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I am trying to reuse a multiple linear regression formula, where I have a set of predictors and set of coefficient values.

This is how they look like (in real example there is ~10 of predictors): 

alpha = 7.601
weight = 2213.940
length = -0.032
height = -0.629
size = 0.345

I know that my multiple linear regression should be constructed like this, i.e. sum of alpha (b0), and multiplication of predictors (xn) with their coefficients (bn)

y = b0 + b1*x1 + b2*x2 + b3*x3 + b4*x4 +b5*x5

I want to reuse the formula, but I have data only describing weight and length, so have no data about predictors b3-5.

The question is, can I just skip parameters that I don't have data for? I.e. instead of using full sum of parameters*coefficient I will just use the ones I have?

I would guess that this is likely not a correct approach. Also, I don't have information about the proportion of explained variability by each predictor, or their significance, to guide me which predictors are more important that others. Thank you for your advises.

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    $\begingroup$ You can't predict from a model, if you don't have data for all predictors. You'll need to develop a new model that only includes available predictors. $\endgroup$
    – Roland
    Feb 7, 2020 at 8:01

2 Answers 2

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You would likely have to use some tricks.

Imagine if your model predicts age using weight and height. If you only have weight for a particular sample that would be the same as assuming its height is 0. So at the very least I would say you should substitute some values for the variables that you are missing. Maybe by using their average from the other samples.

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You can't reuse directly those parameters to fit them again with only part of the descriptive data. You can however use tricks as @Karolis said.

One possible idea is to train a second model with only weight and length as descriptor. Then blend the two models by taking the weighted mean of the predictions of model 1 and 2.

[Edit] I was thinking, maybe you can reuse your first model and fits only parameters weight and length. The idea is to assign value 0 for all other variables. Then feed those sample to the model and compute your loss. And finally perform a gradient descent with small learning rate on your two parameters (it won't affect the other parameters).

If possible you'll need to check that it doesn't worsen results the global dataset.

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  • $\begingroup$ would you like to provide an example bout how to calculate the loss due to setting parameters to zero? i.e. as you say, create one model with 5 variables, then create one model with 2 variables (another 3 set to 0) and find their difference? Thank you again $\endgroup$
    – maycca
    Feb 7, 2020 at 11:43
  • $\begingroup$ The loss - assuming you're estimating the conditional mean - would be the squared sum of (y - (b0 + b1*x1 +b2*x2)) for each training sample. $\endgroup$
    – Samos
    Feb 10, 2020 at 19:24

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