MATLAB Central Newsreader - Linear regression.

Linear regression.

Zebbik — Wed, 12 Mar 2008 19:52:24 -0400

Hello.

My problem is that I am supposed to find trend line /regression of from
the results made in experiment. I know

p = polyfit(x,y,1)

gives me coefficients of line (the correlation is strong almost 1 so
it's linear tendency), where in terms of y = mx + c

p(1) - slope (m)
p(2) - 'c' coefficient

I know also that

yfit = polyval(p, y)

gives me the fit of line such that it's going to be linear reggresion.

Now. The value im looking for is the slope. I would like to find the
slope itself with the error or let's say Delta that the slope could
differ arround like
(Slope - Delta_Slope, Slope + Delta_Slope)

Does any1 know how to do that?

Thanks.

Re: Linear regression.

Paul — Thu, 13 Mar 2008 00:21:02 -0400

Zebbik <zebik@op.pl> wrote in message
<fr9c9t$o1p$1@news.onet.pl>...
> Hello.
>
> My problem is that I am supposed to find trend line
/regression of from
> the results made in experiment. I know
>
> p = polyfit(x,y,1)
>
> gives me coefficients of line (the correlation is strong
almost 1 so
> it's linear tendency), where in terms of y = mx + c
>
> p(1) - slope (m)
> p(2) - 'c' coefficient
>
> I know also that
>
> yfit = polyval(p, y)
>
> gives me the fit of line such that it's going to be linear
reggresion.
>
> Now. The value im looking for is the slope. I would like
to find the
> slope itself with the error or let's say Delta that the
slope could
> differ arround like
> (Slope - Delta_Slope, Slope + Delta_Slope)
>
> Does any1 know how to do that?
>
> Thanks.

I suggest you search the file exchange.

Re: Linear regression.

Arthur G — Thu, 13 Mar 2008 02:38:50 -0400

On 2008-03-12 20:21:02 -0400, "Paul " <par@ceri.memphis.edu> said:

> Zebbik <zebik@op.pl> wrote in message
> <fr9c9t$o1p$1@news.onet.pl>...
>> Hello.
>>
>> My problem is that I am supposed to find trend line
> /regression of from
>> the results made in experiment. I know
>>
>> p = polyfit(x,y,1)
>>
>> gives me coefficients of line (the correlation is strong
> almost 1 so
>> it's linear tendency), where in terms of y = mx + c
>>
>> p(1) - slope (m)
>> p(2) - 'c' coefficient
>>
>> I know also that
>>
>> yfit = polyval(p, y)
>>
>> gives me the fit of line such that it's going to be linear
> reggresion.
>>
>> Now. The value im looking for is the slope. I would like
> to find the
>> slope itself with the error or let's say Delta that the
> slope could
>> differ arround like
>> (Slope - Delta_Slope, Slope + Delta_Slope)
>>
>> Does any1 know how to do that?
>>
>> Thanks.
>
> I suggest you search the file exchange.

If you have the statistics toolbox, the regress function will give 95%
confidence intervals.

Re: Linear regression.

Peter Perkins — Thu, 13 Mar 2008 12:56:07 -0400

Zebbik wrote:

> Now. The value im looking for is the slope. I would like to find the
> slope itself with the error or let's say Delta that the slope could
> differ arround like
> (Slope - Delta_Slope, Slope + Delta_Slope)

POLYCONF in the Statistics Toolbox, or LSCOV in core MATLAB.

Hope this helps.

- Peter Perkins
The MathWorks, Inc.

Re: Linear regression.

Zebbik — Thu, 13 Mar 2008 16:38:20 -0400

Paul wrote:
> Zebbik <zebik@op.pl> wrote in message
> <fr9c9t$o1p$1@news.onet.pl>...
>> Hello.
>>
>> My problem is that I am supposed to find trend line
> /regression of from
>> the results made in experiment. I know
>>
>> p = polyfit(x,y,1)
>>
>> gives me coefficients of line (the correlation is strong
> almost 1 so
>> it's linear tendency), where in terms of y = mx + c
>>
>> p(1) - slope (m)
>> p(2) - 'c' coefficient
>>
>> I know also that
>>
>> yfit = polyval(p, y)
>>
>> gives me the fit of line such that it's going to be linear
> reggresion.
>> Now. The value im looking for is the slope. I would like
> to find the
>> slope itself with the error or let's say Delta that the
> slope could
>> differ arround like
>> (Slope - Delta_Slope, Slope + Delta_Slope)
>>
>> Does any1 know how to do that?
>>
>> Thanks.
>
> I suggest you search the file exchange.
I am not quite sure what you mean.

