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I have runa multiple regression analysis and have three explanatory variables (two quantitative and one categorical).

The categorical variable has 4 levels and therefore i have 3 dummy variables in my regression model.

I am wondering whether in the model equation, I am supposed to include a separate term for each dummy variable of the categorical variable, or I'm supposed to simply write out the term for the categorical variable and not include terms for the dummies?

The variables are: Height(Quantitative),Age(Quantitative), Country(Categorical with four levels: England, Wales, Scotland, Ireland)

So is the equation supposed to be:

1) Life Expectancy = b0 + b1*Height + b2*Age + b3*Country

or

2) Life Expectancy = b0 + b1*Height + b2*Age + b3*Scotland + b4*Wales + b5*Ireland

Note: The reference variable for the dummy variables is England and therefore I did not include it in the second equation as of course the regression model doesn't produce a coefficient for it...

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    $\begingroup$ Could you tell us what you intend "Country" in equation (1) to mean? On the face of it, it's not a number at all, so how are we supposed to make sense of multiplying it by the number "b3" and adding that to other numbers? There is a comparable difficulty with (2) but by reading it generously we can understand "Scotland" etc to refer to numerical binary indicators equal to $1$ for observations from Scotland and $0$ otherwise, for instance. No such reading seems natural or possible for (1). $\endgroup$ – whuber Jan 20 '18 at 20:16
  • $\begingroup$ @whuber Country would be where a participant is from (either of those four countries). $\endgroup$ – Martin Sloane Jan 20 '18 at 20:25
  • $\begingroup$ Obviously. But just as obviously, "country" is not a number, is it? How, then, do you propose to make sense of the arithmetic presented in formula (1)? $\endgroup$ – whuber Jan 21 '18 at 16:05
  • $\begingroup$ If I answered your question to your satisfaction, you can accept my answer by clicking the check mark under the voting arrows. $\endgroup$ – Kodiologist Jan 23 '18 at 19:33
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The first equation resembles R's notation for linear models, but it isn't correct. For example, you didn't estimate a single coefficient b3 for all three dummy variables. You estimated one coefficient for Scotland, one for Wales, and one for Ireland.

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  • $\begingroup$ I didn't do them exactly for those countries though, I did it for those countries relative to the reference - which was England... $\endgroup$ – Martin Sloane Jan 20 '18 at 20:03
  • $\begingroup$ @MartinSloane Yes, I understand that. That's what I mean. $\endgroup$ – Kodiologist Jan 20 '18 at 20:23

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