LINEST Function in Excel

LINEST Function in Excel (Table of Contents)

LINEST Function in Excel
Formula
How to use?

It is a built-in function in MS Excel. LINEST function in Excel is used to calculate the statistics for a line. LINEST in excel uses the least-squares regression and returns an array that describes the straight line that best fits given data.

LINEST Formula in Excel

Below is the LINEST Formula in Excel.

The =Equation for the Line is:

y = mx + b

–or–

y = m1x1 + m2x2 + m3x3 + … + b

The LINEST in Excel has two arguments out of which one is required. Where,

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known_y’s = It is a required parameter and indicates the set of y-values already known in the relationship y = mx + b.
- If the range of known_y’s is in a single column, each column of known_x’s is interpreted as a separate variable.
- If the range of known_y’s is in a single row, each row of known_x’s is interpreted as a separate variable.
known_x’s = It is an optional parameter and indicates the set of x-values that already known in the relationship y = mx + b.
- The range of known_x’s can have one or more set of variables. If only one variable is used, known_y’s and known_x’s can be the ranges of any shape, if they have equal dimensions.
- If more than one variable is used, known_y’s must be a vector (i.e., a range with a height of one row or a width of one column).
const = It is an optional parameter and represents a logical value (TRUE/FALSE) specifying whether to force the constant b to be equal to 0.
- If const is TRUE or skipped, b is calculated normally.
- If const is FALSE, b is set equal to 0 and the m-values are adjusted to fit y = mx.
stats = It is an optional parameter and represents a logical value (TRUE/FALSE) specifying whether to return additional regression statistics.
- If stats is TRUE, LINEST in excel returns the additional regression statistics; as a result, the returned array is {mn , mn-1,…,m1,b;sen,sen-1,…,se1,seb;r2,sey;F,df;ssreg,ssresid}.
- If stats are FALSE or skipped, LINEST in Excel returns only the m-coefficients and the constant b.

How to Use LINEST Function in Excel?

The said function is a Worksheet (WS) function. As a WS function, LINEST function in excel can be entered as a part of the formula in a cell of a worksheet. Refer to a couple of examples given below to know more.

Let’s look at the examples given below. Each example covers a different use case implemented using the LINEST function in Excel.

You can download this LINEST Function Excel Template here – LINEST Function Excel Template

LINEST in Excel Example #1 – Slope

=LINEST (B2:B5, C2:C5, , FALSE)

As shown in the above formula, B2:B5 is the known-y’s, C2:C5 is known-x’s. 3rd parameter i.e. const is left blank so it will be calculated. 4th parameter i.e. stats is marked FALSE.

LINEST in Excel Example #2 – Simple Linear Regression

= SUM (LINEST(B1:B6, A1:A6)*{9,1})

As shown in the above LINEST formula in excel, A1:A6 is the month number and B2:B6 indicates the corresponding sales figures. So, based on the sales data of 6 months, sales data for the 9^th month is to be estimated.

Things to Remember

When entering an array constant (such as known_x’s) as an argument, commas can be used to separate values that are present in the same row and semicolons can be used to separate the rows. Separator characters may vary depending on native regional settings.
The y-values predicted by the regression equation may not be valid if they are outside the range of the y-values used to determine the equation.
Formulas that return arrays must be entered as array formulas.
When there’s only one independent x-variable, slope and y-intercept values can directly be calculated by using the following formulas:
- Slope: =INDEX (LINEST (known_y’s, known_x’s),1)
- Y-intercept: =INDEX (LINEST (known_y’s, known_x’s),2)
A straight line can be described with slope and y-intercept:
- Slope (m): To find the slope of a line, often represented as m: – For a line with two points (x1, y1) and (x2, y2); the slope is calculated as: m = (y2 – y1) / (x2 – x1).
- Y-intercept (b): The y-intercept of a line, often represented as b, is the value of y at the point where the line crosses the y-axis.
- The equation of a straight line is y = mx + b. Once the values of m and b are known, any point on the line can be calculated by putting the y- or x-value into the equation. See TREND function in Excel.