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LINEST

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Applies to: Calculated column Calculated table Measure Visual calculation

Uses the Least Squares method to calculate a straight line that best fits the given data, then returns a table describing the line. The equation for the line is of the form: y = Slope1*x1 + Slope2*x2 + ... + Intercept.

Syntax

LINEST ( <columnY>, <columnX>[, …][, <const>] )

Parameters

Term Definition
columnY The column of known y-values. Must have scalar type.
columnX The columns of known x-values. Must have scalar type. At least one must be provided.
const (Optional) A constant TRUE/FALSE value specifying whether to force the constant Intercept to equal 0.
If TRUE or omitted, the Intercept value is calculated normally; If FALSE, the Intercept value is set to zero.

Return value

A single-row table describing the line, plus additional statistics. These are the available columns:

  • Slope1, Slope2, ..., SlopeN: the coefficients corresponding to each x-value;
  • Intercept: intercept value;
  • StandardErrorSlope1, StandardErrorSlope2, ..., StandardErrorSlopeN: the standard error values for the coefficients Slope1, Slope2, ..., SlopeN;
  • StandardErrorIntercept: the standard error value for the constant Intercept;
  • CoefficientOfDetermination: the coefficient of determination (r²). Compares estimated and actual y-values, and ranges in value from 0 to 1: the higher the value, the higher the correlation in the sample;
  • StandardError: the standard error for the y estimate;
  • FStatistic: the F statistic, or the F-observed value. Use the F statistic to determine whether the observed relationship between the dependent and independent variables occurs by chance;
  • DegreesOfFreedom: the degrees of freedom. Use this value to help you find F-critical values in a statistical table, and determine a confidence level for the model;
  • RegressionSumOfSquares: the regression sum of squares;
  • ResidualSumOfSquares: the residual sum of squares.

Remarks

<columnY> and the <columnX>’s must all belong to the same table.

Example 1

The following DAX query:

EVALUATE LINEST(
	'FactInternetSales'[SalesAmount],
	'FactInternetSales'[TotalProductCost]
)

Returns a single-row table with ten columns:

Slope1 Intercept StandardErrorSlope1 StandardErrorIntercept CoefficientOfDetermination
1.67703250456677 6.34550460373026 0.000448675725548806 0.279131821917317 0.995695557281456
StandardError FStatistic DegreesOfFreedom RegressionSumOfSquares ResidualSumOfSquares
60.9171030357485 13970688.6139993 60396 51843736761.658 224123120.339218
  • Slope1 and Intercept: the coefficients of the calculated linear model;
  • StandardErrorSlope1 and StandardErrorIntercept: the standard error values for the coefficients above;
  • CoefficientOfDetermination, StandardError, FStatistic, DegreesOfFreedom, RegressionSumOfSquares and ResidualSumOfSquares: regression statistics about the model.

For a given internet sale, this model predicts the sale amount by the following formula:

SalesAmount = Slope1 * TotalProductCost + Intercept

Example 2

The following DAX query:

EVALUATE LINEST(
	'DimCustomer'[TotalSalesAmount],
	'DimCustomer'[YearlyIncome],
	'DimCustomer'[TotalChildren],
	'DimCustomer'[BirthDate]
)

Returns a single-row table with fourteen columns:

  • Slope1
  • Slope2
  • Slope3
  • Intercept
  • StandardErrorSlope1
  • StandardErrorSlope2
  • StandardErrorSlope3
  • StandardErrorIntercept
  • CoefficientOfDetermination
  • StandardError
  • FStatistic
  • DegreesOfFreedom
  • RegressionSumOfSquares
  • ResidualSumOfSquares

For a given customer, this model predicts total sales by the following formula (the birth date is automatically converted to a number):

TotalSalesAmount = Slope1 * YearlyIncome + Slope2 * TotalChildren + Slope3 * BirthDate + Intercept

Related content

LINESTX
Statistical functions