Correlation_and_trends

Correlation_and_trends - Correlation and Trends Author:...

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Correlation and Trends Author: John M. Cimbala, Penn State University Latest revision: 02 February 2007 Introduction In engineering analysis, we often want to fit a trend line or curve to a set of x-y data. Consider a set of n measurements of some variable y as a function of another variable x . Typically, y is some measured output as a function of some known input , x . In general, in such a set of measurements, there may be: o Some scatter (precision error or random error). o A trend in spite of the scatter, y may show an overall increase with x , or perhaps an overall decrease with x . The linear correlation coefficient is used to determine if there is a trend. If there is a trend, regression analysis is used to find an equation for y as a function of x which provides the best fit to the data. Correlation coefficient The linear correlation coefficient r xy is defined as () 1 22 11 in ii i xy xxyy r x xy y = = == −− = ∑∑ . In the equation above, the mean value of x and the mean value of y are defined in the usual manner as 1 1 i i x x n = = = and 1 1 i i yy n = = = . Some observations about the linear correlation coefficient are worth noting: o By definition, r xy must always lie between 1 and 1, i.e., xy r ≤≤ . o The linear correlation coefficient is always nondimensional , regardless of the dimensions of x and y .
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Correlation_and_trends - Correlation and Trends Author:...

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