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Cyl Engine
Determinates Of Car Price
DETERMINATES OF CAR PRICE
CONTENTS:
INTRODUCTION
PART ONE:
- I. TYPE OF CARS AND THEIR PRICES
- II. MILES PER GALLON AND CAR TYPE
- III. CAR PRICE AND HORSE POWER
PART TWO:
- I. MILES PER GALLON VERSUS PRICES
- II. MILES PER GALLON AND THE ENGINE SIZE
CONCLUSION
REFERENCES
APPENDIXES:
Introduction:
The price of cars will depend on the type, horse power and other factors, the type of cars can be grouped into compact, small, midsize, large, sporty and van. However depending on the manufacturer the price varies, this paper focuses on the type of cars and how the price varies and also the variables that determine the price of cars.
In this paper we will analyze the various factors that affect the cost of cars, the final price of the car will depend on the type of car, from the analysis cars are divided into various categories and their basic price determined, hypothesis tests are also carried out to determine the validity of the conclusion that some cars are more expensive than others.
The paper also focuses on the various variables that affect the value of miles per gallon of a car, one of the factor analyzed include the engine size whereby it is clear that the larger the size the more the consumption per mile. We also comp[are the miles per gallon and the type of car, in this analysis it is clear that small cars have high value of miles per gallon but their price is still low, this shows that some car types are more economical in terms of consumption and still are sold at very low prices.
Type of cars and price:
From the data available for analysis it was clear that the price of cars depended on the car type, the mean price is high for the mid size cars than any other car, the lowest mean price is that of the small type of cars, the table below summarizes the mean values of price:
car type
mean basic price
mean top price
compact
1
15.7
20.7
small
2
8.4
11.9
midsize
3
24.1
30.3
large
4
22.9
25.7
sporty
5
16.9
22.0
van
6
16.2
22.0
From the above table it is clear that mid size cars are more expensive than any other car with a mean price of 24.1 thousand, the low cost cars are the small cars whose mean price is 8.4. the high price may be as a result of the high demand in the market, The chart below summarizes the mean prices for the different type of cars:
From the chart above it is evident that the mid size cars have a higher mean price, followed by the large cars, then the sporty cars and the lowest mean price is the small cars. The prices of cars depend on many factors including the demand and supply level and also other factors associated with the car.
We test the hypothesis that the price for medium cars is higher than the price for the small cars, this will require us to state our null and alternative hypothesis and also find the mean and standard deviation for the two means, the table below summarizes the mean and standard deviation for the two type of cars:
car type
mean basic price
standard deviation
small
2
8.4
1.493031432
large
4
22.9
6.260714452
The above table summarizes the mean basic price of both large and small cars, it also conatins the standard deviation of the basic price mean, the above information will help us to undertake a hypothesis test on the means.
Our null hypothesis is as follows:
H0: S = L
Alternative hypothesis is as follows:
Ha: L> S
Where S is the mean basic price for small cars and L is the mean basic price for the large cars.
L – S
Z = ___________
[(Lσ12/ n1) + (Sσ22/ n2)] ½
Where σ is the standard deviation
Our Z therefore is equal to 7.573550735, at 98% level of test this value exceeds the critical value and therefore we reject the null hypothesis that S = L, for this reason therefore we conclude that the mean price for large cars is higher than the mean price for the large cars.
Miles per gallon versus type of car:
The MPG of cars will differ with the type of car, we expect that small cars will have a large value of mile per gallon than any other car and this depends on the size of the engine and that they are economical and also posses low horse power. The following chart summarizes the miles per gallon for the different types of cars.
Small type of cars have a larger mean mile per gallon than any other car, larger cars on the other hand have the lowest mile per gallon, this mean that small cars are more economical than larger cars, the higher the miles per gallon means that the car is efficient and more economical than any other car and in our case the small cars fall under this category.
