Home sales in a fictional city

What it is good for

• Fit a multiple regression of price on area, age, distance and district, and interpret coefficients.
• Compare models for price and log(price) and interpret log-scale coefficients as percentages.
• Diagnose multicollinearity (area vs bedrooms) with correlations and VIFs, and explain unstable coefficients.
• Check residual plots for non-constant variance on the raw price scale.

Methods: multiple regression, log transformation, dummy variables, variance inflation factor, residual diagnostics, correlation matrix.

Data quality notes

• price_sar is right-skewed; log(price) is close to symmetric.
• area_m2 and bedrooms are highly correlated (r ≈ 0.87): the bedrooms coefficient can flip sign when area is included.
• Distance and district overlap (outer districts are farther away).
• No missing values.

Provenance and licence

District drawn first; distance to centre depends on district. Area is log-normal (median ≈250 m²). Bedrooms ≈ 1 + area/80 + noise (so strongly tied to area); bathrooms follow bedrooms. Building age is gamma. log(price) = constant + 0.9·log(area/250) + district premium − 0.006·age − 0.02·distance + 0.06·garage + 0.02·bathrooms + Normal(0, 0.15); bedrooms have no effect of their own once area is known. Prices rounded to 1 000 SAR.

Synthetic data · CC0-1.0 (synthetic data generated by Statistics Quest) · generated deterministically (seed 20241016). It does not describe real people or organisations; any resemblance is coincidental.