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• Level: GCSE
• Subject: Maths
• Word count: 1841

# The aim of this project is to investigate which factors influence the costs of second hand cars. The makes we were looking into include Ford, Peugeot, Renault and Vauxhall.

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Introduction

Write Up

The aim of this project is to investigate which factors influence the costs of second hand cars. The makes we were looking into include Ford, Peugeot, Renault and Vauxhall.

To aid us with our research, we were given a bank of secondary data of one hundred and ninety nine cars. Along with these cars, we were given nine variables for each car; colour, engine size, petrol/diesel, year of manufacture, mileage, cost, preliminary cost, make and model. We later had to add an age column for each.

We have been asked which features make most difference. My predictions for which makes the most difference are as follows:

FACTOR                                IMPORTANCE                RANGE

1. Age                                most important factor                1yr-16yrs
2. Mileage                                                                1200-150,000
3. Cost                                                                 375-132,500
4. Petrol/Diesel                                                        Petrol/Diesel
5. Engine size                                                        1,000-2,500
6. Year                                                                1989-2002
7. Model                                                                106-Vectra
8. Make                                                                Ford-Vauxhall
9. Preliminary Cost                                                        6,000-20,020
10. Colour                                least important factor                Black-Yellow

Looking through the data, I can see that it is not perfect. There are many missing fields of data, and I had to remove one rogue piece of data, being a Renault Laguna. I knew it was not right from my general knowledge of cars, the price being too high.

I will draw up scatter graphs, histograms and cumulative frequency curves (for cost compared with the whole population’s age followed by individual Makes)

to try and distinguish any correlation’s (patterns) in the cost distribution.

Middle

What I think will happen is-

As age increases,      the cost will decrease.

This is because there is a very strong correlation between these factors. I will look at one model for one example because if I look at a group of similar cars, I can be confident that any observations I make are because of the cost and not anything else. For this model, I draw a scatter graph of cost against age.

For this scatter graph, I put Age on the X axis and Cost on the Y axis as Cost depends on Age. This makes Cost the dependent variable. I also included a line of best fit and an R2 measure of correlation where R=1 is a perfect correlation.

On examining this graph, there’s a very strong negative correlation between cost and age. Based on these findings, I can easily make my first hypothesis:

There is a fairly strong correlation between Cost and Age.

2nd Hypothesis

I am now going to investigate the variable that I believe would be next important in determining the second hand cost. This is Mileage. I think that like the age variable, there may be a sign of negative correlation between Mileage and Cost. Like before, I will make scatter graphs based on each make of my sample, except this time it will be for Mileage and Cost.

Conclusion

These estimates are only moderately reliable as the correlation between cost and age is only moderately strong. Based on this analysis of my sample (which was a reasonably good representation), I believe I have evidence to support the first hypothesis.

There are clearly other factors influencing the cost, so I will now move on to mileage. Firstly, I will draw box plots for mileage. From these I can see that on average, Ford cars have the lowest median. This seems strange as they were the oldest on average.

Vauxhalls are the most spread out which fits in with that age being spread out. I will now draw a scatter graph for the sample and for each make. I believe that on the whole, these broadly confirm my hypothesis. The whole sample shows a weak/moderate negative correlation.

It seems to me that I was correct. My initial prediction that age is the most important variable, but mileage is also important was true. The next thing I am going to do is indicate on the cost against age scatter graphs for each make, the mileage for point and the engine size to see if this gives me any insight into the influence of mileage or engine size.

Having looked at these, I don’t see a very clear pattern. Although, on average, cars with a lower mileage have higher prices, but as always, there are exceptions.

This student written piece of work is one of many that can be found in our GCSE Gary's (and other) Car Sales section.

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