# Manuals/calci/LINEST

LINEST (YRange,XRanges,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 0,
• is a logical value TRUE or FALSE, that decides whether to return additional regression statistics.
• LINEST(), returns the parameters of a linear trend.

## Description

• This function is an array function that calculates the statistics for a line by using the 'least squares' method to calculate a straight line that closely fits the input data.
• If 'Y' is the point on y-axis, 'X' is the point on x-axis, 'm' is a constant indicating slope of the line and 'b' is the constant value at which the line crosses y-axis (Y intercept),

then equation of line is -

``` ```
• For multiple ranges of X-values,
``` ```
• Argument values and should be numeric, else Calci displays NaN error message.
• The length of array of X values should be equal to length of array of Y values, else Calci displays #NULL error message.
• is a logical value that decides whether to make constant 'b' equal to 0.
• If = TRUE or omitted, 'b' is calculated normally. If = FALSE, 'b' is made equal to 0.
• is a logical value that decides whether to display additional regression statistics.
• If = TRUE, calci returns additional regression statistics. If = FALSE or omitted, Calci returns the values of 'm'(slope) and the constant 'b'.
• When there is only one independent X variable, Slope(m) and 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 multipliers for straight line 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

 Y co-ordinates X co-ordinates 1 2 5 4 4 6 3 8 2 10
```=LINEST(A2:A6,B2:B6,TRUE,FALSE) : Calculates the statistics of line with Y co-ordinates in cells  A2 to A6 and X co-ordinates in cells B2 to B6. Returns m=0 and b=3 as a result.
=LINEST(A2:A6,B2:B6,FALSE,FALSE): Calculates the statistics of line with Y co-ordinates in cells  A2 to A6 and X co-ordinates in cells range B2 to B6. Returns m=0.4090909090909091 and b=0 as a result.

=LINEST(A2:A6,B2:B6,FALSE,TRUE) : Displays the additional regression statistics of line with Y co-ordinates in cells A2 to A6 and X co-ordinates in cells B2 to B6 as shown below:
```
 0.409091 0 0.14374 0.669421 2.1320071635561044 8.1 4 36.8182 18.181818181818183

LINEST