Basic question: does `lm(y~x_1*x_2)`

correspond to y_i = \beta_0 + \beta_1x_{1,i} + \beta_2x_{2,i}+\beta_3x_{1,i}x_{2,i} or just y_i = \beta_0 +\beta_1x_{1,i}x_{2,i}?

The * represents crossing, I.e. your first interpretation. For the other replace with colon :

Thanks, that's great.

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