Re: Linear regression.

Zebbik — Thu, 13 Mar 2008 18:20:58 -0400

Peter Perkins wrote:
> Zebbik wrote:
>
>> Now. The value im looking for is the slope. I would like to find the
>> slope itself with the error or let's say Delta that the slope could
>> differ arround like
>> (Slope - Delta_Slope, Slope + Delta_Slope)
>
> POLYCONF in the Statistics Toolbox, or LSCOV in core MATLAB.
>
> Hope this helps.
>
> - Peter Perkins
> The MathWorks, Inc.
The thing i am looking for is in Excel, however, i would like to find it
in MATLAB to be honest. I will try to explain that on Excel example

In EXCEL there is a formula called LINEST and has the form below

LINEST(knowm_y value cells, known_x values cells, CONST, STATS)

This formula produce more or less such results as:
SLope Coeff Point Of intercept
Slope Coeff Error Point Of Intercep Error
...
...
...

I dont know that yet but i believe in produces results with 95%
confidence intervals. The other values are not important here at the
moment. The Slope Error is the thing i am looking for in MATLAB.
Can someone please be so kind and help me to find/understand that.

Regards

Re: Linear regression.

Yuri Geshelin — Thu, 13 Mar 2008 18:50:19 -0400

Hello,

I had the same problem and did not find anything in matlab.
Below is the code, which I wrote up for this purpose. It
contains the reference to the source, which I used. Perhaps
I will consider uploading it to file exchange, but for now
I will just copy-paste it. Hope you will cope with text
wrapping and figure it out.

Yuri
------------------------
%*******************************
function [sesl, cisl, sein, ciin] = secisi(X,Y,pr);

% Returns Standard Errors and Confidence Intervals
% for the Slope and Intercept of a regression.

% Author: Yuri Geshelin, 2002.

% Source: N. R. Draper and H. Smith, 1966:
% Applied Regression Analysis, 407 p. Publ. by
% John Wiley and Sons, Inc. New York - London - Sydney.

% Input:
% 1-D arrays X and Y, for which the regression
% Y = B0 + B1 * X is computed
% pr - probability (e.g. if we want 95%
% confidence level, then pr = 95.

% Output:
% sesl - standard error for slope B1
% clsl - pr%-confindence interval for slope B1
% sein - standard error for intercept B0
% clin - pr%-confindence interval for intercept B0

if pr < 10 | pr > 99.9
   error('pr should be between 10 and 99.9!')
end

n = length(X);
if length(Y) ~= n
   error('X, Y should be the same lengths!')
end

n2 = n - 2; % n - 2 degrees of freedom

if n2 < 121 % if n2 = 120, then we already would
            % have to use the next-to-last line
            % of the table on p. 305: this code is only
            % for the last line.
   error('This code only works with n > 120!')
end

% The following line is the result of
% prob = 100 * ...
% (1 - [0.9:-0.2:0.3 0.2 0.1 0.05 0.02 0.01 0.001]) ...
% (see p. 305):

prob = [10 30 50 70 80 90 95 98 99 99.9]; % percentage

pp = [0.126 0.385 0.674 1.036 1.282 ...
      1.645 1.960 2.326 2.576 3.291]; % last line of the
table,
                                      % p. 305.

% Compute total corrected sum of squares (SS) of the Y's
% (see p.14 and table on p. 16):

SStot = sum((Y - mean(Y)).^2);

% Compute SS due to regression (see p. 16):

SX2 = sum(X .^ 2);
SSrgr = ...
(sum(X .* Y) - sum(X) * sum(Y) / n) ^2 / ...
(SX2 - sum(X) ^2 / n);

% Compute SS due to residual (see p. 16):

SSres = SStot - SSrgr;

% Compute mean square about regression
% (see tables on pp. 15, 16):

s2 = SSres / n2;

% Compute estimate of variance of slope B1 (p. 19)

sesl = sqrt(s2 / sum((X - mean(X)) .^2 ));

% Found the interpolated value from the table
% (page 305):

val_int = interp1(prob,pp,pr);

% Compute confidence limit for slope:

cisl = val_int * sesl;

% Compute estimate of variance of intercept B0 (p. 21)

sein = sesl * sqrt(SX2 / n);

% Compute confidence limit for intercept:

ciin = val_int * sein;
%***********************************

Re: Linear regression.

