I have taken a sample size of 35 cars this will allow me to get a good set of results and thus allow me to draw to a good conclusion, and these results must also be all relative to my investigation. For this investigation I will have to work out the percentage decrease and I have to work out the midpoint of all the miles per gallon to give me a fair class width and therefore makes the results easy to translate into a graph. I will use my results to give myself a clear idea of what affects the price of second hand cars all the graphs I choose I hope will help me to come to a conclusion that will allow me to
Results
The age and Percentage decrease (correlation coefficient)
To work out the correlation coefficient I used the formula that I provided before and the results that I got resulted in this graph. I worked out the correlation coefficient the number that I ended up with was 0.7692875 this is relatively high and this shows that the line of best fit is very relative to the points that have been plotted. If the correlation coefficient were 1 then it would be a perfect positive correlation if it were –1 then it would be a perfect negative correlation. Evidently this means that if the correlation coefficient were 0 it would have no correlation. But overall this graph shows that the older the car gets the bigger the percentage decrease gets i.e. the age of the car is directly proportional to the percentage decrease in the price of the car. This is the working that I used to work out the correlation coefficient:
The Mileage And Percentage Decrease
This graph shows that the mileage has a fairly big affect on the price of second hand cars, I can tell this as the plotting make a fairly positive correlation, the correlation coefficient is 0.578187 this shows that the correlation is quite strong but this correlation is not as strong as the correlation in the age and percentage decrease graph. The graph shows that the mileage affects the percentage decrease in price a lot and if the computer did not do the line of best fit it would show a curve. This curve would mean that as the mileage get past a certain point the percentage decrease increases a lot more rapidly. Since the cars value will never reach 100% decrease in price and therefore be free, the curve will become vertical if the graph was continued
Mileage And Percentage Decrease
This graph has proved my prediction wrong. All the topics that I was covering, I thought affected the price of second hand cars slightly but this shows that the MPG did not affect the percentage decrease of the price of cars. The correlation coefficient of this graph is 0.014142 this shows that there is no positive or negative meaning that the MPG is completely useless in this investigation i.e. the graph has no correlation.
The Number Of Owners And The Percentage Decrease
This graph shows that when the number of owners increases, the percentage decrease also increases. This means that the more people that a car is owned by, the lower the price of it second hand. This is because the car would be in a worse condition. This graph showed a positive correlation, which shows this reasoning perfectly. The step from two owners to three owners is higher that the step between one to two. This is because having had three owners would have deteriorated the car even more then having two for the same amount of time. There haven’t been many values individually shown on the graph but this is because and average has been taken for each number of drivers and then the bar chart made from the information.
Insurance Group And Percentage Decrease
This graph shows that the insurance group does affect the price of second hand cars, the graph has a very strong positive correlation the correlation coefficient is 0.527447 this shows that the correlation is fairly strong and that the insurance group has a large effect on the price difference. This would probably be because the higher insurance group the car is in the more the owners would have to pay for the car and this evidently deters them from buying the car. This usually means that the car will not have any damage to it before hand, as the insurance would have covered it. As you can see there are some areas in which you can see that the results do not completely correspond to the correlation this is mainly toward the bottom.
Evaluation
The ways in which I could have improved this project started off with the way I chose my graphs. Some of the graphs that I chose did not show my predictions well enough and left me with little to say about them and little information to work with. Also the lines of best fit were not very accurate. In future I will do them by hand so that a curve can be reached rather than a straight line which gives wrong values. With the averaging I should have made class widths and therefore construct a histogram by hand, which I feel would have demonstrated my point much better. I should have used more than one type of graph for each to get a variety of visuals and a better feel of whether there was an actual affect on the price reduction. I could also have done more than one graph for each. I should have found the range of values for each one and compared how the percentage difference compared with all of the other factors I used. This would have made it much easier to tell which one of the factors was actually the main factor affecting the price of second hand cars. I also realised that the number of owners compared to the age of the car is connected so I should have produced a graph showing the relationship, this may have allowed me to give a more of a reasoning behind my results
I predicted that the factor that would affect the price of second handcars the most would most probably be the mileage, I was not that wrong but in as wrong in saying that the mileage is the biggest factor because I found out by the use of the correlation coefficient that the age is the biggest factor. After the age it was the mileage and then the insurance group. This was a surprise to me as I thought that the number of owners would have had a bigger affect but evidently not as much as the others, I find this hard to comment on because I feel that I have chosen the wrong graph do demonstrate the point that I wanted to show, I should have used a histogram or maybe a frequency polygon. I feel that the results are slightly bias as all of the results that I chose where chosen as I thought that they would all affect the price of second hand cars rather than choosing a random selection of topics for discussion, this would be a way of eliminating the bias. I also think that if I had chosen a bigger sample size I would have achieved more accurate results, as the correlation coefficient will probably become more accurate and may have changed the results of my whole project.
Jaysal Bodhani 10 MMB
