Author: Oscar Cronquist Article last updated on October 30, 2018

The LOGEST function returns an array of values representing the parameters of an exponential curve that fits your data, based on the "least squares" method. This function must be entered as an array formula.

Array formula in cell range C15:D15:

=LOGEST(B3:B12)

To enter an array formula, type the formula in a cell then press and hold CTRL + SHIFT simultaneously, now press Enter once. Release all keys.

The formula bar now shows the formula with a beginning and ending curly bracket telling you that you entered the formula successfully. Don't enter the curly brackets yourself.

### Excel Function Syntax

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

### Arguments

The equation for the curve is y = b*m^x or y = (b*(m1^x1)*(m2^x2)* ...) if multiple x-values are used. y, x and m can be vectors and LOGEST returns the following array: {mn, mn-1, ..., m1, b}. The m-values correspond to the x-values.

 known_y's Required. Single column - Each row is a separate variable. Single row - Each column is a separate variable. [known_x's] Optional. Known x points, default values are 1, 2, 3, ... [const] Optional. A boolean value determining if constant b is equal to 0 (zero). TRUE - constant b is calculated. Default. FALSE - constant b is 0 (zero). [stats] Optional. A boolean value determining whether to calculate additional regression statistics. TRUE - Returns additional regression statistics. {mn, mn-1, ..., m1, b;sen, sen-1, ..., se1, seb;r2, sey;F, df;ssreg, ssresid} FALSE - returns only m and b.

The following table shows what the LOGEST function returns if [stats] argument is TRUE.

 Statistic Description se1, se2, ..., sen The standard error values. seb The standard error value for the constant b. seb returns #N/A when const argument is FALSE. r2 The coefficient of determination. A perfect correlation is 1 and 0 (zero) means no correlation based on comparing the actual and the LOGEST functions estimated y-values. sey The standard error for the estimated y-values. F The F statistic, or the F-observed value. Determines if the observed relationship between the dependent and independent variables occurs by chance. df The degrees of freedom assists you in finding F-critical values, then compare the values to the F statistic to get the confidence level for the model. ssreg The regression sum of squares. ssresid The residual sum of squares.