ANALYSIS OF GRAPH
From the above graph it is clearly noticeable that as the car gets older price goes down. Thus representing the fact that a new car depreciates at a faster rate than an older car. For example, a new car that is about a year old must depreciate at an excessive rate than that of a 10-year-old car. Furthermore, suggesting that as the age goes up the price depreciates less. At closer examination another judgment can be made. The price of a new car is harder to determine than that of a car that is relatively old.
CONCLUSION
- As the age of the car increases, the price decreases.
- As the age of a car increases, it is easier to establish its price.
Now I am going to plot a graph for mileage against the second hand price. As I stated in my hypothesis I believe if the car has been driven a lot that there will surely be a decrease in its price.
ANALYSIS OF GRAPH
Similar to the first graph this graph shows comparable outcomes. In this graph the price drops as the mileage increases. In addition to this the graph also shows a negative correlation due to the fact that the price drops when the car is younger. In this graph there are two obvious outliers that lie in no relation to the other points. The reason for this is this particular which is a Bentley, has a higher second hand price compared to the other cars. Furthermore, it is clear that its mileage is much higher than that of the rest suggesting its frequent use. The second outlier isn’t as distorted as the first one but it is for the same reasons that resulted in its position on the graph.
CONCLUSION
- As the mileage increase the price decreases.
- Although certain cars have very low mileages this is dependant on several variables such as the make and engine size
- The increase of mileage grows to be a more overriding variable in working out the factors that affect the price of a car.
So far, it is clear that from the first two graphs age and mileage are contributing factors to the price. I can make this judgement by simply looking at the graphs it is clear that the graphs are somewhat similar suggesting the relationship between age and mileage which fits my hypothesis. Now I am going to plot a graph for the age and mileage hoping to see a correlation.
ANALYSIS OF GRAPH
The graph shows an obvious correlation between age and mileage, signifying the relationship between age and mileage. Reminiscent of the previous graphs I again have an outlier this particular outlier has age of 10 and a mileage of 124000, thus resulting in its displacement on the graph. It is clear that the car has been driven a lot and is very old. I have got an equation for the graph9 (y=8148x+6070.1) the gradient (“m” coefficient of x) is close to 8000 to the nearest thousand that shows the relationship between age and mileage is about 8000 miles per year. Furthermore, the R-value is close to 1 suggesting a strong positive correlation between age and mileage. I have also included a box plot for the age that should give me a clearer picture of the age. I have also calculated the standard deviation for the age which is 2.292. Using the mean I confirm the standard deviation values has deviated to the left suggesting there is a negative correlation. I am now going to include a histogram for the milage.
Variable N N* Mean StDev Q1 Median Q3 IQR Skewness
Age 36 0 5.250 2.792 3.000 6.000 7.000 4.000 -0.08
Upon closer inspection it is also clear that the deviation for the mileage has deviated to the left suggesting that.
Descriptive Statistics: Mileage
Variable N N* Mean StDev Minimum Q1 Median Q3 Maximum
Mileage 36 0 48847 26548 8000 27250 47500 63750 124000
To further look at the correlation between age and mileage I use spearman’s rank to see if there was a correlation.
Rank correlation of Mileage and Age = 0.857 . 0.857 is very close to 1 suggesting there is a strong positive correlation between age and mileage.
CONCLUSION
-
There is a clear relationship between age and mileage.
- The average mile per year is 8000 miles per year.
- Using the correlation coefficient I was able to determine the strong relationship between age and mileage.
ANAYLSIS
As I stated in my hypothesis I felt that engine size wouldn’t have a great effect on the price. In factual terms the engine size would normally make the increase the price. It seems I have got a weak positive correlation although the R- squared suggests otherwise. The graph clearly shows weak positive correlation.
CONCLUSION
- I expected not to see a correlation but the graph suggest a week positive correlation.
- I still feel that although my results outcome shows a correlation, that the engine size will not affect the price as much as age and mileage.
Like above I am now going to see the relationship between engine size and the price when new. I hope to see some sort of correlation, because as I mentioned earlier, in factual terms engine size affects the price.
ANALYSIS
Once again I am experiencing an unexpected correlation in the data. The graph shows a positive correlation. Similar to my earlier graph to do with engine size the graph suggests there is a relationship between engine size and the cost. I prefer this outcome as it relates to a real life situation, 2 identical cars will cost the same due to the engine size.
CONCLUSION
- It is clear that there is a relationship between the engine size and cost.
- From the graph it is conclusive that, the increase of engine size by 1 litre is the price increases by 23450. I feel that the conclusion is wrong. I don’t the price of a car can increase by 23,450 pounds every year, in some cases it is possible but looking at the data I have it suggests otherwise. There could be a mistake in the data that resulted in an unexpected correlation.
