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#Statistical

SLOPE

Excel Functions

Get slope of linear regression line

Syntax

EXCEL 
=SLOPE(known_ys, known_xs)

Arguments

Parameter Description
known_ys An array or range of numeric data points (dependent values).
known_xs An array or range of numeric data points (independent values).

Return Value

Calculated slope as a number

Details

The SLOPE function returns the slope of a regression line based on known y values and known x values. A regression line is a "best fit" line based on known data points. The slope of a line is a measure of steepness. Mathematically, slope is calculated as "rise over run", or change in y over the change in x. For example, if a line has a slope of 2/1 (2), then if y increases by 2 units, x increases by 1 unit. In the example shown, the formula in E5 is: This formula returns -2, based on known_ys in C5:C9, and known_xs in B5:B9. In statistics, a best fit line does not normally lie exactly on the known x and y points. The equation used by the SLOPE function in Excel is based on the mean of known x's and y's:

Examples

Example

In the example shown, the formula in E5 is:

EXCEL 
=SLOPE(B5:B9,C5:C9) // returns -2
Equation

For the example shown, this formula can be manually recreated like this:

EXCEL 
=SUM((B5:B9-AVERAGE(B5:B9))*(C5:C9-AVERAGE(C5:C9)))/SUM((B5:B9-AVERAGE(B5:B9))^2)

See Also

INTERCEPT LINEST