Gradient = y
x
= £1500 - £6000 s= -£4500 s= -£0.0642 / mile
75000miles – 5000miles 70000miles
This means that on average, for every 10,000 miles travelled the car’s value depreciates by £642.86.
There is no real correlation that is visible here, emphasised by the fact that there are various prices for the same engine size, for a few different engine sizes. From this it is suggested that engine size does not affect the price of a used car.
The scatter diagram above is similar to the one for ‘Mileage vs. Price for Ford Cars’ which indicates that age has an affect similar to that of mileage on the selling price of a used car. If you look at the line of best fit drawn you can work out the gradient to show the average depreciation per year. On looking at the graph we see that the gradient is approximately -£7000 s= an average depreciation of £1000 per year.
7 years
I will now analyse the data that I have collated for Nissan cars from the database. As you can see there are only a small number of cars produced by Nissan, however I felt that 6 cars was a sufficient amount for analysis.
The graph shows the age of the cars against their selling price, and despite the fact there are only 6 cars, I believe that a pattern of negative correlation is visible. From looking at the line of best fit, a rough estimation of the gradient can be found. This gradient will show the average depreciation of Nissan cars over time.
Gradient = £1500 - £4000
6 years
= -£2500 = depreciation of £416.67 per year
6
From this calculation we can say that Nissan cars depreciate by less than half the amount of Ford cars, which means that buyers may be attracted to purchase Nissan cars.
This graph shows mileage against second hand selling price. Once again the small number of cars makes it difficult to see a clear correlation, however a negative pattern similar to that of age vs. price can be seen, emphasising that mileage and age influence price in similar ways.
There is no correlation once again for the engine size, adding further emphasis to the argument that engine size is not a main influence of price, although it would appear to be quite important. This suggests that engine size cannot solely influence the price of a car whereas age and mileage will have a greater influence on price.
Now I will explain the graphs I have produced from the data I collected from the appendix, on Rover cars.
The graph for mileage against price is extremely flat, hence a it has a very small gradient.
Gradient = -£3000 = £0.0375 / mile
80000M
This shows that for every 10,000miles travelled the car depreciates by only £375. The graph shows that as mileage increases price decreases, due to the negative correlation, however this ignores the outlier and if this were to be included, the graph would be a lot steeper and the average depreciation per 10,000miles travelled would be much higher.
This graph above shows much clearer correlation between age and price than mileage and price. The gradient shows that the average depreciation per year is -£9000 ÷ 5.5 years, which gives an approximate value of £1636.36. This is a very high value for the average annual depreciation, and the fact that the first point deviates the most from the straight line of best fit indicates that cars depreciate the most in their first year since they were newly bought.
The graph above showing engine size against price is the first one of its sort to show any signs of correlation. The relationship visible is positive correlation, and with the exception of 1 outlier the points are generally close to the line of best fit. This demonstrates that as engine size increases so does price, hence price is a function of engine size.
Another quite populous make of car that is present in the database is Vauxhall. I will now analyse the data for this make of cars.
The red line of best fit indicates that there is quite a strong negative correlation between some of the points. However there are quite a few outliers as well, thus I don’t believe any solid conclusions can be drawn from the graph. Nevertheless, the fact that there is some correlation suggests that in general mileage has a similar effect on price for Vauxhall as it does for most other cars. It could be that there is a wider selection of ‘specialised’ cars, the prices of which are not influenced as much by mileage as the other Vauxhalls in the database.
In the graph above there is a similar problem: it appears that there is negative correlation however there are many different price values for cars which are of the same age. Therefore a line of best fit cannot really be drawn and so no justifiable conclusions can be interpreted from the data. However, there is yet again a matching pattern for the effects of mileage and age, so it could be that there are a few more specialised cars in the database.
Once again there is no correlation between engine size and price, so it is starting to seem as if engine size has no meaningful effect on price.
I will now analyse the data from the spreadsheet for Fiat cars, another abundant make of car I have sampled from the database.
There is quite a strong negative correlation here, apart from a couple of points where two different cars have a difference of 20000 for the mileage but are priced the same. The gradient of the graph = -£4000 ÷ 60000miles = £666.67 average depreciation per 10,000miles travelled.
For the above graph there is almost perfect negative correlation. This is the strongest indication yet that age is a very important determinant of price. The gradient of the graph is approximately -£3000 ÷ 5 years = £600 average depreciation per year, which is relatively low and would attract buyers as it may be seen as an investment to buy the car.
There is absolutely no correlation once again between engine size and price.
Volkswagen is another of the populous makes of car. Here I will analyse the graphs I have produced from the data I gathered from the appendix.
There is a visible negative correlation between mileage and selling price in the graph above, even though there are only 6 cars whose data has been used. Besides one, the points do not vary much from the line so we can say that the graph is strongly correlating. The results displayed add further emphasis to the idea that mileage influences price.
I cannot say that there is much correlation in the above scatter diagram, probably because there are not enough cars to establish any pattern in this case. However a line of best fit can still be drawn if we disregard the outlying point.
