Correlation coefficient

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Data

Rowsrows (max 500)

No.	$x_i$	$y_i$	Delete row
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Use the arrow keys to move between cells. Enter moves to the next row, and adds one at the bottom. Pasting two columns copied from Excel or a spreadsheet fills x and y at once.

Result

Item	Symbol and formula	Value
Number of values	$n$	-
Mean of x	$\bar{x}$ $\displaystyle = \frac{1}{n}\sum x_i$	-
Mean of y	$\bar{y}$ $\displaystyle = \frac{1}{n}\sum y_i$	-
Sum of squared deviations of x	$S_{xx}$ $\displaystyle = \sum (x_i - \bar{x})^2$	-
Sum of squared deviations of y	$S_{yy}$ $\displaystyle = \sum (y_i - \bar{y})^2$	-
Sum of products of deviations	$S_{xy}$ $\displaystyle = \sum (x_i - \bar{x})(y_i - \bar{y})$	-
Sample standard deviation of x	$s_x$ $\displaystyle = \sqrt{\frac{S_{xx}}{n-1}}$	-
Sample standard deviation of y	$s_y$ $\displaystyle = \sqrt{\frac{S_{yy}}{n-1}}$	-
Sample covariance	$s_{xy}$ $\displaystyle = \frac{S_{xy}}{n-1}$	-
Population covariance	$\sigma_{xy}$ $\displaystyle = \frac{S_{xy}}{n}$	-
Correlation coefficient	$r$ $\displaystyle = \frac{S_{xy}}{\sqrt{S_{xx} S_{yy}}}$	-
Coefficient of determination	$r^2$	-

Press Calculate to see the values and the scatter plot.

Notes

$r$ measures the strength of a linear relationship only. A curved relationship can still leave $r$ near 0, so read it alongside the scatter plot.
Only rows with both $x$ and $y$ filled in are used. Rows holding a cell that cannot be read as a number are also left out.

Correlation Coefficient Calculator | Updraft - Mechanical Engineering Calculators