Linear regression with categorical predictor & quadratic term - dataset

Hey!

I am trying to construct a dataset array as below(matlab help) in order to do a regression:

>> load carsmall
>> ds = dataset(MPG, Weight);
>> ds.Year=nominal(Model_Year);
>> mdl = fitlm(ds, 'MPG~Year+Weight^2')

mdl = 

Linear regression model:
    MPG ~ 1 + Weight + Year + Weight^2

Estimated Coefficients:
                   Estimate      SE            tStat      pValue    
    (Intercept)        54.206        4.7117     11.505    2.6648e-19
    Weight          -0.016404     0.0031249    -5.2493    1.0283e-06
    Year_76            2.0887       0.71491     2.9215     0.0044137
    Year_82            8.1864       0.81531     10.041    2.6364e-16
    Weight^2       1.5573e-06    4.9454e-07      3.149     0.0022303

Number of observations: 94, Error degrees of freedom: 89
Root Mean Squared Error: 2.78
R-squared: 0.885,  Adjusted R-Squared 0.88
F-statistic vs. constant model: 172, p-value = 5.52e-41

But unfortunately, i get an error message when I try to do it with my data:

>> ds=dataset(price, size, weight, speed);
>> ds.postcode=nominal(postcode);
 mdl = fitlm(ds, 'price~postcode+size+weight+speed')

Which is:

Index of element to remove exceeds matrix dimensions.

Error in classreg.regr.modelutils.designmatrix>dummyVars (line 432)
    X0 = eye(ng); X0(:,1) = [];

Error in classreg.regr.modelutils.designmatrix (line 279)
            [Xj,dummynames] = dummyVars(dummyCoding{j},Xj,catLevels{j});

Error in classreg.regr.TermsRegression/designMatrix (line 316)
                [design,~,~,coefTerm,coefNames] ...

Error in LinearModel/fitter (line 654)
            [model.Design,model.CoefTerm,model.CoefficientNames] =
            designMatrix(model,X);

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

Error in LinearModel.fit (line 857)
            model = doFit(model);

Error in fitlm (line 111)
model = LinearModel.fit(X,varargin{:});

Thank you for your help!

[dpb]

Looks like perhaps there's insufficient data for the added variable postcode, maybe?

[Tania]

I am using the same amount of data as for the other variables. Is it possible that the problem is that I use more different variables than in the example?Do I need a different code than? Or is the problem that my postcode is more complex than in the example ( I have several different postcodes). In the example they only differentiate between year 1976/1982 yes/ no:

fitlm creates two dummy (indicator) variables for the nominal variables, Year. The dummy variable Year_76 takes the value 1 if the model year is 1976 and takes the value 0 if it is not. The dummy variable Year_82 takes the value 1 if model year is 1982 and takes the value 0 if it is not. 1970 is the reference year .....

Thank you!

[Roger Wohlwend]

Save the variable postcode in a mat-file an post it here. It is a lot easier to help when you can reproduce the error on your own machine. And in your case it seems difficult to find the problem without knowing the input variables.

[Tania]

I just saw that the postcodes are replaced by NaN ... that might be the problem. How do I import the postcode as it is not a number? Thanks :)

[Roger Wohlwend]

I'm glad we could help! :-)

[Tania]

Does this look right to you? I have quite a lot of variables because of the dummy variables... but it still seems to work or?

[Roger Wohlwend]

I would need a lot more of data to be in a position to assess the quality of the regression. But judging by the R-squared value and the F-statistic the result seems quite good. The huge amount of x-variable is a bit troublesome ...

[Tania]

I might try it with a decision tree instead of dummy variables in order to have not so many variables. But for now I am happy you helped me to get this one working :)

[dpb]

I don't know; Rsq is only roughly 40% (leaving 60% of total unexplained) and just glancing thru it appears that a very few of the coefficients are significant out of the "cast of thousands". Superficially I wouldn't say it looks like a very good model and certainly isn't high on the candidates list for a parsimonious one... :)

I'd guess the model estimated on only

 (Intercept)        0.090898
    bedroom          1.0747e-22
    postcode_NW1       0.072403
    postcode_SW1X      0.026157

would perform nearly as well.

[Tania]

Thanks, this is just the beginning for me.will try to work with the data with other models afterwards and hopefully get better results. but this help me a lot to get my first matlab analysis working. thanks :)