LOGEST function

This article describes the formula syntax and usage of the LOGEST function in Microsoft Excel.

Description

In regression analysis, calculates an exponential curve that fits your data and returns an array of values that describes the curve. Because this function returns an array of values, it must be entered as an array formula.

The equation for the curve is:

y = b*m^x

or

y = (b*(m1^x1)*(m2^x2)*_)

if there are multiple x-values, where the dependent y-value is a function of the independent x-values. The m-values are bases corresponding to each exponent x-value, and b is a constant value. Note that y, x, and m can be vectors. The array that LOGEST returns is {mn,mn-1,...,m1,b}.

Syntax

LOGEST(known_y's, [known_x's], [const], [stats])

The LOGEST function syntax has the following arguments:

  • Known_y's    Required. The set of y-values you already know in the relationship y = b*m^x.

    • If the array known_y's is in a single column, then each column of known_x's is interpreted as a separate variable.

    • If the array known_y's is in a single row, then each row of known_x's is interpreted as a separate variable.

  • Known_x's    Optional. An optional set of x-values that you may already know in the relationship y = b*m^x.

    • The array known_x's can include one or more sets of variables. If only one variable is used, known_y's and known_x's can be ranges of any shape, as long as they have equal dimensions. If more than one variable is used, known_y's must be a range of cells with a height of one row or a width of one column (which is also known as a vector).

    • If known_x's is omitted, it is assumed to be the array {1,2,3,...} that is the same size as known_y's.

  • Const    Optional. A logical value specifying whether to force the constant b to equal 1.

    • If const is TRUE or omitted, b is calculated normally.

    • If const is FALSE, b is set equal to 1, and the m-values are fitted to y = m^x.

  • Stats    Optional. A logical value specifying whether to return additional regression statistics.

    • If stats is TRUE, LOGEST returns the additional regression statistics, so the returned array is {mn,mn-1,...,m1,b;sen,sen-1,...,se1,seb;r 2,sey; F,df;ssreg,ssresid}.

    • If stats is FALSE or omitted, LOGEST returns only the m-coefficients and the constant b.

For more information about additional regression statistics, see the LINEST function.

Remarks

  • The more a plot of your data resembles an exponential curve, the better the calculated line will fit your data. Like LINEST, LOGEST returns an array of values that describes a relationship among the values, but LINEST fits a straight line to your data; LOGEST fits an exponential curve. For more information, see LINEST.

  • When you have only one independent x-variable, you can obtain y-intercept (b) values directly by using the following formula:

    Y-intercept (b):
    INDEX(LOGEST(known_y's,known_x's),2)

    You can use the y = b*m^x equation to predict future values of y, but Microsoft Excel provides the GROWTH function to do this for you. For more information, see GROWTH function.

  • Formulas that return arrays must be entered as array formulas.

    Note    In Excel Online you cannot create array formulas.

  • When entering an array constant such as known_x's as an argument, use commas to separate values in the same row and semicolons to separate rows. Separator characters may be different depending on your regional settings.

  • You should note that the y-values predicted by the regression equation may not be valid if they are outside the range of y-values you used to determine the equation.

Example

Example 1

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

Month

Units

11

33100

12

47300

13

69000

14

102000

15

150000

16

220000

Formula

Description

Result

=LOGEST(B2:B7,A2:A7, TRUE, FALSE)

Note The formula in the example must be entered as an array formula in the Excel program. After copying the example to a blank worksheet, select the range C9:D9 starting with the formula cell. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the single result is 1.4633.

1.4633

495.3048

Example 2

Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.

Month

Units

11

33,100

12

47,300

13

69,000

14

102,000

15

150,000

16

220,000

Formula

Result

=LOGEST(B2:B7,A2:A7,TRUE,TRUE)

1.4633

Applies To: Excel 2016 Preview, Excel 2010, Excel Starter, Excel 2013, Excel Online, Excel 2016 for Mac, Excel for Mac 2011, Excel 2007



Was this information helpful?

Yes No

How can we improve it?

255 characters remaining

To protect your privacy, please do not include contact information in your feedback. Review our privacy policy.

Thank you for your feedback!

Support resources

Change language