Car price and horse power:
We hypothesis that the price of cars will depend on the level of horse power, horse power refers to the driving power of a car, for this reason we check the various types of cars and their mean horse power and compare with the price. We expect that the higher the horse power level then the higher is the price per unit for a car. the following table summarizes the mean horse power and the mean basic prices for each car type:
car type
mean basic price
horse power
compact
1
15.7
131.0
small
2
8.4
91.0
midsize
3
24.1
173.1
large
4
22.9
179.5
sporty
5
16.9
160.1
van
6
16.2
149.4
From the above table we summarize the mean price and horse power for the various types of cars, the small cars have low horse power level while large cars have a high horse power level, it is therefore evident that a small car will have a low price due to the low horse power level while the large cars will have a higher price due to the horse power level, the following chart shows a scatter diagram demonstrating the x axis as the horse power level and Y axis as the price:
The above chart shows the excel output of a scatter diagram of horse power versus the price, the line shows the trend line that depicts a line of best fit. From the chart it is clear that as the level of horse power increases then the higher is the price, this shows that cars with a higher horse power level will cost more. We can therefore conclude that the price of cars will depend on the horse power whereby the higher the horse power level of a car then the higher is the price.
Miles per gallon versus the price:
We now analyze the relationship between miles per gallon versus the price, in this case we will compare all the cars prices versus the price, for this reason we will use the entire sample to analyze this relationship. It is evident from previous analysis that a high level of miles per gallon will be associated with the small cars that have low cost price, for this reason therefore we expect that the higher the basic price then the lower the miles per gallon, the following chart summarizes the entire sample and shows the relationship between miles per gallon and the basic price:
The above is an excel output showing a scatter diagram portraying the relationship between the price and miles per gallon, the trend lien shows the line of best fit and it clearly shows that the higher the level of miles per gallon then the lower is the price, from the output also we achieve a regression model for the data which states that Y = -0.4X + 29.22. Where Y is the price and X is the miles per gallon, this means that when we increase the miles per gallon by one unit then the level of price declines by 0.4thousand dollars and that if the level of miles per gallon is zero then the price level would be 29.22. For this reason the cars with lower miles per gallon will be highly priced while those with higher miles per gallon then the lower the price.
The R squared or the correlation of determination for this regression is 0.388 meaning that only 38.8% of deviation in prices is explained by the level of miles per gallon. The correlation coefficient for the data is -0.62288 meaning that there is a strong negative relationship between the two variables, the negative correlation means that as one variable increase then the other variable will be declining.
We now test the statistical significance of the estimated regression, this will involve
The table below summarizes the standard error of our estimated coefficients:
std error
a
3.521786342
b
0.152766014
Having determined our standard error we can determine whether they are statistically significant:
The slope b:
Null hypothesis
H0: b = 0
Alternative hypothesis
Ha: b ≠ 0
Z = b/std error
Z = -0.4/0.152766014
Z = -2.618383434
At 95% level of test we conclude that the slope coefficient is statistically significant because the calculated value of Z exceeds the critical value, for this reason therefore we accept the alternative hypothesis and state that the slope is statistically significant.
The autonomous value:
The constant a:
Null hypothesis
H0: a = 0
Alternative hypothesis
Ha: a ≠ 0
Z = a/std error
Z = 8.296925811
At 95% level of test we conclude that the constant coefficient is statistically significant because the calculated value of Z exceeds the critical value, for this reason therefore we accept the alternative hypothesis and state that the constant is statistically significant.
Miles per gallon and the engine size:
We now analyze the relationship between the engine size and the miles per gallon, we expect that the larger the engine size then the lower the level of miles per gallon per car, this is because we expect that the larger the car the more the consumption level of fuel, the chart below summarizes the entire data:
The above diagram shows the scatter diagram depicting the miles per gallon and the engine size, the diagram shows the trend lien that depict that as the engine size increases then the miles per gallon declines, this is to state that cars with bigger engines are less economical due to the high consumption of fuel.
Regression of the data shows that Y = -3.846X + 32.62 where Y is miles per gallon and X is the engine size, when the engine size increases by one unit according to this estimated model then the miles per gallon level decline by 3.846, however if the engine size is zero then the level of miles per gallon will be32.62 according to the model.
