<< Click to Display Table of Contents >> LOGEST (statistics of an exponential regression)

Syntax:

LOGEST(y_values [, x_values] [, Constant] [, Stats])

Description:

This returns statistics of an exponential regression.

Exponential regression is a statistical technique that adapts an exponential curve to a set of data points (for example, the results of a series of measurements).

The equation for this exponential curve is as follows:

y = b*m^x

If more than one range of x values is given, the equation is:

y = b * (m1^x1) * (m2^x2) * ... * (mn^xn)

The LOGEST function calculates this exponential line from the given y values and x values, and then returns an array in the form {mn , mn-1 , ... , m2 , m1 , b}.

If the optional argument Stats is used, several statistics of the regression (standard error, coefficient of determination, etc.) are added to the resulting array.

The LOGEST function expects the following arguments:

y_values: Here, you specify the existing y coordinates, that is, the dependent values. y_values can be either a cell reference or an array.

x_values: Here, you have the option of specifying the x coordinates, that is, the independent values. x_values also can be either a cell reference or an array. If x_values are omitted, the function automatically uses the values 1, 2, 3, ... (according to the number of existing y_values).

Constant (optional) is a logical value that lets you specify if the constant b should be set to 1 (one):

TRUE or omitted: b is automatically calculated from the available data.

FALSE: b is forced to equal 1 (one). The m coefficients are adjusted accordingly.

Stats (optional) is a logical value that lets you specify if additional regression statistics should be returned:

FALSE or omitted: Do not return additional statistics.

TRUE: Return additional statistics. In this case, the function returns an array that not only includes m and b, but also the following values:

{mn , mn-1 , ... , m2 , m1 , b ; smn , smn-1 , ... , sm2 , sm1 , sb ; R2 , sey ; F. df ; ssreg , ssresid}

A graphical representation of this array would look as follows:

The above abbreviations represent the following values:

Note:

Formulas using this function have to be entered as an array formula. For more information, see Working with arrays.

See also:

LINEST, TREND, GROWTH