How can I fit a model with different intercepts?

Question

I am reading a book and following along with examples. Currently, I am looking at a problem involving this data

     age weight gender
   <dbl>  <dbl>  <chr>
 1    39   2817 Female
 2    40   2935 Female
 3    40   3231 Female
 4    36   2729 Female
 5    38   2754 Female
 6    40   3421   Male
 7    37   2539 Female
 8    37   2847   Male
 9    38   3176   Male
10    37   2628   Male

The book talks about analytically fitting a model with a linear model with different intercepts for gender, but the same regression coefficient. More precicely, it wants to fit

$$ \text{weight}_j = \alpha_j + \beta x_{ij} $$

Here $j = 0,1$ depending on if the weight belongs to a male or female.

Is there a way to do this in R? I'm not sure how to code an interaction term for an intercept.

Answer 1

Two intercepts is equivalent to a true intercept and a binary variable.

All you have to do is say that $\text{gender}$ is a binary variable: 0 for male, 1 for female. You will fit the model: $$\text{weight}=\alpha+\beta_1\text{gender}+\beta_2\text{age}$$

Then $\alpha$ is the intercept for male, $\alpha+\beta_1$ is the intercept for female.