What factors effect the Price depreciation of a car and how?

rs = 1 – 22182

                    n(n²-1)

rs = 1 – 22182

                  50(50²-1)

rs = 1 – 22182

                  50x2499

rs = 1 – 22182

                   124950

rs = 1 – 0.177527011

rs = 0.822472989

This is the rank table

Outliers

        As most data I expect that my data would have some outliers, to calculate outliers I will use the formula x ± 2δx . In theory this would show 5% of outliers if the data were perfectly distributed. As my data is not perfectly distributed I expect that I will either have a higher or a lower percent of outliers

 

My first Hypothesis “The Older the car the higher the Price Depreciation”.

Primary Data:

The mean for Price depreciation for Age was

56.71%  :  5.56

This means that if a car is 5.56 Years old it would depreciate in price by 56.71%  

There were three outliers:

16, 15, 15, 14

Spearman’s Rank Correlation Coefficient:

0.822472989

Secondary Data

The mean for Price depreciation for Age was

62.10%  :  4.88

This means that if a car is 4.88 Years old it would depreciate in price by 62.10%  

There was only one outlier:

11

Spearman’s Rank Correlation Coefficient:

0.783049

Both graphs show a trend. Both trends are very similar. They both show as the Age increases so does the price depreciation. But these are not directly proportional. The higher the age the bigger the increase in the Price depreciation. This causes the curve. In the secondary data the Price depreciation increases more to the age than the primary data.

The primary data has 4 outliers which is 8 % of the results, The secondary data only shows one outlier which is therefore only 2 %. Both percentages are 3 % out which means that the both results are 3% from being distributed perfectly.

The Spearman’s rank correlation coefficient is similar for both my primary and secondary data. I would think that for the data collected and the way that it was collected that a correlation coefficient of 0.8 or around that would be quite good. MY primary data has a higher correlation coefficient, therefore the correlation in my primary data is higher then in my secondary data.

My second Hypothesis “The higher the Mileage the higher the Price Depreciation”.

Primary Data:

The mean for Price depreciation for Mileage was

56.71%  :  47920

This means that if a car travelled 47920 Miles it would depreciate in price by 56.71%  

There were three outliers:

124000, 143000, 180000

Spearman’s Rank Correlation Coefficient:

0.68557

Secondary Data:

The mean for Price depreciation for Mileage was

62.10%  :  42312

This means that if a car travelled 42312 Miles it would depreciate in price by 62.10%

There were three outliers also:

96000, 96000, 98000

Spearman’s Rank Correlation Coefficient:

0.827275

Similar to the Age/Price Deprecation both graphs show a trend. Both trends are very similar. They both show as the mileage increases so does the price depreciation. But these also are not directly proportional. The higher the mileage the bigger the increase in the Price depreciation. This causes the curve. In the secondary data the Price depreciation increases more to the mileage than the primary data.

The primary data has 3 outliers which is 6 % of the results, The secondary also has 3 outliers. So both Primary and secondary data are similarly distributed.

The Spearman’s rank correlation coefficient for my primary data is a lot lower than the Spearman’s rank for the Secondary data, therefore there is a better correlation in my secondary data.

My Third Hypothesis “The Engine Size would have a very little correlation if any, but if it does the correlation would be, the Bigger the Engine Size the Lower the Price Depreciation   ”.

Primary Data:

Spearman’s Rank Correlation Coefficient:

0.153661

Secondary

Spearman’s Rank Correlation Coefficient:

0.012485

Correlation:

        By looking at the two graphs it is easy to determine that there is little correlation if any between the price depreciation and the engine size. Due to this there was no point in making a line of best fit.

        The primary data showed a higher Spearman’s Rank Correlation Coefficient then the secondary data but is still very low, the secondary data showed a very low correlation. From this I determined that there is no correlation.

Analysis

        From the data obtained I have rounded the correlation coefficient to give me a weight of the variable factor. This weight tells me how much the factor effects the price depreciation. So now I can calculate by how much has a car depreciated in price. To do this I will use the equation for the line of best fit and the weight from the Age/Price Depreciation and the Mileage/Price Depreciation graphs, then substitute the age and the mileage. I have decided not to include the results from the Engine Size/Price depreciation graph because there was no correlation. As the spearman’s rank correlation coefficients are both rounded up I cannot relay on my formulae.

Primary:

%d = 8(0.2746Ln(Age) + 0.1465) + 7(0.1997Ln(Mileage) - 1.537)

                                 15

E.g.

If  Age = 10 / Mileage = 100000

%d = 77.1%

Secondary:

%d = 8(0.2279Ln(Age) + 0.3056) + 7(0.1845Ln(Mileage) - 1.2992)

                                         16

E.g.

If  Age = 10 / Mileage = 100000

%d = 77.6%

        In both examples the price depreciation are very similar so both primary and secondary data are quite similar.

Evaluation

         By comparing my results with a randomly chosen car from a car magazine.

 

And I have used both formulae

Primary

d% = 61.1%

Secondary

d% =  61.6%

The car has not depreciated in price by the % that I predicted and therefore would not be a good deal.

Improvements

        I collected my data by what I thought was a reasonable amount for this task but obviously if I included a wider range then my results would be more accurate. As well as the three factors I considered there are many other to consider such as air bags or air conditioning. Otherwise there are not many other improvements I could have made

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Secondary Data

Primary