Peter Perkins — Thu, 13 Mar 2008 19:30:56 -0400

Zebbik wrote:

> The thing i am looking for is in Excel, however, i would like to find it
> in MATLAB to be honest. I will try to explain that on Excel example

Again, POLYCONF in the Statistics Toolbox, or LSCOV in core MATLAB.

Re: Linear regression.

Yuri Geshelin — Thu, 13 Mar 2008 19:43:02 -0400

Peter Perkins <Peter.PerkinsRemoveThis@mathworks.com> wrote
in message <frbvdg$7t7$1@fred.mathworks.com>...
> Zebbik wrote:
>
> > The thing i am looking for is in Excel, however, i
would like to find it
> > in MATLAB to be honest. I will try to explain that on
Excel example
>
> Again, POLYCONF in the Statistics Toolbox, or LSCOV in
core MATLAB.

Hi,

Here is what Zebbik wrote:

"The Slope Error is the thing i am looking for in MATLAB."

Does lscov or polyconf accomplish this task?

Re: Linear regression.

Peter Perkins — Fri, 14 Mar 2008 13:13:13 -0400

Yuri Geshelin wrote:

> Here is what Zebbik wrote:
>
> "The Slope Error is the thing i am looking for in MATLAB."
>
> Does lscov or polyconf accomplish this task?

Yuri, "yes" to LSCOV (depending on what is meant by "error"), but you're
right, my suggestion of polyconf was off track; I I wasn't paying enough
attention.

Zebbik, if by "error", you mean a standard error, then LSCOV will give
you that as its second output.

If you want a confidence interval for the coefficient, then REGRESS in
the Statistics Toolbox (as pointed out by Arthur G) returns that as its
second output.

In both cases, all you have to do is to create the design matrix X as

X = [ones(length(x),1) x(:)]

where x and y are vectors containing your data.

Re: Linear regression.

Zebbik — Tue, 18 Mar 2008 14:01:56 -0400

Yuri Geshelin wrote:
> Hello,
>
> I had the same problem and did not find anything in matlab.
> Below is the code, which I wrote up for this purpose. It
> contains the reference to the source, which I used. Perhaps
> I will consider uploading it to file exchange, but for now
> I will just copy-paste it. Hope you will cope with text
> wrapping and figure it out.
>
> Yuri
> ------------------------
> %*******************************
> function [sesl, cisl, sein, ciin] = secisi(X,Y,pr);
>
> % Returns Standard Errors and Confidence Intervals
> % for the Slope and Intercept of a regression.
>
> % Author: Yuri Geshelin, 2002.
>
> % Source: N. R. Draper and H. Smith, 1966:
> % Applied Regression Analysis, 407 p. Publ. by
> % John Wiley and Sons, Inc. New York - London - Sydney.
>
> % Input:
> % 1-D arrays X and Y, for which the regression
> % Y = B0 + B1 * X is computed
> % pr - probability (e.g. if we want 95%
> % confidence level, then pr = 95.
>
> % Output:
> % sesl - standard error for slope B1
> % clsl - pr%-confindence interval for slope B1
> % sein - standard error for intercept B0
> % clin - pr%-confindence interval for intercept B0
>
> if pr < 10 | pr > 99.9
> error('pr should be between 10 and 99.9!')
> end
>
> n = length(X);
> if length(Y) ~= n
> error('X, Y should be the same lengths!')
> end
>
> n2 = n - 2; % n - 2 degrees of freedom
>
> if n2 < 121 % if n2 = 120, then we already would
> % have to use the next-to-last line
> % of the table on p. 305: this code is only
> % for the last line.
> error('This code only works with n > 120!')
> end
>
> % The following line is the result of
> % prob = 100 * ...
> % (1 - [0.9:-0.2:0.3 0.2 0.1 0.05 0.02 0.01 0.001]) ...
> % (see p. 305):
>
> prob = [10 30 50 70 80 90 95 98 99 99.9]; % percentage
>
> pp = [0.126 0.385 0.674 1.036 1.282 ...
> 1.645 1.960 2.326 2.576 3.291]; % last line of the
> table,
> % p. 305.
>
> % Compute total corrected sum of squares (SS) of the Y's
> % (see p.14 and table on p. 16):
>
> SStot = sum((Y - mean(Y)).^2);
>
> % Compute SS due to regression (see p. 16):
>
> SX2 = sum(X .^ 2);
> SSrgr = ...
> (sum(X .* Y) - sum(X) * sum(Y) / n) ^2 / ...
> (SX2 - sum(X) ^2 / n);
>
> % Compute SS due to residual (see p. 16):
>
> SSres = SStot - SSrgr;
>
> % Compute mean square about regression
> % (see tables on pp. 15, 16):
>
> s2 = SSres / n2;
>
> % Compute estimate of variance of slope B1 (p. 19)
>
> sesl = sqrt(s2 / sum((X - mean(X)) .^2 ));
>
> % Found the interpolated value from the table
> % (page 305):
>
> val_int = interp1(prob,pp,pr);
>
> % Compute confidence limit for slope:
>
> cisl = val_int * sesl;
>
> % Compute estimate of variance of intercept B0 (p. 21)
>
> sein = sesl * sqrt(SX2 / n);
>
> % Compute confidence limit for intercept:
>
> ciin = val_int * sein;
> %***********************************
>
thanks for that =))

