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In regression analysis, the LOGEST function 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.
Note: If you have a current version of Office 365, then you can simply enter the formula in the top-left-cell of the output range, then press ENTER to confirm the formula as a dynamic array formula. Otherwise, the formula must be entered as a legacy array formula by first selecting the output range, entering the formula in the top-left-cell of the output range, and then pressing CTRL+SHIFT+ENTER to confirm it. Excel inserts curly brackets at the beginning and end of the formula for you. For more information on array formulas, see Guidelines and examples of array formulas.
Description
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:
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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.
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
You must enter the above formula as an array formula in Excel for it to work correctly. After you enter the formula, press Enter if you have a current Office 365 subscription; otherwise press Ctrl+Shift+Enter. If the formula is not entered as an array formula, the single result is 1.4633.
Need more help?
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You can always ask an expert in the Excel Tech Community, get support in the Answers community, or suggest a new feature or improvement on Excel User Voice.
Perhaps the most common Data Analysis tool that you’ll use in Excel is the one for calculating descriptive statistics. To see how this works, take a look at this worksheet. It summarizes sales data for a book publisher.
In column A, the worksheet shows the suggested retail price (SRP). In column B, the worksheet shows the units sold of each book through one popular bookselling outlet. You might choose to use the Descriptive Statistics tool to summarize this data set.
To calculate descriptive statistics for the data set, follow these steps:
Click the Data tab’s Data Analysis command button to tell Excel that you want to calculate descriptive statistics.
Excel displays the Data Analysis dialog box.
In Data Analysis dialog box, highlight the Descriptive Statistics entry in the Analysis Tools list and then click OK.
Excel displays the Descriptive Statistics dialog box.
In the Input section of the Descriptive Statistics dialog box, identify the data that you want to describe.
To identify the data that you want to describe statistically: Click the Input Range text box and then enter the worksheet range reference for the data. In the case of the example worksheet, the input range is $A$1:$C$38. Note that Excel wants the range address to use absolute references — hence, the dollar signs.
To make it easier to see or select the worksheet range, click the worksheet button at the right end of the Input Range text box. When Excel hides the Descriptive Statistics dialog box, select the range that you want by dragging the mouse. Then click the worksheet button again to redisplay the Descriptive Statistics dialog box.
To identify whether the data is arranged in columns or rows: Select either the Columns or the Rows radio button.
To indicate whether the first row holds labels that describe the data: Select the Labels in First Row check box. In the case of the example worksheet, the data is arranged in columns, and the first row does hold labels, so you select the Columns radio button and the Labels in First Row check box.
In the Output Options area of the Descriptive Statistics dialog box, describe where and how Excel should produce the statistics.
To indicate where the descriptive statistics that Excel calculates should be placed: Choose from the three radio buttons here — Output Range, New Worksheet Ply, and New Workbook. Typically, you place the statistics onto a new worksheet in the existing workbook. To do this, simply select the New Worksheet Ply radio button.
To identify what statistical measures you want calculated: Use the Output Options check boxes. Select the Summary Statistics check box to tell Excel to calculate statistical measures such as mean, mode, and standard deviation. Select the Confidence Level for Mean check box to specify that you want a confidence level calculated for the sample mean.
Note: If you calculate a confidence level for the sample mean, you need to enter the confidence level percentage into the text box provided. Use the Kth Largest and Kth Smallest check boxes to indicate you want to find the largest or smallest value in the data set.
After you describe where the data is and how the statistics should be calculated, click OK. Here are the statistics that Excel calculates.
Statistic Description Mean Shows the arithmetic mean of the sample data. Standard Error Shows the standard error of the data set (a measure of the
difference between the predicted value and the actual value).Median Shows the middle value in the data set (the value that
separates the largest half of the values from the smallest half of
the values).Mode Shows the most common value in the data set. Standard Deviation Shows the sample standard deviation measure for the data
set.Sample Variance Shows the sample variance for the data set (the squared
standard deviation).Kurtosis Shows the kurtosis of the distribution. Skewness Shows the skewness of the data set’s distribution. Range Shows the difference between the largest and smallest values in
the data set.Minimum Shows the smallest value in the data set. Maximum Shows the largest value in the data set. Sum Adds all the values in the data set together to calculate the
sum.Count Counts the number of values in a data set. Largest(X) Shows the largest X value in the data set. Smallest(X) Shows the smallest X value in the data set. Confidence Level(X) Percentage Shows the confidence level at a given percentage for the data
set values.
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Here is a new worksheet with the descriptive statistics calculated.