mortgage (whole number %)
MATBUY	Got 1st mortgage in the same year bought unit
DWNPAY	Main source of down payment on unit

Question 1

Plot some relationships and tell a story.

Question 2

• Fit a linear regression model with the following specifications:
  • Outcome variable: \(\log(VALUE)\)
  • Predictors: all but AMORT and LPRICE

Question 3

• Refit the linear regression model, retaining only statistically significant predictors from Question 1.
• Compare the revised model to the initial model from Question 2 using:
  • \(\beta\) estimates
  • \(R^2\)
  • RMSE
  • Residual plots

Question 4

• Fit a logistic regression model with the following specifications:

  • Outcome variable: \(\text{GT20DWN}\) (indicating whether the buyer made a down payment of 20% or more)
  • Predictors: All available variables except AMORT and LPRICE

• The outcome variable is defined as: \[ \begin{align} \text{GT20DWN} \,=\,\begin{cases} 1 & \text{if}\; \frac{\text{LPRICE} - \text{AMMORT}}{\text{LPRICE}} > 0.2 \\ 0 & \text{otherwise} \end{cases} \end{align} \]

• Analyze and interpret the following relationships:

• The association between first-time homeownership (\(\text{FRSTHO}\)) and the probability of making a 20%+ down payment.

• The association between number of bedrooms (\(\text{BEDRMS}\)) and the probability of making a 20%+ down payment.

Question 5

• Refit the logistic regression model, adding interaction terms:
  • Predictors: all previously included predictors in Question 4 plus the interaction between \(\text{FRSTHO}\) and \(\text{BEDRMS}\)
• Interpret how the relationship between \(\text{BEDRMS}\) and the probability of a 20%+ down payment varies depending on whether the buyer is a first-time homeowner (\(\text{FRSTHO}\)).

Question 6

• Fit separate logistic regression models (with the same model specification as in Question 4) for two subsets of home data:

1. Homes worth \(\text{VALUE} \geq 175k\).
2. Homes worth \(\text{VALUE} < 175k\).

• Compare residual deviance, \(RMSE\), and classification performance between the two models.

Part 2. Jupyter Notebook Blogging

• Write a blog post about Part 1 of Homework 2 - Beer Markets using Jupyter Notebook, and add it to your online blog.