# [R] How to interpret lm's coefficients?

Bert Gunter bgunter.4567 at gmail.com
Thu Sep 8 16:59:27 CEST 2016

```Petr Pikal said:

"The explanation is not for few lines of plain text short mail.

But maybe others will disagree."

Not I -- you should consult your teachers or texts (as Petr said) for
basic statistical questions.

I'll add a nugget to Petr's reply, however: it is very often the case
(for correlated regressors/covariates) that individual coefficients
cannot and should not be interpreted -- the "fit" is merely a
prediction engine.''

Cheers,
Bert
Bert Gunter

"The trouble with having an open mind is that people keep coming along
and sticking things into it."
-- Opus (aka Berkeley Breathed in his "Bloom County" comic strip )

On Thu, Sep 8, 2016 at 5:43 AM, Matti Viljamaa <mviljamaa at kapsi.fi> wrote:
> I’m trying to understand how to interpret the return values, specifically “Coefficients:”, of R’s lm function. I’m using it with a dichotomic predictor (mom_hs).
>
> lm(data\$kid_score ~ data\$mom_hs) returns
>
> Coefficients:
> #   (Intercept)  data\$mom_hs
> # 77.55        11.77
>
> I read that the (Intercept) value is the “y-intercept” value b, i.e. the y value where the line intercept the y-axis.
>
> The second value is the value of the term m (or “slope”) in the equation of a line y=mx+b.
>
> However,
>
> These two numbers also have the following interpretations:
>
> b or (Intercept) value is the same as:
> The mean of those data\$kid_score that have data\$mom_hs == 0.
> Why is this a valid interpretation?
>
> m or data\$mom_hs value is the same as:
> The difference of means between those data\$kid_score that have data\$mom_hs == 1
> and those data\$kid_score that have data\$mom_hs == 0.
> Why is this a valid interpretation?
>
> Can someone explain?
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