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POLeast-Squares Regression of Matrices with Numpy
 

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  1. POLeast-Squares Regression of Matrices with Numpy
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    <p>If this has been answered somewhere I couldn't find, feel free to forum slap me. </p> <p>I'm looking to calculate least squares linear regression from an N by M matrix and a set of known, ground-truth solutions, in a N-1 matrix. From there, I'd like to get the slope, intercept, and residual value of each regression. Basic idea being, I know the actual value of that should be predicted for each sample in a row of N, and I'd like to determine which set of predicted values in a column of M is most accurate using the residuals. </p> <p>I don't describe matrices well, so here's a drawing:</p> <pre><code>(N,M) matrix with predicted values for each row N in each column of M... ##NOTE: Values of M and N are not actually 4 and 3, just examples 4 columns in "M" [1, 1.1, 0.8, 1.3] [2, 1.9, 2.2, 1.7] 3 rows in "N" [3, 3.1, 2.8, 3.3] (1,N) matrix with actual values of N [1] [2] Actual value of each sample N, in a single column [3] </code></pre> <p>So again, for clarity's sake, I'm looking to calculate the lstsq regression between each column of the (N,M) matrix and the (1,N) matrix.</p> <p>For instance, the regression between</p> <pre><code>[1] and [1] [2] [2] [3] [3] </code></pre> <p>then the regression between </p> <pre><code>[1] and [1.1] [2] [1.9] [3] [3.1] </code></pre> <p>and so on, outputting the slope, intercept, and standard error (average residual) for each regression calculated.</p> <p>So far in the numpy/scipy documentation and around the 'net, I've only found examples computing one column at a time. I had thought numpy had the capability to compute regressions on each column in a set with the standard </p> <pre><code>np.linalg.lstsq(arrayA,arrayB) </code></pre> <p>But that returns the error </p> <pre><code>ValueError: array dimensions must agree except for d_0 </code></pre> <p>Do I need to split the columns into their own arrays, then compute one at a time? Is there a parameter or matrix operation I need to use to have numpy calculate the regressions on each column independently?</p> <p>I feel like it should be simpler? I've looked it all over, and I can't seem to find anyone doing something similar. </p>
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    1. COYou say your matrices are (N,M) (1,N). Lstsq expects (N, M) and (N), did you try using the transpose of arrayB? I get a slightly different exception from you though (LinAlgError: Incompatible dimensions), I'm using Python2.7, with numpy1.6
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