Forum Discussion

Szymeqpl_'s avatar
Szymeqpl_
Copper Contributor
Nov 04, 2023
Solved

Questions about LINEST function.

Good morning, I was attempting to use the LINEST function to determine the coefficients in the following equation: n(T) = aT^2 + bT + c. I believe that I should be able to find the values of a, b, a...
  • JoeUser2004's avatar
    Nov 04, 2023

    Szymeqpl_ 

     

    None of your examples of LINEST is correct.  See below for details.

     

    -----

    First, it is always bests to attach an Excel file that demonstrates the problem.  That is out of respect for those who want to help; do not force them to re-enter your data and formulas.  And it might result in a more accurate response; we might not be able to reproduce your results because the posted data is rounded.

     

    "If a picture is worth a 1000 words, an Excel file is worth 1000 pictures". (wink)

     

    But when you post images, always include row numbers as well as column names.  I had to infer the row numbers from the cell references in your text.

     

    -----

    Second, it is always wise to copy formulas from the Formula Bar and paste them into your posting, instead of retyping them. 

     

    I was unable to reproduce your results because you posted LINEST formulas of the form  =LINEST(U21:U36, V21:V36...).

     

    But then I looked at "x" and "y" in U20 and V20, and I guessed that the actual formulas are of the form =LINEST(V21:V36, U21:U36....).  That is, switching the U and V references.  Now my results for "a", "b" and "c" appear to be similar to yours, to wit (see the attached Excel file for details):

     

     

    -----

    Finally, none of your examples of LINEST is correct.

     

    The correct usage is demonstrated in AB21:AD25.  With that range selected, enter the formula =LINEST(V21:V36, U21:U36^{1,2}, 1, TRUE)

     

    Note:  The formula must be array-entered (press ctrl+shift+Enter instead of just Enter) in versions of Excel before Excel 365 and Excel 2016.

     

    Then the coefficients "a", "b" and "c" are in AB21:AD21.  And r^2 is in AB23.

     

    RSQ can also be calculated with the formula =RSQ(V21:V36, W21:W36) in W38.  W21:W36 ("est y") is based on formulas of the form (W21) =SERIESSUM(U21, 2, -1, $AB$21:$AD$21)

     

    Aside....  When displaying trendline formulas in charts, it is prudent to increase the number of decimal places by clicking the trendline, then Format Trendline Label. For example, note that the coefficient "a" is more accurately -6.94843E-08, not -7E-08.

     

    -----

    PS....  Although I recommend the array-entered LINEST formula above -- it is more efficient -- you can calculate the individual coefficients and r^2 with the following non-array formulas:

     

    a: =INDEX(LINEST($V$21:$V$36, $U$21:$U$36^{1,2}, 1, TRUE), 1, 1)
    b: =INDEX(LINEST($V$21:$V$36, $U$21:$U$36^{1,2}, 1, TRUE), 1, 2)
    c: =INDEX(LINEST($V$21:$V$36, $U$21:$U$36^{1,2}, 1, TRUE), 1, 3)
    r^2: =INDEX(LINEST($V$21:$V$36, $U$21:$U$36^{1,2}, 1, TRUE), 3, 1)

Resources