by roundsquare
Last Updated September 19, 2019 21:19 PM

**Background**

I'm trying to measure the causal impact of `action`

on `outcome`

(sorry for the vague names, but trying to keep this general). My data consists of the following for each record:

- m
`other_features`

[the result of TruncatedSVD to a much larger number of features] `action`

which is a binary`outcome`

which is continuous [in all cases here, I use the log of the actual value]

Based on business knowledge of the situation, I'm confident in a causal model that states:

- the
`other_features`

have a causal effect on`action`

- the
`other_features`

also have a causal effect on`outcome`

- the
`action`

have a causal effect on`outcome`

I tried two techniques and got different results - I wanted to know how to interpret these results.

**Attempt 1: Vanilla Linear Regression**

First, I tried to regress `outcome`

against `other_features`

and `action`

. When I did this, I got the following results (I'm using $\beta$ to refer to linear coefficients):

- $R^2 = 0.793$
- $\beta_{action} = 0.0943$

This implies that the `action`

has the effect of ~9.5% increase on `outcome`

.

**Attempt 2: Looking at Action vs Residuals**

Second, I tried to regress `outcome`

against `other_features`

(i.e. without `action`

). When I did this, I got the following results:

- $R^2 = 0.793$ [very little difference with the original regression).

Then, I looked at the residuals of those with and without action and got the following:

This seems to indicate that `action`

has about a ~-8.3% impact on `outcome`

.

**Questions**

- Is attempt 2 a valid way to proceed?
- If yes, how should I interpret the difference between the two approaches?
- Is there anything I ought to be weary/careful/aware of in using this approach?

(Please let me know if it additional data/results would be helpful in interpreting these results, I can supplement the information here).

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