LINEST function

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Returns a table of statistics for a straight line that best fits a data set.


LINEST(yvalues; xvalues; allow_const; stats)

yvalues is a single row or column range specifying the y coordinates in a set of data points.
xvalues is a corresponding single row or column range specifying the x coordinates. If xvalues is omitted it defaults to 1, 2, 3, ..., n. If there is more than one set of variables xvalues may be a range with corresponding multiple rows or columns.
LINEST finds a straight line y = a + bx that best fits the data, using linear regression (the "least squares" method). With more than one set of variables the straight line is of the form y = a + b1x1 + b2x2 ... + bnxn.
if allow_const is FALSE the straight line found is forced to pass through the origin (the constant a is zero; y = bx). If omitted, allow_const defaults to TRUE (the line is not forced through the origin).
LINEST returns a table (array) of statistics as below and must be entered as an array formula (for example by using  Cntrl  +  ⇧ Shift  +  ↵ Enter  rather than just  ↵ Enter )
If stats is omitted or FALSE only the top line of the statistics table is returned. If TRUE the entire table is returned.

Calc linest output.png
b1 to bn are the line gradients; a is the y-axis intercept.
σ1 to σn are the standard error values for the line gradients; σa is the standard error value for the y-axis intercept.
r2 is the determination coefficient (RSQ); σy is the standard error value for the y estimate.
F is the F statistic (F-observed value); df is the number of degrees of freedom.
ssreg is the regression sum of squares; ssresid is the residual sum of squares.


Calc linest example.png

In the example above, cells A2:B8 contain the x,y values for a set of points. LINEST(B2:B8;A2:A8;1;1) returns the statistics for the best fit line through those points.

Calc linest example2.png

In the example above, you measure the floor area and count the windows of a sample of houses in the area, and make a table with the corresponding sale value (cells A2:C8). To predict the value of other houses in the area you might use: value = a + b1*floor_area + b2*num_windows, where a, b1 and b2 are constants. LINEST(A2:A8;B2:C8;1;1) returns appropriate statistics for that equation.


  • You need a good understanding of the statistics involved.
  • Empty cells in the output array show #N/A (in Calc and Excel).

See Also
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