Consider the simple linear regression model
$y_i = \beta_0 + x_i\beta_1 + e_i$, $i = 1, \dots, n$,
where the $x$ variable has been centered and scaled so that $\sum x_i = 0$, $\sum x_i^2 = 1$.
(A) Write the model matrix, X
(B) Write the expression for $X^TX$, and solve the normal equations.