The R squared value or the correlation of determination is 0.504 meaning that 50.4% of deviation in the miles per gallon is explained by the engine size, the correlation coefficient r in this case is -0.71meaning that there is a strong but negative correlation between the two variables, negative correlation here means that as one variable increases then the other variable is decreasing.
The standard error for the slope coefficient is 0.399913 while that for the constant a is 10.3516, having calculated our standard error we can test hypothesis on the significance of the coefficients. we stated our model as Y = A + bX where Y is the miles per gallon and X is the engine size we check for the statistical significance of our estimated coefficients as follows using test hypothesis:
Having determined our standard error we can determine whether they are statistically significant:
The slope b:
Null hypothesis
H0: b = 0
Alternative hypothesis
Ha: b ≠ 0
Z = b/std error
Z = -9.617084576
At 95% level of test we conclude that the slope coefficient is statistically significant because the calculated value of Z exceeds the critical value, for this reason therefore we accept the alternative hypothesis and state that the slope is statistically significant.
The autonomous value:
The constant a:
Null hypothesis
H0: a = 0
Alternative hypothesis
Ha: a ≠ 0
Z = a/std error
Z = 3.15120306
At 95% level of test we conclude that the constant coefficient is statistically significant because the calculated value of Z exceeds the critical value, for this reason therefore we accept the alternative hypothesis and state that the constant is statistically significant.
Conclusion:
From the above analysis it is clear that the price of cars will depend on the type of car, the types of cars are grouped into categories which include large cars, sporty cars, medium size, compact cars and vans. The lowest mean price is the small cars smaller cars have a lower basic price compared to the medium size cars which have the highest mean basic price. The price difference depends on the engine size and other factors.
Our next analysis involved checking the relationship between miles per gallon and the basic price, from this analysis it was evident that Small type of cars have a high mean mile per gallon than any other car, larger cars on the other hand have the lowest mile per gallon, this mean that small cars are more economical than larger cars, the higher the miles per gallon in this analysis showed that a high miles per gallon is a symbol of efficiency and the cost of maintenance.
It was also evident that there was a difference in the horse power and the type of car, the small type of cars had low mean horse power level compared to the larger cars it was therefore evident that small car will have a low price due to the low horse power level while the large cars will have a higher price due to the horse power level.
Regression analysis was also undertaken to determine the relationship between the miles per gallon and the other variables, for the relationship between miles per gallon and the price it was evident that those cars with a high miles per gallon had a low price in the market, the model estimated was stated as Y = -0.4X + 29.22 Where Y was the price and X was the miles per gallon, meaning that increasing the miles per gallon by one unit will reduce the price by 0.4 thousand. Statistical hypothesis testing also showed that the estimated coefficients were statistically significant.
The other regression was undertaken to determine the relationship between the relationship between the miles per gallon and the engine size, the estimated model showed that Y = -3.846X + 32.62 where Y was miles per gallon and X was the engine size, this model shows that when the engine size increases by one unit then the miles per gallon level decline by 3.846, this clearly shows that the bigger the engine then the lower the miles per gallon, from this analysis it was evident that the bigger the engine the higher the consumption and therefore the less efficient the car.
The above analysis therefore could help in guiding buyers and sellers to the best choice of cars, buyers are aiming at maximizing their utility by reducing the maintenance cost and yet getting the car they desire, for this reason therefore the above analysis would be helpful in further understanding of the products offered in the market and therefore help in making optimal decision.
