Quadratic and cubic regression in Excel

0 votes

I have the following information:

  Height    Weight

    170     65
    167     55
    189     85
    175     70
    166     55
    174     55
    169     69
    170     58
    184     84
    161     56
    170     75
    182     68
    167     51
    187     85
    178     62
    173     60
    172     68
    178     55
    175     65
    176     70

In Excel, I want to create a quadratic and cubic regression analysis. I'm aware of how to perform it in Excel using linear regression, but what about cubic and quadratic functions? Despite doing extensive research, I was unable to come across anything useful.

Sep 30 in Others by Kithuzzz
• 20,660 points
99 views

1 answer to this question.

0 votes

You need to use an undocumented trick with Excel's LINEST function:

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

Background

A regular linear regression is calculated (with your data) as:

=LINEST(B2:B21,A2:A21)

which returns a single value, the linear slope (m) according to the formula:

enter image description here

which for your data:

enter image description here

is:

enter image description here

Undocumented trick Number 1

You can also use Excel to calculate a regression with a formula that uses an exponent for x different from 1, e.g. x1.2:

enter image description here

using the formula:

=LINEST(B2:B21, A2:A21^1.2)

which for your data:

enter image description here

is:

enter image description here

You're not limited to one exponent

Excel's LINEST function can also calculate multiple regressions, with different exponents on x at the same time, e.g.:

=LINEST(B2:B21,A2:A21^{1,2})

Note: if locale is set to European (decimal symbol ","), then comma should be replaced by semicolon and backslash, i.e. =LINEST(B2:B21;A2:A21^{1\2})

Now Excel will calculate regressions using both x1 and x2 at the same time:

enter image description here

How to actually do it

The impossibly tricky part there's no obvious way to see the other regression values. In order to do that you need to:

  • select the cell that contains your formula:

    enter image description here

  • extend the selection the left 2 spaces (you need the select to be at least 3 cells wide):

    enter image description here

  • press F2

  • press Ctrl+Shift+Enter

    enter image description here

You will now see your 3 regression constants:

  y = -0.01777539x^2 + 6.864151123x + -591.3531443

Bonus Chatter

I had a function that I wanted to perform regression using some exponent:

y = m×xk + b

But I didn't know the exponent. So I changed the LINEST function to use a cell reference instead:

=LINEST(B2:B21,A2:A21^F3, true, true)

With Excel then outputting full stats (the 4th paramter to LINEST):

enter image description here

I tell the Solver to maximize R2:

enter image description here

And it can figure out the best exponent. Which for you data:

enter image description here

is:

enter image description here

answered Oct 1 by narikkadan
• 37,660 points

Related Questions In Others

0 votes
1 answer

SharePoint - Excel Online - Edit in Excel and Edit in Browser multiple users

Here is the Microsoft article regarding co-authoring https://support.office.com/en-us/article/Collaborate-on-Excel-workbooks-at-the-same-time-with-co-authoring-7152aa8b-b791-414c-a3bb-3024e46fb104?ui=en-US&rs=en-US&ad=US When ...READ MORE

answered Oct 3 in Others by narikkadan
• 37,660 points
162 views
0 votes
1 answer

Apache POI - watermark in Excel - different appearance in Excel and LibreOffice

There is nothing that apache poi could ...READ MORE

answered Oct 9 in Others by narikkadan
• 37,660 points
115 views
0 votes
1 answer
0 votes
1 answer

Comparing two Excel files in R and returning different titles

Solution: library(tidyverse) dat <- read_xlsx("Book1.xlsx") dat2 <- read_xlsx("Book2.xlsx") book1_output <- anti_join(dat,dat2, ...READ MORE

answered Oct 14 in Others by narikkadan
• 37,660 points
55 views
0 votes
1 answer

How to add regression line equation and R2 on graph?

Below is one solution: # GET EQUATION AND ...READ MORE

answered Jun 1, 2018 in Data Analytics by DataKing99
• 8,240 points
6,027 views
0 votes
1 answer

Retrieve epay.info Balance with VBA and Excel

This code should log you in, provided ...READ MORE

answered Sep 5, 2018 in Blockchain by digger
• 26,720 points
449 views
0 votes
1 answer

ImportError: openpyxl is required for loading excel format files

Forget the PsychoPy complications for the time ...READ MORE

answered Oct 3, 2018 in Python by Priyaj
• 58,100 points
395 views
0 votes
1 answer

In Blue Prism how to split excel column data into TWO columns

This is how I am doing it. Dim ...READ MORE

answered Oct 15, 2018 in RPA by Priyaj
• 58,100 points
3,366 views
0 votes
1 answer

What are the RGB and HEX codes of the 3 color conditional format in Excel?

In Excel 2016 at least the colors ...READ MORE

answered Sep 24 in Others by narikkadan
• 37,660 points
316 views
0 votes
1 answer

Excel - add all X in column and then multiply

Use countif for the count then multiply ...READ MORE

answered Oct 1 in Others by narikkadan
• 37,660 points
42 views
webinar REGISTER FOR FREE WEBINAR X
REGISTER NOW
webinar_success Thank you for registering Join Edureka Meetup community for 100+ Free Webinars each month JOIN MEETUP GROUP