Linear regression

01The problem

The property company wants more than a number. Landlords ask: "How much more could I charge if I made the flat serviced? Is 24-hour power worth it?" A model that predicts rent well is useful; a model that also explains what drives rent is far more useful, because it answers those questions too.

Linear regression does both. It's the oldest and simplest machine learning model, and still one of the most used, precisely because you can read it. This lesson fits one, finds an important flaw, and fixes it with one line of code.

02The concept

What linear regression learns

It predicts the target as a weighted sum of the features:

rent ≈ intercept + w₁ × bedrooms + w₂ × size + w₃ × serviced + w₄ × (is it in Ikoyi?) + …

Training finds the weights (the coefficients) that make the predictions as close as possible to the real rents in the training data.

The flaw: prices multiply, they don't add

A linear model says being serviced adds a fixed amount, say ₦1.5m, everywhere. But in reality it adds a percentage: about the same proportion in Kubwa as in Ikoyi, so many more naira in Ikoyi. Prices, salaries and sales usually behave like this.

The fix: model the log of the target

Train on np.log(rent) and convert predictions back with np.exp. On the log scale, percentage effects become additive, which is exactly what a linear model can learn. A coefficient c then means: this feature multiplies rent by exp(c), a change of (exp(c) − 1) × 100 percent.

Reading the error

Use the same test set and the same measure (MAE) as the baselines, so the comparison is fair. Add R² to see how much of the variation the model explains.

03Example

The setup, then a plain linear regression:

import pandas as pd
import numpy as np
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LinearRegression
from sklearn.metrics import mean_absolute_error, r2_score

rentals = pd.read_csv("https://academy.cloudtechanalytics.com/datasets/rentals/listings.csv")
typical = rentals.groupby(["area", "property_type", "bedrooms"])["annual_rent_ngn"].transform("median")
rentals = rentals[rentals["annual_rent_ngn"] <= 4 * typical].copy()
rentals["size_sqm"] = rentals["size_sqm"].fillna(
    rentals.groupby(["property_type", "bedrooms"])["size_sqm"].transform("median")
)
features = ["area", "property_type", "bedrooms", "bathrooms", "size_sqm", "serviced",
            "furnished", "power", "parking_spaces", "year_built"]
X = pd.get_dummies(rentals[features], drop_first=True, dtype=int)
y = rentals["annual_rent_ngn"]
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2, random_state=42)

plain = LinearRegression().fit(X_train, y_train)
pred = plain.predict(X_test)
print("Plain linear MAE:", round(mean_absolute_error(y_test, pred)), " R²:", round(r2_score(y_test, pred), 3))

Plain linear MAE: 2216317  R²: 0.759

Better than the area baseline (₦2.87m), but only a little. Now the same model on the log of rent:

log_model = LinearRegression().fit(X_train, np.log(y_train))
pred_log = np.exp(log_model.predict(X_test))
print("Log-rent linear MAE:", round(mean_absolute_error(y_test, pred_log)), " R²:", round(r2_score(y_test, pred_log), 3))

Log-rent linear MAE: 827735  R²: 0.934

The error falls by almost two-thirds. Same features, same model, one transformation. And now the coefficients answer the landlords' questions:

effect = (np.exp(pd.Series(log_model.coef_, index=X.columns)) - 1) * 100
effect[["serviced_Yes", "furnished_Yes", "power_Prepaid meter", "bedrooms"]].round(1)

serviced_Yes           29.4
furnished_Yes          19.3
power_Prepaid meter    -8.9
bedrooms               24.3
dtype: float64

Read them as: a serviced flat rents for about 29% more than a similar unserviced one; furnished adds about 19%; a flat with only a prepaid meter rents for about 9% less than one with 24-hour power (the reference category); each extra bedroom adds about 24%, holding the other features constant.

04Walkthrough

1. Run the cells. Compare both models' MAE with your baselines from lesson 3.
2. Plot predicted against actual rent for the log model (plt.scatter(y_test, pred_log)), with log scales on both axes. The points should lie close to a diagonal line.
3. Look at the area coefficients: effect.filter(like="area_").sort_values(). They're relative to Ajah, the reference area.
4. Find a listing in the test set with a large error. Can you see why the model got it wrong?
5. Write down the log model's MAE: it's the number to beat in lesson 5.

05Practice

06Check your understanding