Error vs residual in simple linear regression

Question

In my textbook the following definition were presented

However, it was presented previously that

Thus if we were to minimise the sum of squared residuals, shouldn't we be minimising $Q=\sum_{i=1}^n(y_i-\hat{y})^2=\sum_{i=1}^n(y_i-\hat{\beta_0}-\hat{\beta_1}x_i)^2$?

Answer 1

You may understand in this way that $\beta_0$ and $\beta_1$, they denote a solution of $Q$, while $\hat{\beta}_0$ and $\hat{\beta}_1$, they are an optimal solution for the minimization problem $Q$.