The LINEST Function - A powerhouse in Excel for linear regression analysis.

In this article, we delve into the intricacies of the LINEST function, one of Excel's statistical tools highly favored for its robustness.

Description: The function returns an array describing a straight line using the method of least squares.

Syntax: LINEST(known_y's, [known_x's], [const], [stats])

Here's the breakdown:

- known_y's: The known y-values in the relationship y = bm^x, which is a required parameter.

+ If known_y's are in a single column or row -> each column or row of known_y's is understood as a separate variable.

- known_x's: The known x-values in the relationship y = bm^x, which is an optional parameter.

+ known_x's can encompass one or multiple sets of variables.

+ If known_x's are omitted -> it is assumed to be an array of the same size as known_y's.

- const: A logical value determining the value of constant term b, an optional parameter with the following values:

+ const = True or omitted -> b is computed as usual.

+ const = False or omitted -> b = 1 and m is adjusted such that: y = m^x.

- stats: A logical value determining the type of additional regression statistics returned, including values like {mn,mn-1,...,m1,b;sen,sen-1,...,se1,seb;r2,sey;F,df;ssreg,ssresid}.

Note:

- Any straight line can be described by its slope and y-intercept:

+ Slope (m):

To find the slope of a line m, take two points on that line, (x1,y1) and (x2,y2) -> the slope is (y2 - y1)/(x2 - x1).

+ Y-Intercept (b):

The y-intercept of a line b, is the value of y at the point where the line intersects the y-axis.

The equation of the line is y = mx + b. Any point on the line can be calculated by inputting the value of y or x into this equation.

- When there's only one independent variable -> use the formula:

+ Slope: 

=INDEX(LINEST(known_y's,known_x's),1)

+ Y-Intercept:

=INDEX(LINEST(known_y's,known_x's),2)

+ Use commas to separate values within the same row.

+ Use semicolons to separate rows from each other.

- When there are multiple independent variables x -> use the formula:

m=∑(x−

∑(x−¯¯¯x)2$m=\frac{\sum \left(x-\overline{x}\right)\left(y-\overline{y}\right)}{\sum {\left(x-\overline{x}\right)}^2}$

b=¯¯¯y−m¯¯¯x$b=\overline{y}-m\overline{x}$

Where:  x = AVERAGE(known x's) and y = AVERAGE(known_y's).

Example:

Calculate the slope and y-intercept of the line corresponding to the x, y values in the data table below:

- Calculate the slope m of the line corresponding to the x, y values. In the cell to compute, enter the formula: =LINEST(C6:C10,D6:D10,FALSE)

- Press Enter -> the slope m of the line corresponding to the x, y values is:

- Calculate the y-intercept of the line corresponding to the x, y values. In the cell to compute, enter the formula: =LINEST(C6:C10,D6:D 10,TRUE)

- Press Enter -> the y-intercept of the line corresponding to the x, y values is:

Here is the guide and some specific examples when using the LINEST function in Excel.

Wishing you success!