References:
Burbidge S. (1993) Statistics: An Introduction to Quantitative Research,McGraw Hill, New York
Bridge D. (1994) Statistics: An Introduction to Quantitative Economic Research, Rand McNally publishers, Michigan
Chambers R (2003) Analysis of Survey Data, Wiley publishers, New York
D Amaratunga and et al (2002) Quantitative and qualitative research, McGraw Hill publishers, New York
R. Bogdan and K. Biklen (1992) Qualitative Research: Introduction to Theory and Methods, MIT press, London
Appendixes:
1=compact
Manufacturer
Model
Car Type
Basic price
Top Price
MPGTown
MPGBest
AirBag
Cyl
HP
Length
Engine size
PassCap
RPM
Weight
mean
15.7
20.7
22.7
29.9
0.8
4.1
131.0
182.1
2.3
5.1
5362.5
2918.1
stad deviation
5.873155739
7.960946342
1.92245503
2.9410882
0.65510813
0.5
22.77133
3.792537
0.267628
0.442531
461.6998
216.386
median
14.1
18.5
23.0
30.0
1.0
4.0
132.0
181.5
2.3
5.0
5450.0
2970.0
mode
13
18.3
20
31
1
4
110
184
2.2
5
5600
3085
2 SMALL
Model
Car Type
Basic price
Top Price
MPGTown
MPGBest
AirBag
Cyl
HP
Length
Engine size
PassCap
RPM
Weight
mean
8.4
11.9
29.9
35.5
0.2
3.9
91.0
167.2
1.6
4.6
5633.3
2312.9
stad deviation
1.493031432
2.803297378
6.10971124
5.6090913
0.43643578
0.358569
21.15656
10.15686
0.269214
0.497613
469.3968
267.304
median
8.2
11.3
29.0
33.0
0.0
4.0
90.0
172.0
1.6
5.0
5600.0
2345.0
mode
8.4
10
29
33
0
4
92
172
1.8
5
6000
2295
3=midsize
Manufacturer
Model
Car Type
Basic price
Top Price
MPGTown
MPGBest
AirBag
Cyl
HP
Length
Engine size
PassCap
RPM
Weight
mean
24.1
30.3
19.5
26.7
1.1
5.5
173.1
192.5
3.1
5.1
5336.4
3400.0
stad deviation
10.15233004
15.08554324
1.89554045
2.5105837
0.71016125
1.224745
52.49844
6.037401
0.735274
0.560226
596.4542
321.355
median
23.1
27.4
19.0
26.5
1.0
6.0
169.0
191.5
3.0
5.0
5300.0
3472.5
mode
14.2
18.4
19
26
1
6
110
188
3
5
5200
#N/A
4=large
Manufacturer
Model
Car Type
Basic price
Top Price
MPGTown
MPGBest
AirBag
Cyl
HP
Length
Engine size
PassCap
RPM
Weight
mean
22.9
25.7
18.4
26.7
1.4
6.7
179.5
204.8
4.2
6.0
4672.7
3695.5
stad deviation
6.260714452
6.668746645
1.50151439
1.2720778
0.50452498
1.00905
21.84199
11.35622
0.793038
0
544.2259
254.1403
median
19.9
21.9
19.0
26.0
1.0
6.0
170.0
203.0
3.8
6.0
4800.0
3570.0
mode
#N/A
21.7
19
28
1
6
170
203
3.8
6
4800
3470
5=sporty
Manufacturer
Model
Car Type
Basic price
Top Price
MPGTown
MPGBest
AirBag
Cyl
HP
Length
Engine size
PassCap
RPM
Weight
mean
16.9
22.0
21.8
28.8
1.0
4.9
160.1
175.2
2.5
3.7
5392.9
2899.6
stad deviation
7.895345687
8.573098738
3.90617994
3.6411869
0.67936622
1.320451
74.40622
10.47472
1.149223
0.726273
574.0735
407.6219
median
13.7
21.2
22.5
28.5
1.0
4.0
147.5
174.5
2.3
4.0
5450.0
2857.5
mode
#N/A
#N/A
19
25
1
4
160
179
3.4
4
4600
3240
6=van
Manufacturer
Model
Car Type
Basic price
Top Price
MPGTown
MPGBest
AirBag
Cyl
HP
Length
Engine size
PassCap
RPM
Weight
mean
16.2
22.0
17.0
21.9
0.3
5.7
149.4
185.7
3.2
7.1
4744.4
3830.6
stad deviation
2.027929979
3.009152705
1.22474487
1.4529663
0.5
0.707107
19.2426
7.466592
0.634429
0.333333
320.5897
154.0991
median
16.6
21.7
17.0
22.0
0.0
6.0
151.0
187.0
3.0
7.0
4800.0
3735.0
mode
14.7
#N/A
18
23
0
6
170
194
3
7
4800
3715
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