How To Calculate Polynomial Regression Coefficients 


How To Calculate Polynomial Regression Coefficients  Excel 
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Hi,
I wanted to know a way to calculate the polynomial regression coefficients in
excel as chart does. I have seen many help sites but it has not helped one of
it was JWALK.com which was good but did not work for me. I am using 4th
degree polynomial regression. The y and x values are as below.
X values 0.00 0.03 0.07 0.10 0.13 0.17 0.20 0.23 0.26 0.30 0.33
Y values 0.000 0.000 0.000 0.002 0.005 0.012 0.023 0.041 0.069 0.107 0.159
The coefficients from chart obtained are
c4 9.8202
c3 1.4485
c2 0.1041
c1 0.0057
b 0.0000
I hope somebody can help

Joham
Message posted via OfficeKB.com
http://www.officekb.com/Uwe/Forums.a...lnew/200508/1
I wanted to know a way to calculate the polynomial regression coefficients in
excel as chart does. I have seen many help sites but it has not helped one of
it was JWALK.com which was good but did not work for me. I am using 4th
degree polynomial regression. The y and x values are as below.
X values 0.00 0.03 0.07 0.10 0.13 0.17 0.20 0.23 0.26 0.30 0.33
Y values 0.000 0.000 0.000 0.002 0.005 0.012 0.023 0.041 0.069 0.107 0.159
The coefficients from chart obtained are
c4 9.8202
c3 1.4485
c2 0.1041
c1 0.0057
b 0.0000
I hope somebody can help

Joham
Message posted via OfficeKB.com
http://www.officekb.com/Uwe/Forums.a...lnew/200508/1
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Similar Topics
What I want to do seems simple, but ...
Adding a polynomial trendline to an XY scatter chart is easy. How do I get the individual coefficients of that equation that is displayed on the chart into variables. I'm basically trying to fit a sixthorder polynomial to a set of measured data, and want to find the maximum value within a know range. If I know the coefficients of the polynomial regression  it's pretty simple from there.
How do I get the polynomial regression coeffcients automatically?
Adding a polynomial trendline to an XY scatter chart is easy. How do I get the individual coefficients of that equation that is displayed on the chart into variables. I'm basically trying to fit a sixthorder polynomial to a set of measured data, and want to find the maximum value within a know range. If I know the coefficients of the polynomial regression  it's pretty simple from there.
How do I get the polynomial regression coeffcients automatically?
What I want to do seems simple, but ...
Adding a polynomial trendline to an XY scatter chart is easy. How do I get the individual coefficients of that equation that is displayed on the chart into variables. I'm basically trying to fit a sixthorder polynomial to a set of measured data, and want to find the maximum value within a know range. If I know the coefficients of the polynomial regression  it's pretty simple from there.
How do I get the polynomial regression coeffcients automatically?
Adding a polynomial trendline to an XY scatter chart is easy. How do I get the individual coefficients of that equation that is displayed on the chart into variables. I'm basically trying to fit a sixthorder polynomial to a set of measured data, and want to find the maximum value within a know range. If I know the coefficients of the polynomial regression  it's pretty simple from there.
How do I get the polynomial regression coeffcients automatically?
Hello.
Can anyone explain how Excel computes the coefficients step by step when carrying out the full regression procedure for several variances (multiple regression).
Please note I said 'multiple regression', that is including several variables in the regression model and not just 2 as in a conventional linear regression (in which case the coeffiecients could simply be calculated as the slopes with the =SlOPE function.
Regards,
Chris
I have 201 data points and I want to fit a polynomial to the data using Solver.
Currently the polynomial is 5th order : a + bx + cx^2 + dx^3 + ex^4 + fx^5
but I will want to extend that further when it is working properly.
The data is in A1:A201
the coefficients are in $E$2:$E$7
x runs from 0 to 200 by means of (ROW()1)
The polynomial values are in B1:B201
The square of difference are in C1:C201
The sum of squares of differences is in $E$1
Solver is asked to target $E$1, varying $E$2:$E$7, for minimum
You might think that this would take a long time, and would vary all 6 coefficients,
but it almost instantly exits, saying it has found a solution,
but it has only varied a couple of coefficients,
and I have found better solutions manually.