Re: Linear regression.

Zebbik — Tue, 18 Mar 2008 14:04:06 -0400

Peter Perkins wrote:
> Yuri Geshelin wrote:
>
>> Here is what Zebbik wrote:
>>
>> "The Slope Error is the thing i am looking for in MATLAB."
>>
>> Does lscov or polyconf accomplish this task?
>
> Yuri, "yes" to LSCOV (depending on what is meant by "error"), but you're
> right, my suggestion of polyconf was off track; I I wasn't paying enough
> attention.
>
> Zebbik, if by "error", you mean a standard error, then LSCOV will give
> you that as its second output.
>
> If you want a confidence interval for the coefficient, then REGRESS in
> the Statistics Toolbox (as pointed out by Arthur G) returns that as its
> second output.
>
> In both cases, all you have to do is to create the design matrix X as
>
> X = [ones(length(x),1) x(:)]
>
> where x and y are vectors containing your data.
It's np. thanks for ur answer it is always helpful to know something new.

Re: Linear regression.

ashkan — Wed, 13 Apr 2011 01:15:07 -0400

Zebbik <zebik@op.pl> wrote in message <froi4p$e0s$2@news.onet.pl>...
> Peter Perkins wrote:
> > Yuri Geshelin wrote:
> >
> >> Here is what Zebbik wrote:
> >>
> >> "The Slope Error is the thing i am looking for in MATLAB."
> >>
> >> Does lscov or polyconf accomplish this task?
> >
> > Yuri, "yes" to LSCOV (depending on what is meant by "error"), but you're
> > right, my suggestion of polyconf was off track; I I wasn't paying enough
> > attention.
> >
> > Zebbik, if by "error", you mean a standard error, then LSCOV will give
> > you that as its second output.
> >
> > If you want a confidence interval for the coefficient, then REGRESS in
> > the Statistics Toolbox (as pointed out by Arthur G) returns that as its
> > second output.
> >
> > In both cases, all you have to do is to create the design matrix X as
> >
> > X = [ones(length(x),1) x(:)]
> >
> > where x and y are vectors containing your data.
> It's np. thanks for ur answer it is always helpful to know something new.

[b,stats] = robustfit(x,y,'ols')

returns a stats structure with the following fields:
stats.ols_s - sigma estimate (rmse) from least squares fit

stats.robust_s - robust estimate of sigma

stats.mad_s - estimate of sigma computed using the median absolute deviation of the residuals from their median; used for scaling residuals during the iterative fitting

stats.s - final estimate of sigma, the larger of robust_s and a weighted average of ols_s and robust_s

stats.se - standard error of coefficient estimates

stats.t - ratio of b to stats.se

stats.p - p-values for stats.t

stats.coeffcorr - estimated correlation of coefficient estimates

stats.w - vector of weights for robust fit stats.h - vector of leverage values for least squares fit

stats.dfe - degrees of freedom for error

stats.R - R factor in QR decomposition of X matrix

Re: Linear regression.

John D'Errico — Wed, 13 Apr 2011 03:30:08 -0400

"Yuri Geshelin" wrote in message <frbt1b$9nn$1@fred.mathworks.com>...
> Hello,
>
> I had the same problem and did not find anything in matlab.

You did not look that hard then.

I can point out at least three places at a glance.

john