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Multiple regression question

MathsManiac · 2017-09-23 11:15:09

I have an intriguing question about how best to use data to make a regression-based prediction. Scenario: Quantity Y is known to have a linear association with quantities X1 and X2. I have 10,000 observations of pairs (X1, Y). For 50 of these observations, I also have an observation for X2. I want to get as good an…

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23-09-2017 12:15pm

#1

MathsManiac

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I have an intriguing question about how best to use data to make a regression-based prediction.

Scenario:

Quantity Y is known to have a linear association with quantities X1 and X2.
I have 10,000 observations of pairs (X1, Y).
For 50 of these observations, I also have an observation for X2.

I want to get as good an estimate of an unknown Y as possible from new observation of X1 and X2.

I could ignore X2 entirely, use my 10,000 data points as the basis of a regression model for Y on X1 to get an estimate.

Or, I could ignore 9950 of my observations, and create a regression model for Y on X1 and X2.

In each case, I seem to be ignoring useful information.

Any ideas?

One option I'm considering is getting two separate estimates from simple regression - one using Y on X1 with 10,000 data points, the other using Y on X2 alone based on 50 data points, and combining these by weighting in proportion to the respective squared correlations.

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