How to interpret R contrasts when given continuous and categorical explanatory variables?

Question

Let's say I have run a linear regression model that models the sugar content in a Jelly Bean as a function of its colour and weight:

lm(sugar ~ color + weight)

The summary of the above model outputs the following:

Coefficients:

           Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.07934    0.28625   0.277   0.7823
coloured    0.41976    0.09952   2.208   0.0296 *
weight      2.54078    0.35643   7.128 1.81e-10 ***

What is the mean sugar content of a coloured Jelly Bean?

Would it be 0.07934 + 0.41976 + 2.54078? Or is it not possible to calculate without knowing the mean weight of a coloured Jelly Bean?

I would be very grateful for any help with this. Please note this is not a homework question.

Answer 1

The complete model is:

$sugar content = 0.07934 + 0.41976*(coloured) + 2.54078*(Weight)$

There is a strong correlation as weight goes up there is more sugar content. At zero weight there is nearly zero sugar (apparently there was noise in the readings from original dataset). I am not sure how what the coloured (yes/no??) variable represents.

To answer your question, the model knows nothing about the weight of a Jelly bean only the relationship between weight and sugar content. So yes you will need to know the mean weight of a Jelly bean to know the expected sugar content.