Statistical - LOGEST Function

Description

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

Syntax

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

Arguments

Argument	Description	Required/ Optional
Known_y's	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.	Required
Known_x's	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.	Optional
Const	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.	Optional
Stats	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,mn1,...,m1,b;sen,sen-1,...,se1,seb;r 2,sey; F,df;ssreg,ssresid}. If stats is FALSE or omitted, LOGEST returns only the mcoefficients and the constant b. For more information about additional regression statistics, refer the LINEST Function.	Optional

Notes

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 xvalue, 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}.
The more a plot of your data resembles an exponential curve, the better the calculated line will fit your data. Both LINEST and LOGEST return an array of values that describes a relationship among the values, but LINEST fits a straight line to your data, whereas LOGEST fits an exponential curve.
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 the GROWTH Function does the same.
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.
If the array of known_x's is not the same length as the array of known_y's, LOGEST returns the #REF! error value.
If any of the values in the supplied known_x's or known_y's arrays are not numeric (this may include text representations of numbers, as the LOGEST Function does not recognize these as numbers), LOGEST returns the #VALUE! error value.
If either of the const or stats arguments cannot be evaluated to TRUE or FALSE, LOGEST returns the #VALUE! error value.

Applicability

Excel 2007, Excel 2010, Excel 2013, Excel 2016

Example

advanced_excel_statistical_functions.htm