Find the equation y = a0 + a1 x of the least squares line that best fi | Mathematics II 2080

Mathematics II20805 marksNumerical: least squares line fitLeast squares problems

Find the equation $y = a_0 + a_1 x$ of the least squares line that best fits the data points (2,1), (5,2), (7,3), (8,3). [5]

Points: $(2,1), (5,2), (7,3), (8,3)$ , with $n = 4$ . $\sum y = na0 + a1\sum x$ $\sum xy = a0\sum x + a1\sum x^2$ $x$ $y$ $x^2$ $xy$ -------------- 2 1 4 2 5 2 25 10 7 3 49 21 8 3 64 24 $\sum x=22$ $\sum y=9$ $\sum x^2=142$ $\sum xy=57$ $9 = 4a0 + 22a1 \quad (1)$ $$57 = 22a0 + 142a1 \quad (2)...

Points: $(2,1), (5,2), (7,3), (8,3)$, with $n = 4$. $$\sum y = na0 + a1\sum x$$ $$\sum xy = a0\sum x + a1\sum x^2$$ $x$ $y$ $x^2$ $xy$ -------------- 2 1 4 2 5 2 25 10 7 3 49 21 8 3 64 24 $\sum x=22$ $\sum y=9$ $\sum x^2=142$ $\sum xy=57$ $$9 = 4a0 + 22a1 \quad (1)$$ $$57 = 22a0 + 142a1 \quad (2)...

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Find the equation y = a0 + a1 x of the least squares line that best fits the data points (2,1), (5,2), (7,3), (8,3).