I haven't been able to grasp the significance of the various Options 
some of the coefficients will probably be very small.
Excel 2000, but I have 2007 available if that is necessary.
Dave
Currently the polynomial is 5th order : a + bx + cx^2 + dx^3 + ex^4 + fx^5
but I will want to extend that further when it is working properly.
The data is in A1:A201
the coefficients are in $E$2:$E$7
x runs from 0 to 200 by means of (ROW()1)
The polynomial values are in B1:B201
The square of difference are in C1:C201
The sum of squares of differences is in $E$1
Solver is asked to target $E$1, varying $E$2:$E$7, for minimum
You might think that this would take a long time, and would vary all 6 coefficients,
but it almost instantly exits, saying it has found a solution,
but it has only varied a couple of coefficients,
and I have found better solutions manually.
I haven't been able to grasp the significance of the various Options 
some of the coefficients will probably be very small.
Excel 2000, but I have 2007 available if that is necessary.
Dave
Hi Guys,
I am doing some statistical work with Excel 2007 and have been using the data analysis addin to do some regression. In terms of a standard linear regression, one can enter the =slope(known y's , known x's) formula to find the regression coefficient for x. My regression is slightly more complicated as it has multiple independent variables (i.e. the y variable is not just a function of x, but also of another variable, say z). I can perform a multiple regression easily but I would like to be able to store the coefficients of the multiple regression as I must eventually add the coefficient estimate for x and z together. The multiple regression output is in a standard format however as I have to repeat this process for 1500 firms (one regression for each) it would be much more convenient if excel just reported the two coefficients for each regression. That way I could copy a formula across all firms and not use the standard regression window 1500 times.
Is there anyway I can perform the multiple regression formulaically, outputting just the two coefficients I require from each regression?
I apologise for the long winded post. Any help is very much appreciated. Thanks in advance.
I am doing some statistical work with Excel 2007 and have been using the data analysis addin to do some regression. In terms of a standard linear regression, one can enter the =slope(known y's , known x's) formula to find the regression coefficient for x. My regression is slightly more complicated as it has multiple independent variables (i.e. the y variable is not just a function of x, but also of another variable, say z). I can perform a multiple regression easily but I would like to be able to store the coefficients of the multiple regression as I must eventually add the coefficient estimate for x and z together. The multiple regression output is in a standard format however as I have to repeat this process for 1500 firms (one regression for each) it would be much more convenient if excel just reported the two coefficients for each regression. That way I could copy a formula across all firms and not use the standard regression window 1500 times.
Is there anyway I can perform the multiple regression formulaically, outputting just the two coefficients I require from each regression?
I apologise for the long winded post. Any help is very much appreciated. Thanks in advance.
I have a data set with fixed X values and corresponding Y values that I can feed in via a formula. There is not necessarily a Y value for each X value. in the cells with no Y data point, a #N/A populates. I can create a scatter plot and fit a polynomial to the data on the chart and it produces the coefficients of the displayed equation. My problem is that I can not get the same coefficients using the linest formula unless I remove all of the data points where the Y values are #N/A. Obviously this is a solution, but each time i pass new Y data into the table it will populate differently, so I need to keep the X values locked in place and not delete them. It seems that if a chart can ignore the #N/A data then the formula might be able to do the same.
I attached the file with the problem for you to look at.
I attached the file with the problem for you to look at.
I have a data set with fixed X values and corresponding Y values that I can feed in via a formula. There is not necessarily a Y value for each X value. in the cells with no Y data point, a #N/A populates. I can create a scatter plot and fit a polynomial to the data on the chart and it produces the coefficients of the displayed equation. My problem is that I can not get the same coefficients using the linest formula unless I remove all of the data points where the Y values are #N/A. Obviously this is a solution, but each time i pass new Y data into the table it will populate differently, so I need to keep the X values locked in place and not delete them. It seems that if a chart can ignore the #N/A data then the formula might be able to do the same.
I attached the file with the problem for you to look at.
I attached the file with the problem for you to look at.
