Positive and Negative Correlation - Article Example

Positive and Negative Correlation Introduction It is a widely accepted notion that as the age of a machine increases, its value generally decreases. This phenomenon can be applied to virtually all kinds of machinery – computers, home appliances, automobiles, etc. However, one model that does not have a significantly published result is that of the relationship between the age of a buyer and the amount of money spent. Ideally, it would be futile to estimate any kind of relationship that would fit in between these two variables: there seems to be no direct relationship that could exist between the two variables. The aim of researchers is to find out relationships between variables if they do not already exist by constant market data collection and statistical inference. The aim of this research paper is to identify where there could exist a regression model i.e. a high degree of correlation, positive or negative, between the ages of automobile buyers and the amount of money they spend on the purchase of an automobile. Data Source There is virtually no existent theory that could justify, predict or estimate the relationship between the age of an automobile buyer and the money spent on the purchase of an automobile. Commons sense, however, dictates that generally older buyers must be having a higher purchasing power and would thus be in a position to spend more on automobiles. Any kind of common sense “relationship” cannot be proved to be correct until and unless it is seconded by collected data and a particular statistical technique is applied to get an accept or reject conclusion. For the scope of this project, I have collected data from an informal source: an old friend of mine has a father in the automobile business. His business is to buy and sell all kinds of cars: brand new and used. He records various details of buyers and sellers in every sale he makes. Amongst the various fields stored, I was able to extract the age of the buyer by calculation: using the Date of Birth provided on the sales deed and the date of sale. The second statistic extracted was the sale amount. A great deal of care and emphasis was kept to maintain confidentiality and privacy of data as per the company rules and regulations. Since the research needed to be carried out on ‘actual’ data, it was necessary that the figures were not fabricated or “random-generated”. However, anonymity in all other aspects was ensured. Out of a total of 1000 records, I obtained a sample of 80 records randomly distributed across the years 2004, 2005, 2006 and 2007. Hypothesis “Is there a positive or negative linear correlation i.e. relationship between the age of a buyer of an automobile and the price of the automobile that could be used as a model for prediction?” The dataset is as follows: Age Price 46 23197 39 20642 48 23372 43 21981 40 20454 56 24052 40 23591 44 25799 46 26651 30 15794 37 27453 39 18263 32 17266 53 35925 29 18021 29 17399 38 28683 30 17968 43 30872 44 20356 32 19587 41 21442 47 23169 41 21722 56 35851 35 19331 42 19251 51 22817 28 20047 44 19766 56 24285 51 20633 50 24324 49 20962 31 24609 41 22845 51 28670 44 26285 26 15546 37 27896 25 15935 42 29076 45 19873 51 32492 56 25251 31 18890 47 25277 39 21740 38 28034 53 22374 51 24533 55 24571 39 27443 40 25449 44 19889 46 28337 46 20004 35 20642 28 17357 47 23613 33 20155 58 24220 35 19688 51 30655 35 23657 41 22442 42 26613 33 17891 35 20895 46 20818 36 20203 47 26237 48 23765 34 20445 53 25783 43 21556 46 26661 37 21639 55 32277 47 24296 We can say that the above data can be divided as: Independent variable: Age Dependent variable: Money spent on automobile purchase Ordered Pairs: [Age, Money spent on automobile purchase] Once again, it is important to understand that the assumption applied is: age is a determinant of the money that a buyer is able to spend on an automobile. The above dataset was plotted using a scatter plot in a simple Excel spreadsheet. The scatter plot for the dataset is as follows: The above plot is the first step towards proving that there exists a significant predictive model between the two variables and finding the specifications of the model. The graph yields a very straight line sloping upwards that can be drawn through the dataset to reveal a trend line. The trend line is the actual predictive model that would exist if the statistical test yields a positive result for the relationship strength between the variables. The CORREL function yields the following value for the correlation coefficient and the coefficient of determination is obtained by taking the square root of the correlation coefficient: R=0.6032 D=+0.7767 The regression model from Excel formula reveals that the following predictive model can be used for the trend line relationship between the two variables: The positive value of the coefficient of determination is selected because of the fact that the trend line drawn for the dataset is sloping upwards. This upward slope makes it ideal for us to test whether there is a positive relationship between the datasets or not: there is no negative relationship strong enough to form a predictive model between the two variables as per the observations from the scatter plot. A regression test will be carried out on the 80-records strong dataset at a 5% level of significance in order to conclude as to whether there is a significant relationship between the two variables, age and money spent on an automobile, that could be used as a predictive model or not. Hence, reject H0. This is because the test carried out at the 95% level of significance provides sufficient evidence that the correlation between the datasets is greater than 0. It is clear that the observations of the scatter graph are further strengthened and corroborated for by the results of the regression test. It can now be concluded that a predictive model exists that could predict the money spent on an automobile by a purchaser if their age is known. However, the limitation of this model is that its scope is narrow and applicable to only the business of my friend’s father. The predictive relationship can be expressed using the following equation: Though there could be various reasons for this kind of a relationship, it cannot be said that this exists across the board. It is particularly strongly applicable to the business in context and can come in as a handy tool for estimating quickly a guess for the automobile spending by a buyer. Works Cited 1. Nathan, J. (1995). Statistical Inference. Chicago: Delton Publishers Inc. 2. Use of Statistics in Business. (2008, July 26). 3. Walpole, R. E. (2002). Introductory Statistics. Los Angeles: Kraft Publishers. 4. Weiss, N. A. (1984). Introductory Statistics, 5th Edition. New York: CRC Press. Read More