How to make a linear regression line?

Hi.

I have a data set with year and wind direction. I have used the plot command to make a figure but I also want to include a linear regression line. Is there an easy way to do this in matlab? Here is my data set:

1973 203

1974 124

1975 223

1976 177

1977 166

1978 104

1979 95

1980 94

1981 26

1982 135

1983 179

1984 210

1985 133

1986 153

1987 150

1988 189

1989 149

1990 184

1991 156

1992 133

1993 173

1994 211

1995 97

1996 92

1997 37

1998 200

1999 196

2000 195

2001 189

2002 155

2003 145

2004 149

2005 195

2006 168

2007 201

2008 173

2009 168

2010 192

2011 193

2012 216

2013 157

Helps is much appreciated!

Kristine

Answer 1

[Kristine]

I get:

Error executing Basic Fitting Output argument "pp" (and maybe others) not assigned during call to "/home/mano/kt31/Documents/MATLAB/R2014a/toolbox/matlab/graph2d/private/bfitcalcfit.m>fitcalcfit".

[Sean de Wolski]

Hi Kristine,

I think you might have a corrupted path or installation (all of your errors thus far are wierd).

First try this to set everything straight:

restoredefaultpath
rehash toolboxcache

If it works, save this new state

savepath

[Kristine]

Thank you! I got it to work:)

Answer 2

[Sean de Wolski]

If you go to "Tools" -> "Basic fitting" in the figure window you can add the line and the equation:

[Abhishek Chakraborty]

How to get the R^2 value?

Answer 3

[Star Strider]

Did you take a close look at your data?

There are two significant shifts from the usual southerly-southwesterly direction to easterly-northeasterly between 1977-82 and again from 1994-8. A linear fit is not going to tell you anything significant about your data, and given the direction shifts, might be misleading.

I don’t know what I’d recommend you do in your data analysis because I don’t know what you want to demonstrate. But a linear fit definitely isn’t it.

[Kristine]

I'm sorry, I did not define my x and y correctly. x is year, and y is trade wind count, so number of trade wind days in a year. I need a linear regression line to see if there is a slight decrease or increase in trade wind days.

[Star Strider]

I appreciate the clarification, but that doesn’t change my interpretation of your data. When I did a linear regression on your data (that I called YD) with polyfit and analysed the parameters with the FEX File polyparci,

[p,S,mu] = polyfit(YD(:,1),YD(:,2),1);
CI = polyparci(p,S);
PCI = [p; CI]

I got:

PCI =

      11.9207e+000   158.1707e+000
     -10.2221e-003   146.3862e+000
      23.8516e+000   169.9553e+000

so the slope (the first parameter, 11.92) isn’t significant, and the interpretation is that there has been no change over that time. (Only the intercept, 158.2, is significantly different from zero.) You might want to see if your data correlate with something else — north Pacific sea surface temperatures, ENSO, the solar cycle, or some such. There is no specific linear trend with respect to time otherwise that I can see, and the regression data support that.

I believe there is interesting information in your data. You simply haven’t found it yet. You definitely have to explain those two multi-year declines in trade wind days.

[Kristine]

I got it to work. It's my professor that wanted me to do this, so he could update a paper written a couple of years ago. But I agree, its very interesting with the two significant declines in trade wind days.

[Star Strider]

I don’t know what the hypothesis of the study is, but if it is to show that there is no linear change in trade wind days, that works. The trend is not significantly different from zero. It just seems to ignore the really interesting stuff.

Answer 4

[Shashank Prasanna]

1) http://www.mathworks.com/help/matlab/ref/polyfit.html

where, n = 1

2) You can also do backslash: http://www.mathworks.com/help/matlab/ref/mldivide.html

3) If you have the statistics toolbox: http://www.mathworks.com/help/stats/fitlm.html

Each page has examples

[Kristine]

I have tried:

>> tbl=table(dato,trade_count);

>> mdl=fitlm(tbl,'linear')

But all I get is errors:

Error using qr LAPACK loading error: dlopen: cannot load any more object with static TLS

Error in LinearModel>lsfit (line 955) [Q,R,perm] = qr(X,0);

Error in LinearModel/fitter (line 660) [model.Coefs,model.MSE,model.CoefficientCovariance,model.R,model.Qy,model.DFE,model.Rtol] ...

Error in classreg.regr.FitObject/doFit (line 220) model = fitter(model);

Error in LinearModel.fit (line 863) model = doFit(model);

Error in fitlm (line 117) model = LinearModel.fit(X,varargin{:});

[Shashank Prasanna]

There is something wrong with your MATLAB path. You must not get errors with LAPACK. I am going to suggest what sean suggested below:

restoredefaultpath
rehash toolboxcache

And then run the same code below:

mdl=fitlm(dato,trade_count,'linear')
plot(mdl)

I get the following results:

                   Estimate      SE        tStat     pValue 
                   ________    _______    _______    _______

    (Intercept)    -1825.1      1178.1    -1.5491    0.12942
    x1             0.99512     0.59113     1.6834    0.10028

[Kristine]

Yes, you were right. There was something wrong with my matlab path. I got it to work, so thank you very much!:)

Answer 5

[Jos (10584)]

The function LSLINE will add a linear regression line to a plot.

[Kristine]

Not in this case, I just get the error:

Warning: No allowed line types or scatterplots found. Nothing done. > In lsline at 45

Answer 6

[Image Analyst]

See my polyfit() regression demo, attached. Adapt it to use order 1 for linear, and to use your specific data arrays.

[Kristine]

Thank you!