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In stepwise regression, you step predictor by predictor, each time selecting the one with the greatest correlation with the measurement, subtracting greedily to leave a residual with no correlation to any of the previous predictors.

Why go stepwise? Why not just pick the predictors with best correlation to the measurement right now, however many you need, and use those? Why is a stepwise approach better? Does it yield smaller 1-norms?

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    $\begingroup$ It was faster to do with slide rules. $\endgroup$ – k20 Apr 1 '14 at 0:17

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