# Manuals/calci/LOGEST

LOGEST (YRange,XRange,Constant,Stats)

where,

• is a set of Y values,
• is an optional set of X values,
• is a logical value TRUE or FALSE, that decides whether to force the constant 'b' to 1,
• is a logical value TRUE or FALSE, that decides whether to return additional regression statistics.
• LOGEST() is an array function that calculates the exponential curve that fits the data values and returns an array of values that describes the curve.

## Description

• If 'YRange' is the set of dependent variable, 'XRange' is the set of independent variable, 'm' is a constant base for X value and 'b' is constant (Y-intercept),

then equation for curve is -

``` ```
• For multiple ranges of X-values,
``` ```
• Argument values and should be numeric, else Calci displays NaN error message.
• The length of array of XRange values should be equal to length of array of YRange values, else Calci displays #NULL error message.
• is a logical value that decides whether to make constant 'b' equal to 1.
• If = TRUE or omitted, 'b' is calculated normally. If = FALSE, 'b' is made equal to 1.
• is a logical value that decides whether to display additional regression statistics.
• If = TRUE, calci returns additional regresstion statistics. If = FALSE or omitted, Calci returns the values of 'm coefficients' and the constant 'b'.
• When there is only one independent X variable, Y intercept (b) can be calculated using following formulas -
``` ```
• The additional regression is displayed in the following format where each statistic value is described as below-  ---    ---        • is an array of constant base values for curve equation
• is the constant value of Y when X=0
• is the standard error value for m1
• is the standard error value for constant b
• is the coefficient of determination
• is the standard error value for Y estimate
• is the observed F value
• is the number of degrees of freedom
• is the regression sum of squares
• is the residual sum of squares

## Examples

 X1 values X2 values Y values 1 15 5 2 17 9 3 23 11 4 28 16 5 30 20

Example 1: With single range of X values -

```=LOGEST(C2:C6,A2:A6,TRUE,TRUE)  : Displays all the regression statistics for curve with Y values in cells C2 to C6 and X values in cells A2 to A6.
```
 1.39765 4.01561 0.0359648 0.119282 0.966539 0.113731 86.6568 3 1.12088 0.0388041

Example 2: With multiple range of X values -

```=LOGEST(C2:C6,A2:B6,TRUE,TRUE) : Displays all the regression statistics for curve with Y values in cells C2 to C6 and X values in  cells A2 to B6.
```
 0.9685 1.59365 0.0573767 0.238787 0.971044 0.129575 33.5356 2 1.1261 0.0335793

LOGEST