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  • Level: GCSE
  • Subject: Maths
  • Word count: 5661

In this project we have been given a large amount of data on used cars to work with, and our aim is to analyse this and investigate any possible correlations between cost and other factors given.

Extracts from this document...

Introduction

Maths Coursework – Used Car Data Investigation

Plan

In this project we have been given a large amount of data on used cars to work with, and our aim is to analyse this and investigate any possible correlations between cost and other factors given.

Brainstorm

I have brainstormed all the possible factors affecting the cost of a second hand car below. From these I will select 3 in which to study in detail.

  • Mileage
  • Age
  • Condition
  • Fuel
  • Make
  • Air conditioning
  • Insurance group
  • Number of owners
  • Engine size
  • Service
  • MPG
  • Central locking
  • Length of MOT
  • Airbags

I will be investigating mileage, age and make of car, primarily because it is easy to gain extra data from other sources on these three, but also because there are possible correlations not only with cost, but also between the three factors I have chosen.

Hypothesis

I have a number of hypothesise which I will explore in this project:

  • As mileage increases, the price of the car will decrease
  • As age of the car increases, the price of the car will also decrease
  • The make of the car will carry higher or lower prices depending on the make; some makes will cause prices to be higher, others will cause prices to be lower.

What I will do in this project

To begin with, I will look at the list I have been given in a general manner, by conducting a brief search through the list, looking at medians, quartiles, etc.

After this I will analyse the above 3 factors and compare them in tables and graphs to the price to find a correlation, in order to come out with a conclusion.

Mileage – from given data

Before studying mileage and it’s effect on price in detail we should briefly examine any possible correlation so we have a better idea of what to look at when studying in depth.

...read more.

Middle

18

Fiesta

5

7500

3178

4322

57.6

19

Fiesta

7

7500

3088

4412

58.8

20

Fiesta

8

7500

3357

4143

55.2

21

Escort

5

8995

3016

5979

66.5

22

Escort

6

8995

3361

5634

62.6

23

Escort

5

8995

3647

5348

59.5

24

Escort

5

8995

3564

5431

60.4

25

Escort

6

8995

3448

5547

61.7

26

Escort

7

8995

3084

5911

65.7

27

Escort

4

8995

3363

5632

62.6

28

Escort

3

8995

3962

5033

56.0

29

Escort

4

8995

3414

5581

62.0

30

Focus

5

14500

8485

6015

41.5

31

Focus

4

14500

9208

5292

36.5

32

Focus

3

14500

10426

4074

28.1

33

Focus

2

14500

10264

4236

29.2

34

Focus

3

14500

9960

4540

31.3

35

Focus

4

14500

9373

5127

35.4

36

Focus

2

14500

10124

4376

30.2

37

Focus

4

14500

8838

5662

39.0

38

Focus

2

14500

10423

4077

28.1

39

Focus

1

14500

9992

4508

31.1

40

Mondeo

2

16995

8106

8889

52.3

41

Mondeo

5

16995

8706

8289

48.8

42

Mondeo

4

16995

7820

9175

54.0

43

Mondeo

2

16995

9705

7290

42.9

44

Mondeo

4

16995

8746

8249

48.5

45

Mondeo

1

16995

9815

7180

42.2

46

Mondeo

3

16995

9295

7700

45.3

47

Mondeo

3

16995

8590

8405

49.5

48

Mondeo

1

16995

9060

7935

46.7

49

Mondeo

2

16995

9824

7171

42.2

50

Mondeo

3

16995

8361

8634

50.8

From this we can construct a graph, which looks incredibly similar to that of mileage. The line of best fit (trend line) is almost at exactly the same as that of mileage so there is not only an obvious positive correlation with price. This means that as the age increases, the price depreciates more and more, meaning that the overall price will go down.


image04.png

Age and Mileage

To examine closer the possible similarities between the mileage and the age of the car I have taken 50 cars from my original data to compare their mileage and age as shown below:

Car

Make

Model

Age

Mileage

1

Ford

Orion

1

7000

2

Mercedes

A140 Classic

1

14000

3

Vauxhall

Vectra

2

20000

4

Vauxhall

Astra

4

30000

5

Nissan

Micra

3

37000

6

Renault

Megane

4

33000

7

Mitsubishi

Carisma GDI

2

24000

8

Rover

623 Gsi

4

30000

9

Renault

Megane

3

41000

10

Vauxhall

Tigra

4

27000

11

Fiat

Bravo

5

51000

12

Vauxhall

Vectra

4

49000

13

BMW

525i SE

8

55000

14

Vauxhall

Corsa

2

24000

15

Fiat

Punto

4

31000

16

Rover

820 SLi

6

51000

17

Mitsubishi

Carisma

2

33000

18

Fiat

Cinquecento

6

20000

19

Rover

416i

6

49000

20

Nissan

Micra

8

47000

21

Daewoo

Lanos

3

42000

22

Rover

114 Sli

6

33000

23

Ford

Escort

7

68000

24

Fiat

Uno

8

51000

25

Rover

Metro

7

43000

26

Vauxhall

Nova

10

75000

27

Toyota

Corrolla

2

25000

28

Vauxhall

Cavalier

10

73000

69

Rover

Club

1

2000

30

Volkswagen

Golf

7

49000

31

Seat

Ibiza

7

45000

32

Rover

214i

8

55000

33

Ford

Fiesta

8

90000

34

Fiat

Tempra

6

81000

35

Ford

Fiesta

11

74000

36

Hyundai

Sonnata

9

65000

37

Renault

Clio

8

47000

38

Citroen

Debut

7

50000

39

Renault

Clio

9

98000

40

Fiat

Tipo

7

32000

41

BMW

316i

6

71000

92

Volkswagen

Polo

5

50000

43

Ford

Fiesta LX

7

60000

44

Nissan

Micra

9

40000

45

Ford

Escort Duet

7

64000

46

Nissan

Sunny

7

41000

47

Vauxhall

Astra

6

58000

48

Hyundai

Accent

6

49000

49

Daewoo

Nubira

4

14730

50

Daewoo

Lanos

3

32400

image05.png

Here we can clearly see there is a positive correlation between mileage and price. However, there appear to be many anomalous, or freak, results. The reason for this is due to the fact every car owner does not do the same number of miles per year; while some may only drive 200 miles in a year others may use the car constantly. This means that we cannot hope to get a perfect correlation, but it does show us a clear link between the two.

We can see from the graph that every year around 6100 miles is done, which is slightly lower than expected.

We can take the relationship further by saying that rather than mileage and age being factors with a correlation, we can say that age actually has little to do with price depreciation, and it is actually mileage which reduces the price of the car. We know this as there is a wide spread of results for each age, and mileage correlates almost perfectly with price, so this means that mileage will increase by an average amount each year, and this will affect price, rather than age.

This means that a two year old car which has done a low mileage may be worth the same amount as a two year old car which has done a high mileage,  

From this we can now draw further conclusions that mileage and age are clearly linked, and now we can try to work out a formula that combines both mileage and age, as there appears to be a correlation.

Examining make and price depreciation per year

If we take the formula for overall price depreciation, and divide it by the number of years that the car has been used for, we get the percentage price depreciation per year – in other words, the amount the car depreciates every year.

This is very useful as it does not so much give an indication of the mileage or age of the car, but more of the value of the car itself from the original price. Here I have taken around 90 of the cars from the given list, all different makes, and found the depreciation per year for each. Only makes with more than 1 car in the list were chosen so a trend line can be made.

Make

Original price

Depreciation per year

BMW

28210

9.8

BMW

13650

8.1

Citroen

5715

10.5

Citroen

7680

13.9

Citroen

14065

10.3

Daewoo

11225

15.5

Daewoo

13850

12.6

Daewoo

9525

18.0

Fiat

6864

9.8

Fiat

10423

14.6

Fiat

8272

11.7

Fiat

7864

14.3

Fiat

10954

38.0

Fiat

10810

26.9

Fiat

7518

12.5

Fiat

10351

13.2

Fiat

8601

13.4

Fiat

6009

11.1

Ford

16000

50.0

Ford

8785

11.7

Ford

7875

7.4

Ford

8748

11.0

Ford

9105

10.7

Ford

12125

21.5

Ford

11800

12.0

Ford

8680

15.8

Ford

14505

19.7

Ford

13230

12.5

Ford

13183

10.5

Ford

17780

13.8

Ford

6590

7.5

Ford

15405

14.8

Ford

7310

10.7

Ford

9995

11.7

Hyundai

11598

10.0

Hyundai

6899

9.9

Mercedes

14425

23.8

Mercedes

26425

16.9

Mercedes

17915

17.2

Mitsubishi

14875

29.8

Mitsubishi

15800

31.0

Nissan

7995

16.7

Nissan

6295

8.9

Nissan

5340

7.8

Nissan

7799

9.5

Nissan

12590

16.5

Nissan

13355

9.0

Peugot

13975

19.5

Peugot

9125

17.8

Peugot

17490

57.1

Peugot

7600

8.4

Peugot

12350

11.3

Renault

13610

15.8

Renault

13175

15.6

Renault

6795

8.8

Renault

7403

8.9

Renault

11695

12.8

Rover

22980

17.4

Rover

21586

13.7

Rover

13586

12.0

Rover

8595

11.8

Rover

6645

12.4

Rover

9565

10.3

Rover

24086

17.5

Rover

17795

16.2

Rover

19530

23.2

Rover

24086

14.6

Rover

5495

9.1

Rover

14486

12.4

Vauxhall

18580

28.5

Vauxhall

14325

13.5

Vauxhall

13510

11.1

Vauxhall

18140

16.0

Vauxhall

8900

21.9

Vauxhall

5599

8.2

Vauxhall

13740

13.1

Vauxhall

7840

9.1

Vauxhall

7440

8.8

Vauxhall

18675

10.4

Vauxhall

9795

11.2

Vauxhall

13435

12.6

Vauxhall

10150

9.2

Volkswagen

9524

8.7

Volkswagen

12999

12.1

Volkswagen

16139

11.3

Volkswagen

14950

9.7

Volkswagen

9960

24.2

Volkswagen

8710

9.2

...read more.