I'm trying to extract polynomial regression coefficients enmasse using this method:
http://www.stfx.ca/people/bliengme/E...Polynomial.htm
My question is this: can I alter that formula ( =LINEST(y, x^{1, 2, 3}) )so that all curves are fit with (0,0) included? (i.e. constant of 0)
http://www.stfx.ca/people/bliengme/E...Polynomial.htm
My question is this: can I alter that formula ( =LINEST(y, x^{1, 2, 3}) )so that all curves are fit with (0,0) included? (i.e. constant of 0)
Hi,
I'm trying to do a Polynomial Regression, and managed to do it. However, I do get different values from those if I do a polynomial trendline with the Excel regression chart. I think I checked everything but still don't find my problem. Anyone has an idea what I'm doing wrong?
Please refer to the attached sheet.
Thanks a lot,
Tobias
Hi all
i have some questions about interpolation and regression
i have x1,x2,x3 y1, y2(to be calculated), y3
i know the linear interpolation formula to estimate the unknown y2
y2=(x2x1)(y3y1)/(x3x1)
now what i know that the function relating these values is not linear ,is that formula is
valid or not , or using the regression option in excel to find an equation for that curve
as a second or third order polynomial is better.
if the function is linear and i can find the coefficients by linest function and the by this
linear function i can estimate any y value for given x what the diff between this way and
the above formula.
thanks in advance
i have some questions about interpolation and regression
i have x1,x2,x3 y1, y2(to be calculated), y3
i know the linear interpolation formula to estimate the unknown y2
y2=(x2x1)(y3y1)/(x3x1)
now what i know that the function relating these values is not linear ,is that formula is
valid or not , or using the regression option in excel to find an equation for that curve
as a second or third order polynomial is better.
if the function is linear and i can find the coefficients by linest function and the by this
linear function i can estimate any y value for given x what the diff between this way and
the above formula.
thanks in advance
I have a graph in excel. I've added a 6th order polynomial trendline. I need the coefficients of that polynomial to appear in some cells below the graph. Please look at my spreadsheet and see if you can help.
Thanks in advance for any help.
kc
Thanks in advance for any help.
kc
I have a set of data that I am using to find a leastsquares fit for. In this specific case I am using Excel to find a 6th order polynomial that best fits my data points.
I can get the coefficients for the polynomial by graphing it and then copying the listed coefficients back onto my spreadsheet but this is very inefficient and I am trying to find a way to automatically get the coefficients without the user having to do all that work. Is there a VBA command for finding the coefficients of a polynomail of order X that does a least squares fit of my data?
I can get the coefficients for the polynomial by graphing it and then copying the listed coefficients back onto my spreadsheet but this is very inefficient and I am trying to find a way to automatically get the coefficients without the user having to do all that work. Is there a VBA command for finding the coefficients of a polynomail of order X that does a least squares fit of my data?
I have investigated linest logest trend and forecast but these seem to deal with straight lines of best fit. Is there a way to generate coefficients for a polynomial best fit curve without making a best fit line and copying the values into different cells from the graph.
I have a chart that displays a series of data. From that, I add a polynomial trendline and extract the coefficients to generate a curve fit equation. Is there a way to generate this polynomial equation (pulling the coefficients) of the data without invoking the charting function??
Thanks.
Thanks.
i can happily create a chart that shows the equation and also rsq value for a few scattered points, and i have looked at LINEST and FORECAST, but i really want excel to produce the coefficients for a polynomial line, rather than me copying it from the chart.
eg if the eqn is
y= 23x^4 + 44x^3 + 11x^2  13x +2
i want the values of
23
44
11
13
2
in cells.
hope this makes sense, thanks in advance.
eg if the eqn is
y= 23x^4 + 44x^3 + 11x^2  13x +2
i want the values of
23
44
11
13
2
in cells.
hope this makes sense, thanks in advance.
I'm trying to build a macro with regression statistics for multivariables. I tried "recording" the regression button from data analysis and manipulating the code but continuously keep getting errors.
All I need are the coefficients so I can build an equation for new data. I need to do this almost 1000 times so I need to know an efficient way to do this.
I would really appreciate it if someone can help me out, thanks!
All I need are the coefficients so I can build an equation for new data. I need to do this almost 1000 times so I need to know an efficient way to do this.
I would really appreciate it if someone can help me out, thanks!
