= Solution
{c}
The <least-squares estimators> choose the intercept and slope to minimize the sum of squared <regression residuals>:
$$
\boxed{(\widehat\alpha,\widehat\beta)\in
\operatorname*{arg\,min}_{a,b\in\mathbb R}\sum_{i=1}^n(Y_i-a-bx_i)^2.}
$$
After observation, replace $Y_i$ by $y_i$ to obtain the numerical <estimates>. Their definition does not require a <normal distribution> for the errors. A unique slope requires some variation in the fixed predictors; under $\sum_i x_i=0$, this is $S_{xx}=\sum_i x_i^2>0$, assumed below. If all $x_i=0$, the slope is unidentifiable.
Back to article page
