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I happened to an interview question of linear regression:

If the capacity of data is very large, we cannot put them into memory simultaneously. Why can we break them down into a few parts for calculation?

Actually I don't much understand the meaning of break them down into a few parts for calculation. Since I only heard the partitioned regression model on features direction, how can we partition the data direction?

Does that mean we divide samples as $D_1$ and $D_2,$ then train their coefficients independently: $\theta_1$ and $\theta_2.$ The final solution is $\theta = (\theta_1 + \theta_2)/2?$

user6703592
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  • I believe threads like https://stats.stackexchange.com/questions/6920 illuminate the issue. Also see https://stats.stackexchange.com/questions/533857 for a simple example. It will reveal the answer is not as neat as your "final solution." For an explicit answer, read about [performing regression with covariance matrices](https://stats.stackexchange.com/questions/135201) and [how to combine covariances](https://stats.stackexchange.com/questions/51622). – whuber Jul 26 '21 at 18:14

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