I am trying to produce a parabolic regression (quadratic spline) for the closing price a stock. Please see below for the equation and click on the link for an examples of how it would look. I have no idea how to apply it to an Excel spreadsheet so I can study it against the stock's closing price and need someone's help to get things started.
This script calculates a parabolic regression (Quadratic Spline) of the data series based on the following 2nd order polynomial function: y(x) = b0 + b1*x + b2*x*x where b0, b1 and b2 are the calculated regression coefficients.
Sample of what the end result should look like:
http://www.sranalyst.com/i/ParabolicReg.gif
For example I would want to see what a 34 period parabolic regression plotted on top of the closing price of a stock. I have also enclosed a sample of the stock's closing price for review.
Thanks, Steven
This script calculates a parabolic regression (Quadratic Spline) of the data series based on the following 2nd order polynomial function: y(x) = b0 + b1*x + b2*x*x where b0, b1 and b2 are the calculated regression coefficients.
Sample of what the end result should look like:
http://www.sranalyst.com/i/ParabolicReg.gif
For example I would want to see what a 34 period parabolic regression plotted on top of the closing price of a stock. I have also enclosed a sample of the stock's closing price for review.
Thanks, Steven
I have some data sets I wish to create equations based on (3rd and 4th degree poly for good fit) but can't figure out how.
I've tried the solutions suggested he
http://www.mrexcel.com/forum/showthr...e+coefficients
http://www.mrexcel.com/forum/showthr...e+coefficients
http://spreadsheetpage.com/index.php...line_formulas/
but they don't seem to work. I get errors when I try to use the LINEST function.
I've copypasted one of the data sets into an empty sheet and uploaded it he
http://www.box.net/shared/tnjgpezc50
What function(s) do I need to use to get the coefficients as listed in the sheet?
Any help is appreciated.
I've tried the solutions suggested he
http://www.mrexcel.com/forum/showthr...e+coefficients
http://www.mrexcel.com/forum/showthr...e+coefficients
http://spreadsheetpage.com/index.php...line_formulas/
but they don't seem to work. I get errors when I try to use the LINEST function.
I've copypasted one of the data sets into an empty sheet and uploaded it he
http://www.box.net/shared/tnjgpezc50
What function(s) do I need to use to get the coefficients as listed in the sheet?
Any help is appreciated.
I have a VBA function that calculates polynomial coefficients for a series of data pairs. One selects the range of cells that the coefficients are to be stored in, and enters the polynomial formula:
{POLFIT(Xa, Ya, N)}
Where Xa is the array of ordinate values, Ya is the array of data values, and N is the polynomial order to be fit.
It is obvious that one needs to select at least N+1 cells when the array funtion is typed in. But, it is easy to select too few cells.
I am looking for a way to test whether enough cells were selected for the range formula: The function declaration is
Function POLFIT(Xa, Ya, N As Integer) As Variant
Various means I have tried to count POLFIT do not return the correct value.
Can anyone provide a method?
Thanks 
Found what I needed  The Application.Caller.Address is the range of cells the array formula is stored in. So i can count those cells to satisy my criteria.
Chaz
{POLFIT(Xa, Ya, N)}
Where Xa is the array of ordinate values, Ya is the array of data values, and N is the polynomial order to be fit.
It is obvious that one needs to select at least N+1 cells when the array funtion is typed in. But, it is easy to select too few cells.
I am looking for a way to test whether enough cells were selected for the range formula: The function declaration is
Function POLFIT(Xa, Ya, N As Integer) As Variant
Various means I have tried to count POLFIT do not return the correct value.
Can anyone provide a method?
Thanks 
Found what I needed  The Application.Caller.Address is the range of cells the array formula is stored in. So i can count those cells to satisy my criteria.
Chaz
Hey there,
I have two arrays of data on which I would like to be able to run a polynomial regression in VBA.
However, when write the following in VBA:
Code:
I get a compile error, as {} are not valid characters. I've tried substituting parenthesis and leaving the brackets out completely, but that does not work either.
Anyone know how to perform a polynomial regression in VBA?
Working with two ranges of cells in a worksheet, the Linest function works just fine. ie, =LINEST(H18:H34, G18:G34^{1,2,3}), so I don't know why it would not be the same in VBA.
