Predicting prices of used BMW cars

Jens Svensmark

May 10, 2021

Source

Source code for this project available on github.

Problem statement

Background

Cars are used throughout the world
Big resale market (due to cost and durability)
Many consumers have no clear idea about car prices
Makes navigating the market and negotiating with car dealers difficult

Goal

Predict resale prices of cars based on historic data
- Target variable is continuous
- Will use R-squared (R²) metric
- This should be close to 1
Make predictions available to consumers

Data

Source

Provided by Datacamp
No details about collection known

Features

Feature	Description	Type
price	Price in USD	numerical
year	Production year	numerical
mileage	Distance driven	numerical
tax	Road tax	numerical
mpg	Miles per gallon	numerical
engineSize	Size of engine	numerical

Feature	Description	Type
model	Car model	categorical
transmission	Type of transmission	categorical
fuelType	Fuel type	categorical

Which features are the most important?

Simple data model

Full data model

Exploring the data

Year and mileage

Car model

Transmission

Tax, mpg and engine size

Fuel type

Predictive model

Linear model

Feature selection

Last added feature	Mean R² test score
mileage	0.543242
year	0.643062
model	0.885855
engineSize	0.918769
transmission	0.924562
…	…

Last added feature	Mean R² test score
…	…
transmission	0.924562
fuelType	0.925534
mpg	0.928286
tax	0.928287

Feature selection

Include: mileage, year, car model, engine size and transmission.
Exclude: fuel type, mpg and tax.

Parameter interpretation

observable	10^coef	10^coef - 1
year	1.106	11%
engineSize	1.206	21%
10000*mileage	0.941	-6%

Parameter interpretation

Price relative to "Automatic"

transmission	10^coef	10^coef - 1
Manual	0.913	-9%
Semi-Auto	1.02	2%

Parameter interpretation

Price relative to "1 Series"

model	10^coef	10^coef - 1
2 Series	1.027	3%
3 Series	1.13	13%
4 Series	1.151	15%
5 Series	1.228	23%
6 Series	1.302	30%
…	…	…

Web interface prototype

Web interface prototype

https://svensmark.jp/dc_cert/predict_price/

Conclusion

Built a linear model for predicting resale prices of BMW cars
Works fairly well
Model coefficients are explainable
Demonstrated web interface prototype

Going forward

Follow up with data collection team

Suspicious values in mpg, engine size and tax

If more accuracy is required

More complex model might help
But risk of overfitting and less explainability

Web interface

Improve design of web front end
Ensure scalability of back end depending on expected usage

Thank you for your attention

Any questions?

Additional background

Metric

R-squared (R²)

A number
Measure of how well the model describes the data
The closer to one the better

Data

Data model 2

Predictive model

Additional assumption

All car prices fall at the same rate with age and mileage, independent on car model and other factors

Parameter interpretation

Price relative to "1 Series"

model	10^coef	10^coef - 1
2 Series	1.027	3%
3 Series	1.13	13%
4 Series	1.151	15%
5 Series	1.228	23%
6 Series	1.302	30%
7 Series	1.542	54%
…	…	…

…	…	…
8 Series	2.07	107%
X1	1.162	16%
X2	1.204	20%
X3	1.435	44%
X4	1.492	49%
X5	1.762	76%
X6	1.791	79%
…	…	…

…	…	…
X7	2.382	138%
M2	1.488	49%
M3	2.183	118%
M4	1.672	67%
M5	1.754	75%
Z4	1.259	26%

90% Prediction interval

90% of car prices expected to be within this interval
Indicates model uncertainty

Example:

Predicted price (p): $10,000
Relative half-width (h): 25%
90% of cars between p/(1+h) and p*(1+h), that is from $8,000 to $12,500

90% Prediction interval with partial data

Last added feature	Relative half-width
mileage	70%
model	41%
year	30%
engineSize	25%
transmission	24%