# Need help with formula to value used cars. Please

• MHB
• foz84
In summary, the conversation discusses the development of a formula to accurately value used cars, using a sample group of similar cars and considering variables such as price, mileage, and deviation. Suggestions are made to improve the formula by using a weighted mean and incorporating other variables. The mathematics involved is more of a statistics problem and may require the expertise of a data scientist or statistician.
foz84
Hello there

I am trying to develop to formula that will derive a used cars value from a database of used car values.

Assume we are trying to value Car A. The first step is to form a sample of cars matching Car A for each header of the database columns (make, model, variant, engine size, transmission etc etc). The sample size is set to min 3, max 9. Once this sample group has been identified we are left with, in most cases 9 records, with two variables; price and mileage. I then use a deviation filter to remove records that deviate heavily from the mean (price and mileage) of the sample. The inverse relationship between price/mileage means that the deviation of these values should cancel out to 0. I have a set value where if this deviates too much from 0 that record is classed as an outlier and removed from the sample.
Once the sample has been judged suitable to use, we then calculate a sample price per mile. This is the price range of sample/mileage range of sample.

Now to calculate the value of Car A, we match to the closest 3 mileage records in sample. We use the mean price of those 3 records + (mean mileage of those 3 records - Car A mileage) * Sample price per mile.

Hope this all makes sense!

Now this seems to be working rather well, but can run into problems when Car A mileage differs significantly the mean of the 3 closest records. If I summarise the final formula as V = P + (M - A) * S. When (M - A) is a large number it creates some funny results, can I somehow weight (unsure of terminology!) the formula so when (M - A) is large number we reduce the vale of S? Or any other approach?

My maths ability is rather limited and I have no idea how to approach this problem? Can algebra even offer a solution? Or is this a calculus problem? Please excuse my ignorance.

Would be extremely grateful for any help or suggestion offered?
Thanks

Last edited:
for reaching out! Your formula and approach seem to be a good starting point for valuing used cars. However, there are a few things to consider in order to improve the accuracy of your formula.

Firstly, instead of just using the mean of the sample, it would be better to use a weighted mean. This means giving more weight to the records that are closer to the car A in terms of mileage. This will help account for the issue you mentioned where the mileage of car A differs significantly from the mean of the closest records.

Secondly, it would be beneficial to include other variables in your formula, such as the age of the car, its condition, and any additional features or modifications. These variables can greatly affect the value of a used car and should be taken into account.

In terms of the mathematics involved, this is more of a statistics problem rather than algebra or calculus. You can use different statistical methods, such as regression analysis, to further improve your formula and account for any outliers or unexpected results.

Overall, developing a formula to accurately value used cars is a complex task and may require the expertise of a data scientist or statistician. But with some further adjustments and considerations, your formula can definitely be improved to provide more accurate results. I hope this helps!

## 1. How is the value of a used car determined?

The value of a used car is determined by a variety of factors, including the make and model of the car, its age, mileage, condition, and market demand. To determine the value, a combination of these factors is taken into consideration and compared to similar cars in the market.

## 2. What is the most commonly used formula for valuing used cars?

The most commonly used formula for valuing used cars is the Kelley Blue Book (KBB) formula. This formula takes into account the make and model of the car, its age, mileage, and condition, and provides an estimated value based on market trends and demand.

## 3. Can I use the same formula to value all types of used cars?

No, the formula used to value a used car may vary depending on the type of car. For example, the formula used for valuing a luxury car may be different from that used for valuing a compact car. It is important to use the appropriate formula for the type of car you are trying to value.

## 4. How accurate are the formulas used to value used cars?

The accuracy of the formula used to value a used car may vary depending on the specific factors of the car and the current market conditions. While the formula can provide a good estimate, it is always recommended to get a professional appraisal or consult multiple sources for a more accurate value.

## 5. Are there any other factors that can affect the value of a used car?

Yes, in addition to the factors used in the formula, there are other factors that can affect the value of a used car. These include the car's maintenance and repair history, any modifications or upgrades, and the location of the car. For example, a car in a high-demand area may have a higher value than the same car in a less-populated area.

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