Least squares

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

1. Warm-up

   The simplest least-squares problem fits a single constant $c$ to data $y_1, y_2, y_3$ by minimizing the sum of squared errors $\sum_{i=1}^{3} (y_i - c)^{2}$. For the data $y_1 = -5$, $y_2 = 6$, $y_3 = 5$, find the least-squares optimal $c$. Give your answer as a fraction (or integer if it reduces to one).

2. Warm-up

   The simplest least-squares problem fits a single constant $c$ to data $y_1, y_2, y_3$ by minimizing the sum of squared errors $\sum_{i=1}^{3} (y_i - c)^{2}$. For the data $y_1 = -8$, $y_2 = -1$, $y_3 = 17$, find the least-squares optimal $c$. Give your answer as a fraction (or integer if it reduces to one).

3. Warm-up

   The simplest least-squares problem fits a single constant $c$ to data $y_1, y_2, y_3$ by minimizing the sum of squared errors $\sum_{i=1}^{3} (y_i - c)^{2}$. For the data $y_1 = 7$, $y_2 = 3$, $y_3 = 8$, find the least-squares optimal $c$. Give your answer as a fraction (or integer if it reduces to one).

Problems shown under their original terms: Generated (template, solver-computed).