LOGEST

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)

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

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

Const   is a logical value specifying whether to force the constant b to equal 1.

Stats   is a logical value specifying whether to return additional regression statistics.

For more information about additional regression statistics, see LINEST.

Remarks

Example

After 10 months of sluggish sales, a company experiences exponential growth in sales after putting a new product on the market. In the subsequent 6 months, sales increased to 33,100, 47,300, 69,000, 102,000, 150,000, and 220,000 units per month. Assume that these values are entered into six cells named UnitsSold. When entered as a formula:


LOGEST(UnitsSold, {11;12;13;14;15;16}, TRUE, TRUE)

generates the following output in, for example, cells D1:E5:

{1.46327563, 495.30477; 0.0026334, 0.03583428; 0.99980862, 0.01101631; 20896.8011, 4; 2.53601883, 0.00048544}

y = b*m1^x1 or using the values from the array:

y = 495.3 * 1.4633x

You can estimate sales for future months by substituting the month number for x in this equation, or you can use the GROWTH function. For more information, see GROWTH.

You can use the additional regression statistics (cells D2:E5 in the above output array) to determine how useful the equation is for predicting future values.

Important   The methods you use to test an equation using LOGEST are similar to the methods for LINEST. However, the additional statistics LOGEST returns are based on the following linear model:

ln y = x1 ln m1 + ... + xn ln mn + ln b

You should keep this in mind when you evaluate the additional statistics, especially the sei and seb values, which should be compared to ln mi and ln b, not to mi and b. For more information, consult an advanced statistics manual.