Conclusion

I have taken this information and put it into a table, and added a formula that should calculate the depreciation of the car:

Ref. No

Age

Original Price

Current Price

Depreciation (%)

Predicted Depreciation (%)

17

1

16995

10255

39.7

=(B2*4)+34.8

21

1

16995

10329

39.2

=(B3*4)+34.8

40

1

16995

10520

38.1

=(B4*4)+34.8

7

2

16995

9927

41.6

=(B5*4)+34.8

30

2

16995

9647

43.2

=(B6*4)+34.8

48

2

16995

9792

42.4

=(B7*4)+34.8

4

3

16995

8880

47.8

=(B8*4)+34.8

8

3

16995

8456

50.2

=(B9*4)+34.8

13

3

16995

9322

45.2

=(B10*4)+34.8

20

3

16995

9588

43.6

=(B11*4)+34.8

41

3

16995

9147

46.2

=(B12*4)+34.8

46

3

16995

9192

45.9

=(B13*4)+34.8

16

4

16995

8772

48.4

=(B14*4)+34.8

23

4

16995

8770

48.4

=(B15*4)+34.8

27

4

16995

8673

49

=(B16*4)+34.8

49

4

16995

7960

53.2

=(B17*4)+34.8

5

5

16995

7904

53.5

=(B18*4)+34.8

10

5

16995

7911

53.5

=(B19*4)+34.8

25

5

16995

8139

52.1

=(B20*4)+34.8

38

5

16995

7774

54.3

=(B21*4)+34.8

43

5

16995

8136

52.1

=(B22*4)+34.8

11

6

16995

7417

56.4

=(B23*4)+34.8

22

6

16995

7419

56.3

=(B24*4)+34.8

35

6

16995

7098

58.2

=(B25*4)+34.8

44

6

16995

7030

58.6

=(B26*4)+34.8

We can now put in the values, and to compare this to the real depreciation, we can examine correlation – while a correlation of 1 is perfect, a correlation of 0 means no correlation at all. I am hoping to get a correlation near to 1, since most the points on the graph are near to the trend line. To get the correlation I have used  the formula “=CORREL(E2:E26,F2:F26)”

Ref. No

Age

Original Price

Current Price

Depreciation (%)

Predicted Depreciation (%)

17

1

16995

10255

39.7

38.8

21

1

16995

10329

39.2

38.8

40

1

16995

10520

38.1

38.8

7

2

16995

9927

41.6

42.8

30

2

16995

9647

43.2

42.8

48

2

16995

9792

42.4

42.8

4

3

16995

8880

47.8

46.8

8

3

16995

8456

50.2

46.8

13

3

16995

9322

45.2

46.8

20

3

16995

9588

43.6

46.8

41

3

16995

9147

46.2

46.8

46

3

16995

9192

45.9

46.8

16

4

16995

8772

48.4

50.8

23

4

16995

8770

48.4

50.8

27

4

16995

8673

49

50.8

49

4

16995

7960

53.2

50.8

5

5

16995

7904

53.5

54.8

10

5

16995

7911

53.5

54.8

25

5

16995

8139

52.1

54.8

38

5

16995

7774

54.3

54.8

43

5

16995

8136

52.1

54.8

11

6

16995

7417

56.4

58.8

22

6

16995

7419

56.3

58.8

35

6

16995

7098

58.2

58.8

44

6

16995

7030

58.6

58.8

By using the correlation function, we can see that the correlation is 0.96888002. This is very near 1, only 0.031119976 from perfect. We can clearly see from this that my predictions were good. However, this correlation is not so much an indicator of my prediction, but merely showing the correlation between the line on the graph (which I have used to base my predictions on) and the points on the graph.

Evaluation

In conclusion, given the time constraints I had, I believe that I have been relatively successful in investigating my hypotheses. I have looked into make, age, mileage and also predicted ages of cars (which would almost definitely correlate well with mileage in addition, as the two are linked). Given more time, I could have done investigations into engine size and other such specifications of cars. I could have also represented my data in other forms, such as box plots, etc, and used standard deviation and skewness in my project.

...read more.

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