After plotting my graphs I feel my conclusions aren’t sufficient enough, that is why I am going to further my line of enquiry. Using my original data I will now workout the price decrease.
Price decrease =
Price when new – second hand price.
Now I am going to plot a graph for price decrease and the second hand price. Hoping to see a constant decrease in the price.
ANALYSIS OF GRAPH
From the graph it is obvious that there is a correlation between price decrease and the second-hand price. The r squared value= 0.7531 suggesting it is a positive correlation. Although there is a positive correlation I feel that the age needs to be taken into consideration. Then I can find the price decrease per year on certain cars.
CONCLUSION
- At this point I don’t think the data can be conclusive, apart from the obvious correlation suggesting the relationship between second hand price and price decrease I strongly feel that to gain a better conclusion I need to work out the price decrease per year.
Now I am going to plot a graph for the price decrease per year and second hand price.
ANALYSIS
The graph appears to have to have a positive correlation inevitably indicating a relationship between the price decrease/age and the second hand price. I still however feel that other variables can affect the price. Earlier I plotted the graph for engine size ans price when new, now I will plot a graph for engine size and price decrease/age. This should hopefully give an insight in to the factors which most effect the price of a car.
ANALYSIS
The graph shows a positive correlation which conflicts with my hypothesis. I stated that engine size would be the least influential factor to determine the price of a car. But it seems I have been proved wrong. The r-squared value suggests otherwise yet my graph shows a positive correlation. In addition I feel that once again I cannot fully trust engine size a defining factor. The main reason being is that I got better correlations for age/mileage etc.
CREATING A MODEL
To further my original line of enquiry I am now ready to create a model using the data and my knowledge. To begin with I am going make the price the focus of my equation as my sole intention was to find what factors affected the price and the formula is used to work out the price. I am using what is called the compound interest model (used in banks to calculate interest). Initially I am going to come up with the model function that will show the product moment correlation coefficient, this will determine whether it is a perfect positive or negative link. I will draw graphs to assist me in coming up with a formula.
To begin with I must ensure that the price never ends up as a negative value that means that the depreciation rate has to be bigger than 0 but smaller than 1. The reason for this is because the rate of decrease per year doesn’t allow the depreciation rate to go over 1 yet it has to be bigger than 0.
So p=price
Op original price (price when new)
R= rate of depreciation.
Y=years.
I can now use this model, as it is somewhat similar to the compound interest where the depreciation occurs per year.
As my main objection is to find he deprecation per year I will now make r the subject of the formula.
R here indicates the depreciation per year. R as a function is very complicated as it includes several other variables that affect it. To simplify the equation I will turn into a y=mx+c based equation. For example it would now read r=0,28x+0.922 where the y intercept is 0.28.
Using this I am now going to substitute into an equation that now involves the price when new the years and second-hand price. The result I got was
so now using my original values the formula looks like this
p=op(1-(0.28=0.922))y. The reason for this is you can work out the equation of a linear graph and substitute it and it will then represent the depreciation per year.
Above is a basic example of a model if I wished to further this I would have turned the equation to the one similar to compound interest as it uses a number and a variable.
CONCLUSION
CONCLUSION
I have now come to a conclusion about my car sales coursework. I personally feel that the investigation was not sufficient enough to determine what affects the price but I feel that my results might have a slight similarity. As I predicted in my hypothesis I felt that age and mileage will be the most contributing factors to the price, and I proved this in my results. I received a good correlation between the age and the mileage using the correlation coefficient and the graph that suggests their relationship. From my graphs it was conclusive that as the age went up so did the mileage to a certain extent.. I also plotted graphs for the mileage and price, for which it was clear that as the price decrease so does the mileage. I received an unexpected correlation in my data. In my hypothesis I had stated that I felt that the engine size would make no difference, yet I received positive correlation for engine size and price when new and engine size for second hand price. Furthermore I feel that the engine size doesn’t affect the depreciation per year it ahs more to do with the price and age. From the depreciation I observed that the rate of depreciation slows down as the mileage and age increases. Using my lines of best fit I was able to look at the equation of the lines and the r squared value to judge the relationship between to variables. There was one particular variable that I didn’t investigate but it has an effect on the price. The make. Different make have different prices and depreciate every year at different rate resulting in sum cars holding their value due the make. I cam up with a formula . If you plot a graph for %depreciation and age and substitute in the values you should end up with a average formula that should fit all brands. I felt that I needed to focus more on this part of the project that would enable me to come up with a formula that could fit certain or all brands. I think that there were sum mistakes in the data that led to some unexpected correlation. In conclusion I felt that the most contributing factors were age and mileage because they played a huge part in my data and showed a close relationship. As the mileage increased so did the age.