LOGEST Function
Basic Description
The Excel LOGEST function returns statistical information on the exponential curve of best fit, through a supplied set of x and y values. The basic statistical information returned is the array of constants, m_{n}, m_{n1}, … , b (or m and b) for the exponential curve equation. However, you can also request that additional regression statistics be returned.
Syntax: LOGEST( known_y’s, [known_x’s], [const], [stats] )
Where the function arguments are listed in the table below:
known_y’s  –  An array known yvalues  
[known_x’s]  –  An optional argument, providing an array of known xvalues
(If provided the [known_x’s] array should have the same length as the known_y’s array; 

[const]  –  An optional logical argument that determines how the constant ‘b’ is treated in the exponential curve equation y = b*m^x. This argument can have the value TRUE or FALSE, meaning:


[stats]  –  An optional logical argument which specifies whether or not you want the function to return additional regression statistics on the calculated curve. This argument can have the value TRUE or FALSE, meaning:

The array of statistics returned from the Excel Logest function has the following form:
m_{n}  m_{n1}  …  m_{1}  b 
se_{n}  se_{n1}  …  se_{1}  se_{b} 
r_{2}  se_{y}  
F  d_{f}  
ss_{reg}  ss_{resid} 
where the statistics returned are:
m_{i}  –  The array of constant base coefficients for the exponential curve equation 
b  –  The constant value of y when x=0 
se_{i}  –  The standard error values for the coefficients, m_{i} 
se_{b}  –  the standard error value for the constant b (returns the #N/A error if the [const] argument is FALSE) 
r_{2}  –  The coefficient of determination 
se_{y}  –  The standard error for the y estimate 
F  –  The F statistic, or the Fobserved value 
d_{f}  –  The number of degrees of freedom 
ss_{reg}  –  The regression sum of squares 
ss_{resid}  –  The residual sum of squares 
To input an array formula, you need to first highlight the range of cells for the function result. Type your function into the first cell of the range, and press CTRLSHIFTEnter.
Go to the Excel array formulas page for more details.
As the Logest function returns an array of values, it must be entered as an array formula. If the function is not entered as an array formula, only the first ‘m’ value in the calculated array of statistical information is returned.
You can see if a function has been input as an array formula, curly brackets will be inserted around the formula, as it is viewed in the formula bar. This can be seen in the examples below.
Logest Function Example 1
Cells A2 – A10 and B2 – B10 of the spreadsheet below list a number of known x and known y values, and also shows these points, plotted on a chart. Cells D1 – E5 of the spreadsheet show the Excel Logest function, used to return statistical information relating to the exponential curve of best fit through these points. The format of the Logest function is seen in the formula bar. The curly brackets around this function show that it has been entered as an array formula.
Cells D1 and E1 give the values of the base, m as 1.482939831, and the yintercept, b as 2.257475168. Therefore, the equation for the exponential curve of best fit through the given points is:
The remaining cells in the range D1 – E5 give the following additional statistics for this curve:
 The standard error value for the base m is 0.014718308
 The standard error value for the constant b is 0.070073164
 The coefficient of determination is 0.990327432
 The standard error for the y estimate is 0.114007527
 The F statistic is 716.6960934
 The number of degrees of freedom is 7
 The regression sum of squares is 9.315412472
 The residual sum of squares is 0.090984014
Logest Function Example 2
Cells A2 – A11, B2 – B11 and C2 – C11 of the spreadsheet below contain three different sets of independent variables (known x values), and cells D2 – D11 of the spreadsheet contain the associated known yvalues. Cells F1 – H3 of the spreadsheet show the Excel Logest function, used to return statistical information relating to the exponential curve of best fit through these points. Again, the format of the Logest function is seen in the formula bar and it can be seen, (from the curly brackets), that the function has been entered as an array formula.
Cells F1 – I1 give the values of the coefficents, m_{3}, m_{2} and m_{1} as 2.010750937, 0.942167056 and 1.31373656, respectively and the yintercept, b as 2.554652779. Therefore, the equation for the exponential curve of best fit through the given points is:
The remaining cells in the range F1 – I5 give the following additional statistics for this curve:
 The standard error values for the coefficients m_{3}, m_{2} and m_{1} are 0.080315977, 0.012928031 and 0.04764347, respectively
 The standard error value for the constant b is 0.275195565
 The coefficient of determination is 0.997749047
 The standard error for the y estimate is 0.057701675
 The F statistic is 886.5125548
 The number of degrees of freedom is 6
 The regression sum of squares is 8.854886129
 The residual sum of squares is 0.0199769
and the unused cells show the #N/A error.
Logest Function Errors
If you get an error from the Excel Logest function this is likely to be one of the following:
#REF!  –  Occurs if the array of [known_x’s] is not the same length as the array of known_y’s 
#VALUE!  –  Occurs if any values in the supplied [known_x’s] or known_y’s arrays are not numeric values
(this may include text representations of numbers, as the Logest function does not recognise these as numbers) 