Running several regressions and storing all the data with regress

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chiefjia on 11 Oct 2021
Edited: chiefjia on 12 Oct 2021
Dear MATLAB expers,
I'm trying to run many linear regressions each one consisting of one dependent variable and an independent variable, but I keep on stumbling upon the following error:
Unable to perform assignment because the left and right sides have a different number of elements.
Error in code (line 739)
tStat(i) = bint; % t-Statistic
It is an error concerning the size of 'tStat', 'Residuals', 'Outliers' and 'RegressStats' and I don't know how to fix it.
[NumRows, NumSeries] = size(stockReturns);
NumAssets = NumSeries - 2;
% Specifying start and end date of the calculation of alphas and betas
StartDate = datestr(stockReturnsDates(1));
EndDate = datestr(stockReturnsDates(end));
Alpha = NaN(1, length(NumAssets));
Beta = NaN(1, length(NumAssets));
tStat = zeros(1818, 2, 2);
Residuals = NaN(length(NumAssets), 2);
Outliers = NaN(length(NumAssets), 2);
RegressStats = NaN(length(NumAssets), 2);
for i = 1:NumAssets
% Set up separate asset data and design matrices
DependentVariable = zeros(NumRows,1);
IndependentVariable = zeros(NumRows,2);
DependentVariable(:) = stockReturns(:,i) - stockReturns(:,1827); % Excess return of each asset
IndependentVariable(:,1) = 1.0; % For calculating alpha
IndependentVariable(:,2) = stockReturns(:,1826) - stockReturns(:,1827); % Excess market return
% Estimate the CAPM for each asset separately.
[b, bint, r, rint,stats] = regress(DependentVariable, IndependentVariable, 5);
% Including values in matrixes
Alpha(i) = b(1); % Intercept
Beta(i) = b(2); % Betas
tStat(i) = bint; % t-Statistic
Residuals(i) = r; % Residuals
Outliers(i) = rint; % Outliers
RegressStats(i) = stats; % Includes R^2, F-stat and p-value
I would really appreciate your help since I've been stuck with this error for a while already.
  1 Comment
chiefjia on 11 Oct 2021
I can't add the data as an attachment since it exceeds the allowed size

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Accepted Answer

Dave B
Dave B on 12 Oct 2021
Edited: Dave B on 12 Oct 2021
You're getting this error because you're trying to store the result of bint (which is a 2 x 2 matrix) in a scalar location (tStat(i)). Note that bint is not the t-statistic, it's the upper and lower confidence intervals of your 2 predictors.
Maybe you wanted tStat(i,:,:) = bint(:)' (which seems to correspond to how you initialized the variable)? But I question your choice of name for this variable, and also would not recommend storing it in this shape of matrix (if anything consider 2 x 2 x 1818 (in which case tStat(:,:,i) = bint)...but what are you planning on doing with these values? It's likely more sensible to keep them in a 1818 x 4 matrix.
You'll run into the same problem with storing the remaining values: you need to specify a storage location that matches the size of the values you're going to store. r, rint, and stats will all be non-scalar. Consult the documentation to determine what size to expect, or run the regression on one column of your data to see what shape it will be. If you're really desparate and just want to store everything blindly without thinking about the size/shape, use a struct or cell array...though I'd discourage this as you're just postponing the inevitable problem of having to think about the size (and meaning) of the results of your regression.
A few other things I notice in your code:
  • You're initializing all of your variables based on length(NumAssets) but you probably want to be using NumAssets (because length(NumAssets) is 1)
  • You specified 5 as the third argument to regress. Looking at the documentation, the third argument (alpha) should be specified as a value between 0 and 1 (I'm thinking you wanted .05)
chiefjia on 12 Oct 2021
Dear Dave,
thanks a lot for your feedback, I really appreciate it! I know get a better understanding of how this function works and the use of parentheses and colons :)

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