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Statistical Correlation

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A correlation between two variables x and y shows how to measure the linear relationship. If one variable changes it causes a proportional change in the other variable. The r is a coefficient of correlation that is a numerical descriptive measurement of the linear association between x and y. It measures the strength of the linear relationship. The symbol r, ranges from -1 to +1, where a prefect correlation is 1 whether it is positive or negative. This means as one variable increases or decreases so does the other variable at the same scale. With a correlation of 0, the variables have no relationship, so if a variable increases, the other many also increase or decrease. “A value of r near or equal to 0 implies little or no linear relationship between y and x. In contrast, the closer r comes to 1 or –1, the stronger the linear relationship between y and x. And if r = 1, or r = –1, all the sample points fall exactly on the least squares line. Positive values of r imply a positive linear relationship between y and x; that is, y increases as x increases. Negative values of r imply a negative linear relationship between y and x; that is, y decreases as x increases” (James T. McClave, 2011).
References
Correlation. (n.d.). Retrieved from http://edl.nova.edu/secure/stats/lesson6.htm
James T. McClave, P. G. (2011). Chapter 10: Simple Linear Regression. In P. G. James T. McClave, Statistics for Business and Economics (pp. 589-590). Pearson

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