Mathematics II207910 marksNumerical: least squares line fitLeast squares problems
Find the equation y = a0 + a1 x of the least square line that best fits the data points (0, 1), (1, 1), (1, 1), (2, 2), (3, 2).
Find the equation $y = a_0 + a_1 x$ of the least square line that best fits the data points (0, 1), (1, 1), (1, 1), (2, 2), (3, 2).[10]
Data points to fit with $y = a0 + a1 x$: $x$ $y$ ---------- 0 1 1 1 1 1 2 2 3 2 Number of data points: $n = 5$ (the point $(1,1)$ appears twice; both are used). $x$ $y$ $x^2$ $xy$ ----------------------- 0 1 0 0 1 1 1 1 1 1 1 1 2 2 4 4 3 2 9 6 $$\sum x = 7,\quad \sum y = 7,\quad \sum x^2 = 15,\qu...