Correlation Test


The correlation coefficient is a single-number summary expressing the utility of linear regression. the correlation coefficient is a dimensionless number between - 1 and + 1. The slope and the correlation have the same positive or negative sign. This single number is used to convey the strength of a linear relationship, so values closer to - 1 or + 1 indicate greater fidelity to a straight-line relationship.                                                                                         The correlation is standardized in the sense that its value does not depend on the means or standard deviations of the x or y values.If we add or subtract the same values from the data (and thereby change the means ),the correlation remains the same.If we multiply all the xs (or the ys)by some positive value,the correlation remains the same.If we multiply either the xs or the ys by a negative number, the sign of the correlation will reverse.                                  As with any oversimplification of a complex situation, the correlation coefficient has its benefits, but also its shortcomings. A variety of values of the correlation are illustrated. Each of these separate graphs consists of 50 simulated pairs of observations. A correlation of 0 in the upper left of no indication of a linear relationship between the plotted variables. A correlation of 0.4 does not indicate much strength, either A correlation of either 0.8 or-0.9 indicates a rather strong linear trend.

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