Office 2007
I have two arrays of data on which I would like to be able to run a polynomial regression in VBA.
However, when write the following in VBA:
Code:
Dim poly_3 as Variant Dim arr1 as Variant Dim arr2 as Variant poly_3 = WorksheetFunction.LinEst(arr1, my_arr2 ^ {1, 2, 3})
I get a compile error, as {} are not valid characters. I've tried substituting parenthesis and leaving the brackets out completely, but that does not work either.
Anyone know how to perform a polynomial regression in VBA?
Working with two ranges of cells in a worksheet, the Linest function works just fine. ie, =LINEST(H18:H34, G18:G34^{1,2,3}), so I don't know why it would not be the same in VBA.
Office 2007
I have a set of data that I've finally got the spreadsheet to provide analysis of, but it still requires the manual transfer of the Trend line coefficients that I have plotted manually transferring into the appropriate data cells.
I'm seeking to do this automatically, possibly by a macro but I need to find how to extract the 4th order polynomial trend line coefficients.
Any Help ??
I'm seeking to do this automatically, possibly by a macro but I need to find how to extract the 4th order polynomial trend line coefficients.
Any Help ??
Hey guys, I have a rather large spreadsheet that I use to get model coefficients from. The current process I plot the data and do a trendline (polynomial, x^2). I would like to automate this process if I can so that the coefficients for the trend function are automatically updated weekly, instead of having to copy them down out of the plot. Is there a way to do this? Thanks
On the attached data file, I want to run multiple regression analysis.
a2:a46 are y_knowns. b2:b46, c2:c46, d2:d46, e2:4e6, f2:f46, g2:g6 are x1 to x6_knowns.
Though I am entering with CSE press on linest, I am not able to see the coefficients for c, d,e,f and g.
a2:a46 are y_knowns. b2:b46, c2:c46, d2:d46, e2:4e6, f2:f46, g2:g6 are x1 to x6_knowns.
Though I am entering with CSE press on linest, I am not able to see the coefficients for c, d,e,f and g.
I know you can view various trend lines in Excel by adding a trend line to an existing chart. Furthermore, you can view the formula on the chart which provides the equation that describes the tend line shown.
Background:
In my model, I'm trying to identify numerous (50+) unique polynomial equations (6th order, based on X/Y scatterplot relationships). Currently, the only way to identify the formula is to build 50+ charts, show the trend line, and then manually enter the regression equation shown.
Question:
Is there a way for excel to automatically generate the regression equation (6th order, polynomial)? This would prevent the entire manual entry process.
Thanks,
Steve
Background:
In my model, I'm trying to identify numerous (50+) unique polynomial equations (6th order, based on X/Y scatterplot relationships). Currently, the only way to identify the formula is to build 50+ charts, show the trend line, and then manually enter the regression equation shown.
Question:
Is there a way for excel to automatically generate the regression equation (6th order, polynomial)? This would prevent the entire manual entry process.
Thanks,
Steve
Hi All,
I am trying to do multivariate polynomial regression in excel, trying to correlate data of the form y=f(x1,x2) with second order polynomials:
Y = c + a1*x1 + a2*x1^2 + a3^x1^3 + b1*x2 + b2*x2^2 + b3*x2^3
Using the following command, I have achieved this:
=LINEST(A2:A10,B2:B10^{1,2,3,0,0,0}*C2:C10^{0,0,0, 1,2,3},TRUE,TRUE)
Can anybody tell me the theory Excel uses for this kind of regression?
Thank you very much in advance!
athanasioskolios
I am trying to do multivariate polynomial regression in excel, trying to correlate data of the form y=f(x1,x2) with second order polynomials:
Y = c + a1*x1 + a2*x1^2 + a3^x1^3 + b1*x2 + b2*x2^2 + b3*x2^3
Using the following command, I have achieved this:
=LINEST(A2:A10,B2:B10^{1,2,3,0,0,0}*C2:C10^{0,0,0, 1,2,3},TRUE,TRUE)
Can anybody tell me the theory Excel uses for this kind of regression?
Thank you very much in advance!
athanasioskolios