The gradient of this line is approximately -£4000 = average depreciation of £500 / year. 8 years
This is a very cheap average depreciation but under similar circumstances to a previous analysis of another make of car, I have disregarded an outlying point. If this point were considered, then we would see the average depreciation rise by a substantial amount. Furthermore, this outlier shows that in the first year the car has probably depreciated by almost half its initial purchase cost.
There is no correlation between engine size and price in the graph above, so I have come to the conclusion that engine size is not as meaningful a determinant of the price of a second hand car, as age and mileage are.
As I have previously stated these results are not perfectly correlating e.g. some cars had higher mileages than others but were still priced higher than them, some cars with the same engine size had varying selling prices etc. What this shows is that the price or depreciation in value of the car is not entirely affected by one sole factor; the various factors together will decide by how much a car falls in value.
Hypotheses
Using these results I feel able to make a few hypotheses:
- The higher the mileage of the car, the lower its price will be
- Cars with larger engine sizes will be more expensive than cars with small ones
- The younger a car is, the more expensive it will be
To find an average value for average annual depreciation I conducted the following calculation:
Mean = £1000 + £416.67 + £1636.36 + £600 + £500 = £830.606
5
I then used this value to help find the standard deviation of these average values:
Standard deviation = √ Σ(x – mean)2 = £449.83
n
mean + 449.83 = 1280.436
mean – 449.83 = 380.776
=> I believe that the average depreciation in value of cars per year will be between £380.78 and £1280.44 for 67% of the cars.
From these basic, separate predictions I am also able to predict one overall hypothesis:
The more expensive cars will have a lower mileage and will be younger in age. The cheapest cars will have a high mileage and small engine size. About 2/3 of the cars will have an average annual depreciation of between £380.78 and £1280.44, i.e. 67% of the cars will be within one standard deviation of the mean.
To test my hypothesis, I created pivot tables using the Excel spreadsheet:
From the table above we can see that the majority of cars on the market are of standard engine sizes such as 1.4 and 1.6, which means that by paying the average price for a car you are likely to have either of these two engines. The fact that the number of cars with larger engine sizes decreases suggests that there are less on the market; this would be because the cars are very expensive. This will therefore justify my prediction that the larger the engine size, the higher the price. The vehicle with a 1400 engine would appear to be lorry, however the fact that there is only 1 vehicle with such a large engine raises questions as to the reliability of the data. Taking this into account, on looking at the price it is clear that no lorry would cost a mere £2497. An error has most probably occurred when inputting data into the spreadsheet, so the actual engine size may only be in fact 1.4 litres.
To test my hypothesis even more thoroughly I collected external data from “What Car?” magazine. As I was refining my search to one specific make of car, I used the random number generator function on my calculator to select a page from the whole car guide. The make of car on that page was Ford. Using that page I collected a sample of 25 cars once again using the random number generator. This was so that I avoided as much bias as possible, even though it may seem biased that I am selecting only specific make of car.
Here is a table containing the car models and other relevant information I collated from the guide:
I then processed the data I had collated and produced another set of scatter graphs showing the effect of mileage on price, age on price and engine size on price.
The graph above clearly demonstrates the inverse effect that mileage has on price; as the mileage of the car increases, the selling price decreases. This proves my hypothesis that “the more expensive cars will have a lower mileage” to be correct. We can say that price is inversely proportional to mileage, and using this statement we can establish a formula to tell us the price of a used car from knowing only its mileage:
y 1
x
y = k
x
when x is 15000, y is 6000 => 6000 = k s
15000
=> k = 6000 x 15000s= 90,000,000
therefore, the final equation is y = 90,000,000
x
However, the values used in this calculation were estimations taken from the computer drawn graph which you see displayed above, and so the actual formula may differ slightly from what I have been able to work out.
There is some negative correlation in the graph above, although there is no strong, definite pattern. This still proves my hypothesis that “The more expensive cars…will be younger in age.” We can still use the graph to obtain a general formula for the average depreciation per year of these cars:
y = mx + c → m = gradient, c = y-intercept
gradient = £4000 - £6000 = -2000 = - 800
6yrs – 3.5yrs 2.5 1
y-intercept ≈ £9000
if we take the point (6,4000), x = 6, y = 4000
substitute into y = mx + c → 4000 = -800x6 + 9000
4000 = -4800 + 9000
-5000 ≈ -4800
Once again the formula was created using estimated figures, and so it is acceptable that when checking the values for the formula the answers were only approximately the same.
Therefore, we can establish the formula for average annual depreciation as:
y = -800‘x’ + 9000 (‘x’ denotes x as a letter rather than a multiplication symbol)
It is clear that there is no correlation between the engine size and the price of a car, suggesting that although it may appear to be quite an important factor, it does not influence the price as much as other factors such as mileage and age. In this sense, this proved my prediction that “cars with larger engine sizes will be more expensive than cars with small ones” to be incorrect, as we can clearly see that some cars have smaller engines yet are more expensive than cars with larger engines.