DSA 250: Housing Price Analysis

1. Project Overview

For DSA 250, I analyzed 1,460 home sales in Ames, Iowa to identify which home features most strongly predict sale price. I examined four predictors — square footage, bathrooms, year built, and bedrooms — first with exploratory analysis, then built a multiple linear regression model to quantify each variable's true impact and make predictions.

Research Questions:

• How strongly does above-ground square footage predict sale price?
• Do homes with more full bathrooms sell for more?
• Are newer homes priced higher than older ones?
• Does bedroom count still predict price once size is controlled for?

2. Data Source & Preparation

Source: Ames Housing Dataset (Kaggle — 81 original columns, 1,460 rows). I narrowed it to 5 key variables.

# Select key variables and drop any incomplete rows
key_vars = ['SalePrice', 'GrLivArea', 'BedroomAbvGr', 'FullBath', 'YearBuilt']
df_clean = df[key_vars].dropna()
# Result: 0 rows dropped — all 1,460 records were complete

A .isnull().sum() check confirmed zero missing values in all five variables — no imputation needed.

3. Exploratory Data Analysis

Distributions

SalePrice and GrLivArea are both right-skewed — most homes are moderate in size and price, but a few large, expensive properties pull the average up. Bedroom and bathroom counts are more symmetric and discrete.

Correlation Heatmap

The heatmap shows that GrLivArea (r = 0.709) and FullBath (r = 0.561) are the strongest individual predictors of SalePrice. Bedroom count (r = 0.168) is surprisingly weak — likely because bigger homes tend to have more bedrooms, so square footage accounts for most of that signal.

4. Color-Encoded Scatter Plots

Each scatter plot uses color to encode a third variable, revealing multi-dimensional relationships at a glance:

• Top-left (LivArea vs Price, color = FullBath): Larger homes tend to have more baths AND cost more — all three rise together.
• Top-right (FullBath vs Price, color = GrLivArea): High-bath, high-price homes are also the largest.
• Bottom-left (YearBuilt vs Price, color = Bedrooms): Newer homes command higher prices regardless of bedroom count.
• Bottom-right (Bedrooms vs Price, color = YearBuilt): 3-bedroom homes are most common; newer ones fetch notably higher prices.

5. Linear Regression Model

I fit two models using scikit-learn, training on 80% of the data (1,168 homes) and testing on the remaining 20% (292 homes).

Model Equation

Why is the bedroom coefficient negative? Once square footage is in the model, adding more bedrooms to the same square footage means smaller rooms — which buyers actually value less. This is a classic example of multicollinearity.

Regression Diagnostics

The diagnostic panel includes: simple vs multiple regression lines, predicted vs actual plot, residual plot, residual distribution, feature importance, and model comparison.

6. Sample Predictions

These predictions were generated by the trained multiple regression model (not a hand-coded formula). The ±1σ range uses the model's RMSE of $47,468.

Note: ±1 RMSE uncertainty band = ±$47,468. The model explains 70.6% of price variance on held-out test data.

7. Key Takeaways