Technical report2026

Used-car Price Valuation

A classical regression study that improves through target transformation, feature engineering, cross-validation and regularisation — not through a product claim.

A coursework investigation, written up as a technical report.

Dataset: A used-car listings dataset with prices denominated in rupees.
Evaluation: Cross-validation for model comparison, with RMSE and R² reported per model.

Research questions

How much does log-transforming a skewed price target actually buy?
Does polynomial expansion help once the target is well behaved?
Do Ridge and Lasso separate meaningfully on this data?

≈0.868R² across the compared models

Ridge and Lasso both reach approximately 0.868; the OLS variants reach 0.867. The models are close enough that the choice between them is not the story.

REPORT-VERIFIEDCM3005 report, model comparison table

≈₹297,654RMSE — Ridge specifically

The lowest RMSE in the comparison, belonging to Ridge. Polynomial OLS reached ≈₹307,600 and log-target OLS ≈₹311,282, so the spread across all four models is about 4%.

REPORT-VERIFIEDCM3005 report, model comparison table

Problem

Predict used-car sale price from listing attributes. It is a well-worn regression problem, which makes it a good vehicle for the actual subject: what each step in a classical modelling progression is worth.

Why the raw target does not work

Price distributions are right-skewed — a long tail of expensive vehicles above a dense mass of ordinary ones. Fitting least squares directly against that target means the residuals are heteroscedastic and the fit is dominated by the tail, because squared error punishes large absolute misses and large absolute misses live at the top of the range.

Log transform

Modelling log price makes the target roughly symmetric, stabilises the variance of the residuals, and changes what the model is optimising: proportional error rather than absolute error. For prices, proportional error is usually the thing you actually care about — being ₹50,000 out on a ₹200,000 car is a different failure from being ₹50,000 out on a ₹2,000,000 one.

This is the single most consequential step in the study.

Progression

Multiple linear regression on the log target, then feature engineering, then cross-validation, then a regularisation comparison.

Model comparison

Model	RMSE	R²
Multiple linear / log-target OLS	≈ ₹311,282	0.867
Polynomial OLS	≈ ₹307,600	0.867
Ridge	≈ ₹297,654	0.868
Lasso	≈ ₹300,915	0.868

Reading the table honestly

The safest single-sentence summary is: R² ≈ 0.868, and Ridge reduced RMSE to roughly ₹298k in the reported comparison.

Two things follow from that phrasing, both deliberate.

First, the ≈₹298k figure belongs to Ridge, not to the study. Quoting it as "the model achieved RMSE 298k" without naming Ridge would attribute the best result to whichever model the reader assumes.

Second, and less flattering: the spread across all four models is about 4% of RMSE, and R² moves by 0.001. Regularisation helped, marginally. Polynomial expansion helped, marginally. The log transform did the real work, and everything after it is refinement.

Leading with "Ridge outperformed OLS" would put the emphasis in the wrong place. The transformation is the result; the regularisation comparison is the confirmation.

Scope

R² of 0.868 on listing attributes alone. Condition, service history and negotiation are not in the data, which is what the remaining variance largely represents.
A single market, so the coefficients are specific to it.
Listing price as the target — what sellers asked rather than what buyers paid.
A random split, appropriate for the modelling comparison this study makes.
Pooled residuals, reported across the full price range.

Where I would take this next

A temporal split, since a valuation model is applied to tomorrow's listings.
Error reported by price band, which is what shows how the model behaves across a heavy-tailed target.
Prediction intervals rather than point estimates — "₹450,000 give or take ₹80,000" is a more useful answer than "₹450,000".