How does LINEST operate in Microsoft Excel ?

I'm using Microsoft Excel 2013.  Please consider following Linear Estimation Formula:

LINEST ( I7 : I9 , H7 : H9)

I7 = 0
I8 = -4000
I9 = 3900

H7 = 637
H8 = 588
H9 = 685

Please explain Linear Estimation and LINEST excel formula ?
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naseeamAuthor Commented:
Is Linear Estimation same as Linear Approximation ?
Ejgil HedegaardCommented:
In general terms I would say you estimate or approximate the real function with a linear expression.
Linest use linear regression, which is a subgroup of linear estimation

Linest use the least square method, meaning that the sum of squared distances from the datapoints to the regression line must be as small as possible,

It is an array formula, so to get both values a and b in y = a * x + b, use 2 cells.
Select 2 cells
Type the formula =LINEST(I7:I9,H7:H9)
Confirm with Ctrl+Shift+Enter to tell Excel it is an array formula, both cells get the same formula
Excel adds { } brackets to the formula, don't type them.

The first cell is the slope a, and the second cell is the constant b.

To get the slope alone use =INDEX(LINEST(I7:I9,H7:H9),1)
And the constant alone use =INDEX(LINEST(I7:I9,H7:H9),2)
That are not array formulas, since Index in itself is an array formula and converts to normal.

The function =CORREL(I7:I9,H7:H9)^2 will tell you how good the regression line fits the data.
The value is between 0 (no fit) and 1 (absolute fit).

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Professor JMicrosoft Excel ExpertCommented:
Good explanation Ejgil
naseeamAuthor Commented:
Very nice explanation!  Thank you!
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