HEFP STATISTICS ASSIGNMENT REPORT

Data Collection: We are asked to find the relationship between prices of ‘51 registered’ cars and variables such as their current new price, mileage and weight by using the regression analysis. To collect full information of these registered cars, we can access to the websites like: However, in this easy, we use the data, which are provided with the assignment by our teachers.

By the sources, 100 cars, which manufacturers include Toyota, Honda, Nissan, Suzuki, are obtained to be sampled from. These Japanese cars can be divided into three groups according to different engine size, which are small engine size, medium engine size and large engine size. The cars’ engines size under or equal to 1.5 liters are considered as small engine cars. Group of medium engine cars are the cars’ engine size between 1.6 to 2.4 liters. Large engine cars are cars’ engine size equal or bigger than 2.5 liters.

The samples are likely to be representative because the method of simple random sampling will be used. The data of cars is wide range, so we use calculation to choose the samples randomly. The processes of sampling are divided into three procedures. Firstly, order all the cars by number them from 1,2,3 until 100. Secondly, decide the number of samples and calculate how many samples should be chose from each group. In this case, I decide to select 30 samples. Finally, use the calculation to randomly choose certain samples from a variety of data. In calculation, press “mode” and then chose fix. After that use the number of cars to be chose from multiple Ran# and add 1, which will give you the representative samples selected by calculation.

The numbers of the cars we choose from each group are calculated as showed below:

32/100 ×30 = 10, so 10 data should be chose from group of small engine cars .

61/100×30 = 18, so 18 cars out of 100 cars of medium engine cars will be chose from.

7/100 × 30 = 2, so just 2 cars should be used as sample from Large engine cars

The 30 data which choose by calculator show below.

Preliminary Analysis:

1. Mileage and asking price

According to the 30 data we selected, the graph above is produced by excel. As we can see from the graph above, the scatter plots indicates the general impression of the trend is positive. Although the graph is not strongly correlating due to limited samples, to some extent, it is suggested that mileage do influence the asking price of the cars. The formula of correlation should be used to prove whether the ...

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The 30 data which choose by calculator show below.

Preliminary Analysis:

1. Mileage and asking price

Correlation coefficient=n Σxy-(Σx)(Σy)/√(n Σx^2-( Σx)^2)(n Σy^2-( Σy)^2)=0.091652

To find the relationship between mileage and price, we should judge whether there is correlation or not. The coefficient of correlation should be compared with critical point. The critical point of 30 data is 0.3061 and obviously, 0.091652 is smaller than 0.3061. Therefore, no strong correlation is found between mileage and price. The correlation between mileage and price is weak probably due to some other factors which affect the asking price.

2. New price and Power

Same procedures will be in the regression analysis of the new price and power. By using the same examples, see the scatter spots below, the trend is quite positive as expected and a perfect correlation was found between power and new price. Again, as can be seen from the diagram below, a line of best fit was drawn.

From the graph, it is illustrated that power is a very important determinant of the new prices of cars. In order to test the relationship between new price and power, the correlation coefficient of these data has to be provided.

Correlation coefficient = n Σxy-(Σx)(Σy)/√(n Σx^2-( Σx)^2)(n Σy^2-( Σy)^2) =0.874814266

The coefficient of correlation between power and new price is 0.874814266, which means there is a strong relationship between power and new price because the result is greater than critical point 0.3061. From the best fit line y = 195.28x - 8243.4, our hypothesis can be testified.

Interpretation:

Let x be of the power cars, and y be the new price. Due to the common sense, x is absolutely greater than 0 because cars can not run without power. m is the change in x per unit increase in y. So, y=mx+c. Since m is positive here, price is increasing with the stronger power. When x equals 1, y=m+c. when x equals 2, y=2m+c. M is also the gradient of this trend line.

The regression equation is y = 195.28x - 8243.4

When the maximum power of the car (x) is 60 bhp, the new price of the car (y) is 195.28 – 8243.4 = £3473.4.

We can predict the new price with the maximum power by using the equation y = 195.28x - 8243.4

Conclusion:

To conclude, on analysing 30 sampled cars above, there are two main finding in this regression analysis:

Firstly, there is no correlation between the mileage and the asking price of used cars. Normally, people always build the higher mileage, the lower prices of the cars in their mind. However, we found that mileage has non-effect on the asking price. There are many reasons caused this result. Besides mileage, we should consider other factors such as weight, colour, interior, age, and engine capacity of the cars. So mileage is not the only determinant factor. Moreover, 30 samples are not enough to examine the relationship between asking price and the mileage accurately. Further more, among large amounts of cars we just focus on specific Japanese car group, which might not well represent the whole car industry.

Secondly, some significant correlation can be found between the current new prices and maximum powers of cars. For the relationship between current new price and maximum power, my investigation showed that there is a strong correlation. As a result, maximum power is an important determinant factor which influences the current new price. The stronger the maximum power, the higher the new price of the cars. However, due to the limitation of the samples and original data, the result cannot be to be representative. And there are also other factors are able to influence the price of cars, such as the colours, design, brand, taxation, fuel saving, and different agencies.

In spite of the limitations, we can still examine the general trend and predict the price of cars. Regression analysis might help car dealers to set the price and it might let the consumers gain some knowledge of price depreciation.