# Statistics Essay

**Topics:**Regression analysis, Simple linear regression, Statistics

**Pages:**6 (1405 words)

**Published:**February 24, 2013

In this assignment I compiled the data of the Nissan GT-R 3.8 (R35). The Data collected includes the age, type and price which allowed me to make a statistic about how the age affects the price of this certain model over several years. I will be using the correlation regression and scatter diagram to get the regression line. As we can see, the price drops the elder the car is. Inside the range of the diagram the prediction might be accurate. So we can tell very precisely how much the car is going to cost in the next few years, but we won’t be able to give a very precise prediction on how much the car is going to cost after a long term (more than 10 years). This project shows the readers to justify why the age of the car affects the price of the car. The results vary for different cars but ultimately, the results that were found in this assignment are valuable in terms of understanding the automobile market.

Table of Content

1.0 Correlation and Regression

Generally, regression locates bivariate data in terms of a mathematical relationship, able to be graphed as a line or curve while correlation describes the nature of the spread of the items about the line or curve. (Francis, p.165, 2004) Regression is concerned with obtaining a mathematical equation which describes the relationship between two variables. The equation can be used for a comparison or estimation purposes (Francis, p.173, 2004) while correlation is concerned with describing the strength of the relationship between two variables by measuring the degree of “scatter” of the data values (Francis, p.192, 2004) The term simple regression analysis indicates that the value of the dependent variable is estimated on the basis of one independent variable. (Kazmier, p.242, 1988) In contrast to regression analysis, correlation analysis measures the degree of relationship between the variables. As was true, in our coverage of regression analysis, which is concerned only one independent variable and the dependent variable. (Kazmier, p.246, 1988) The correlation between two random variables X and Y is a measure of the degree of linear association between the two variables. Two variables are highly correlated if they move well together. Correlation is indicated by the correlation coefficient. (Aczel-Sounderpandian, p.429, 2009) -------------------------------------------------

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r=n εxy-εx(εy)nεx2- εx2[ nεy2-(εy)²

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2.0 Data Collection

Model: NISSAN GT-R 3.8l V6 BiTurbo, 2008-2011

Nr.| Model| Age Y| Price (CHFx00) X|

1| Nissan GT-R 3.8| 4| 900|

2| Nissan GT-R 3.8| 3| 890|

3| Nissan GT-R 3.8| 3| 880|

4| Nissan GT-R 3.8| 3| 925|

5| Nissan GT-R 3.8| 2| 848|

6| Nissan GT-R 3.8| 2| 139.9|

7| Nissan GT-R 3.8| 2| 76.9|

8| Nissan GT-R 3.8| 2| 94.9|

9| Nissan GT-R 3.8| 1| 149.9|

10| Nissan GT-R 3.8| 1| 139.9|

3.0 Scatter diagram

4.0 Product moment correlation

No.| X| Y (CHF’00)| X²| Y²| XY|

1| 4| 900| 16| 810000| 3600|

2| 3| 890| 9| 792100| 2670|

3| 3| 880| 9| 774400| 2640|

4| 3| 925| 9| 855625| 2775|

5| 2| 848| 4| 719104| 1696|

6| 2| 1399| 4| 1957201| 2798|

7| 2| 769| 4| 591361| 1538|

8| 2| 949| 4| 900601| 1898|

9| 1| 1499| 1| 2247001| 1499|

10| 1| 1399| 1| 1957201| 1399|

N = 10| ∑X=23| ∑Y=10458| ∑x²=61| ∑y²=11604594| ∑XY=22513|

r=n ∑xy-∑x(∑y)⎷n∑x2- ∑x2[ n∑y2-(∑y)²

r=10 (22513)- (23)(10458)⎷10(61)- 232[ 10(11604594)-(22513)²

r=-15404⎷8892885971

r = - 0.1633473706

Comment on the product moment correlation coefficient:

The product moment correlation coefficient shows a weak negative correlation efficient between the age (x) and the selling price (y) of Nissan...

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