Let's consider this simple regression model $$y_i = β_0 + β_1x_i + u_i$$ where the Gauss-Markov hypotheses are met. Suppose we know that $β_0=0$
a) Write the constraint model (assuming $β_0=0$) et write the sum of squares associated with this model.
b) Find the first order conditions et the OLS estimator for $β_1$ in this model.
My issues here is that I can't seem to find what a constraint model is. I do not believe it was taught in my class and I can't find anything online. Thank you.
a.2) The sum of squares associated with the constrained model. $$ S(\beta_1) = \sum_{i=1}^n ( y_i - \beta_1 x_i ) ^2, $$ b) The first order condition is $$ \frac{\partial}{\partial \beta_1} S(\beta_1) \rvert_{ \beta_1 = \hat{\beta}_1 } -2 \sum_{i=1}^n ( y_i - \beta_1 x_i ) = 0 $$