# How to find correlation coefficient

The quantity *r*. called the *linear correlation coefficient*. measures the strength and

the direction of a linear relationship between two variables. The linear correlation

coefficient is sometimes referred to as the *Pearson product moment correlation coefficient* in

honor of its developer Karl Pearson.

The mathematical formula for computing*is:*

**r**where *n* is the number of pairs of data.

(Aren't you glad you have a graphing calculator that computes this formula?)

The value of*r*is such that -1

__<__

*r*

__<__+1. The + and – signs are used for positive

linear correlations and negative linear correlations, respectively.

*Positive correlation:*If

*x*and

*y*have a strong positive linear correlation,

*r*is close

to +1. An *r* value of exactly +1 indicates a perfect positive fit. Positive values

indicate a relationship between *x* and *y* variables such that as values for *x* increases,

values for *y* also increase.

*Negative correlation:*If

*x*and

*y*have a strong negative linear correlation,

*r*is close

to -1. An *r* value of exactly -1 indicates a perfect negative fit. Negative values

indicate a relationship between *x* and *y* such that as values for *x* increase, values

for *y* decrease.

*No correlation:*If there is no linear correlation or a weak linear correlation,

*r*is

close to 0. A value near zero means that there is a random, nonlinear relationship

between the two variables

Note that*r*is a dimensionless quantity; that is, it does not depend on the units

employed.

A*perfect*correlation of ± 1 occurs only when the data points all lie exactly on a

straight line. If *r* = +1, the slope of this line is

positive. If *r* = -1, the slope of this

line is negative.

A correlation greater than 0.8 is generally described as*strong*. whereas a correlation

less than 0.5 is generally described as *weak*. These values can vary based upon the

"type" of data being examined. A study utilizing scientific data may require a stronger

correlation than a study using social science data.

**Coefficient of Determination, r 2 or R 2 :**

*coefficient of determination,*

*r*2. is useful because it gives the proportion of

the variance (fluctuation) of one variable that is predictable from the other variable .

It is a measure that allows us to determine how certain one can be in making

predictions from a certain model/graph.

The*coefficient of determination*is the ratio of the explained variation to the total

variation.

The*coefficient of determination*is such that 0

__<__

*r*2

__<__1, and denotes the strength

of the linear association between *x* and *y*.

*coefficient of determination*represents the percent of the data that is the closest

to the line of best fit. For example, if *r* = 0.922, then *r* 2 = 0.850, which means that

85% of the total variation in *y* can be explained by the linear relationship between *x*

and *y* (as described by the regression equation). The other 15% of the total variation

in *y* remains unexplained.

*coefficient of determination*is a measure of how well the regression line

represents the data. If the regression line passes exactly through every point on the

scatter plot, it would be able to explain all of the variation. The further the line is

away from the points, the less it is able to explain.

Source: mathbits.comCategory: Forex

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