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# Is there any link between original price and insurance group, and if so, is it affected by other variables?

Extracts from this document...

Introduction

Is there any link between original price and insurance group, and if so, is it affected by other variables?

Insurance vs. Original Price

Problem

I want to find out the effect of age on what insurance group a car is in. I am doing this investigation to ensure I get a good deal on my insurance.

Question

Is there any correlation between the original price of a car, and what insurance group it is in? If so, how much correlation?

Hypothesis

I think that the more expensive the car, the higher the insurance rate. This is mainly because the car would be more expensive to replace/pay for. Also, people may think they can drive recklessly or carelessly because they own an expensive car. On the other hand, more expensive cars may be more reliable than older cars, therefore more safe, and be in a lower insurance group.

However, I think there will be medium to high, positive correlation, because of the points above.

Data

I will retrieve my information from a used car statistics sheet from the Internet. This data is from “Gary’s Car Sales”. This lists make, model, price when new, current price, age, colour, engine, fuel, MPG, mileage, service history, owners, length of MOT, tax left(in months), insurance group, no. of doors, style, gearbox, air con, airbags.

Sampling

Middle

71050

10420

8

108576400

64

83360

10423

9

108638929

81

93807

10800

9

116640000

81

97200

10810

5

116856100

25

54050

10954

5

119990116

25

54770

12125

5

147015625

25

60625

12590

5

158508100

25

62950

13435

10

180499225

100

134350

13510

10

182520100

100

135100

13586

10

184579396

100

135860

13850

11

191822500

121

152350

14065

9

197824225

81

126585

14505

6

210395025

36

87030

14875

10

221265625

100

148750

17490

12

305900100

144

209880

21586

11

465955396

121

237446

28210

15

795804100

225

423150

32995

20

1088670025

400

659900

Calculations:

n = 32

Σa = 387300

Σe = 237

Σa² = 5809458546

Σe² = 2211

Σae = 3505658

ā = Σa ÷ n

= 387300 ÷ 32

= 12103.125

ē = Σe ÷ n

= 237 ÷ 32

= 7.406 [3dp]

SD of a = √ Σa²/n - ā²

= √ (5809458546/32) - 146485634.8

= √ 181545579.563 [3dp] - 146485634.8

= √ 35059944.763 [3dp]

= 5921.1439 [3dp]

SD of e = √ Σe²/n - ē²

= √ (2211/32) - 54.849 [3dp]

= √ 69.093 [3dp] - 54.849 [3dp]

= √ 14.245 [3dp]

= 3.774 [3dp]

Covariance = Σae/n - āē

= 3505658/32 - 12103.

Conclusion

rd owners mark.

Total conclusion

The original question that I asked was “is there any link between original price and insurance group, and if so, is it affected by other variables?”

For an answer I could say yes. It is clear that there is a link between original price and insurance, as there is a very strong Pearson correlation - 0.891. Also, from the data that I had, insurance is affected by colour and possibly by no. of previous owners. The average insurance group was higher for blue cars than red, so it appears that this does in fact affect the insurance group. This may just be chance, and if we took the entire population of blue and red cars, there might be a different result. However, this is just speculation, and from the data we have, insurance group is affected by colour. When I investigated the number of owners against insurance group, the answer was not as apparent, and there wasn’t a clear answer. However, because of line graph data, and part of the mean average data, it is possible that there is correlation, but the data is not conclusive. So, to finally conclude, there is a strong connection and high correlation between original price and insurance group, there is some connection with colour, and possibly a small connection with the number of original owners.

This student written piece of work is one of many that can be found in our AS and A Level Probability & Statistics section.

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