SLOPE function

This article describes the formula syntax and usage of the SLOPE function (function: A prewritten formula that takes a value or values, performs an operation, and returns a value or values. Use functions to simplify and shorten formulas on a worksheet, especially those that perform lengthy or complex calculations.) in Microsoft Excel.

Description

Returns the slope of the linear regression line through data points in known_y's and known_x's. The slope is the vertical distance divided by the horizontal distance between any two points on the line, which is the rate of change along the regression line.

Syntax

SLOPE(known_y's, known_x's)

The SLOPE function syntax has the following arguments (argument: A value that provides information to an action, an event, a method, a property, a function, or a procedure.):

  • Known_y's    Required. An array or cell range of numeric dependent data points.
  • Known_x's    Required. The set of independent data points.

Remarks

  • The arguments must be either numbers or names, arrays, or references that contain numbers.
  • If an array or reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
  • If known_y's and known_x's are empty or have a different number of data points, SLOPE returns the #N/A error value.
  • The equation for the slope of the regression line is:

Equation

where x and y are the sample means AVERAGE(known_x’s) and AVERAGE(known_y’s).

  • The underlying algorithm used in the SLOPE and INTERCEPT functions is different than the underlying algorithm used in the LINEST function. The difference between these algorithms can lead to different results when data is undetermined and collinear. For example, if the data points of the known_y's argument are 0 and the data points of the known_x's argument are 1:
    • SLOPE and INTERCEPT return a #DIV/0! error. The SLOPE and INTERCEPT algorithm is designed to look for one and only one answer, and in this case there can be more than one answer.
    • LINEST returns a value of 0. The LINEST algorithm is designed to return reasonable results for collinear data, and in this case at least one answer can be found.

Example

The example may be easier to understand if you copy it to a blank worksheet.

ShowHow do I copy an example?

  1. Select the example in this article. If you are copying the example in Excel Online, copy and paste one cell at a time.
    Important: Do not select the row or column headers.

Selecting an example from Help

Selecting an example from Help

  1. Press CTRL+C.
  2. Create a blank workbook or worksheet.
  3. In the worksheet, select cell A1, and press CTRL+V. If you are working in Excel Online, repeat copying and pasting for each cell in the example.
    Important: For the example to work properly, you must paste it into cell A1 of the worksheet.
  4. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

After you copy the example to a blank worksheet, you can adapt it to suit your needs.

 
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Known y Known x
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Formula Description (Result)
=SLOPE(A2:A8,B2:B8) Slope of the linear regression line through the data points above (0.305556)
 
 
Applies to:
Excel 2010, Excel Web App, SharePoint Online for enterprises, SharePoint Online for professionals and small businesses