# Multiple Regression Coefficient output

I am a University student running an analysis of data collected during a field trip.

The goal of this analysis is to determine whether the length and species of a limpet are good predictors of where on a rock the limpet may be found (variable = height).

I have run a multiple regression on R, using the model:

limpets.2 <- lm(height ~ length + species, data = limpets)

The response variable height is continuous, as is the predictor variable length. The predictor variable species is a factor with three levels for the three species. Co, Cr and Cd.

Output:

Call:
lm(formula = height ~ length + species, data = limpets)

Residuals:
Min      1Q  Median      3Q     Max
-73.190 -23.358  -0.449  18.919 102.919

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 126.3523     4.8989  25.792  < 2e-16 ***
length       -1.6840     0.1446 -11.644  < 2e-16 ***
speciesCo     6.0416     3.0087   2.008  0.04494 *
speciesCr   -12.6376     3.8076  -3.319  0.00094 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 32.14 on 889 degrees of freedom
Multiple R-squared:  0.2554,    Adjusted R-squared:  0.2529
F-statistic: 101.7 on 3 and 889 DF,  p-value: < 2.2e-16


My question is, while R has given the coefficients of Co and Cr, where do I find the coefficient for Cd?

Thank you in advance.

It just gets 'absorbed' into the intercept term. It turns out that to represent a factor with $$n$$ levels, you need $$n-1$$ 'dummy' variables in your regression equation. In your case, species has levels Co, Cr and Cd, so $$n = 3$$. This means you need $$n - 1 = 2$$ dummy variables. Using these two dummy variables, you can represent your factor, species, like this
• Cd: $$x_0 = x_1 = 0$$,
• Co: $$x_0 = 1, x_1 = 0$$ and,
• Cr: $$x_0 = 0, x_1 = 1$$