Q4Advanced Engineering Mathematics

Using the method of least squares to fit a straight line equation of the form $y=a+bx$. We calculate the necessary sums from the observation table:

$\sum x=15,\sum y=30,\sum x^2=55,\sum xy=110,n=5$.

We then construct the two normal equations for a straight line: $\sum y=na+b\sum x⟹30=5a+15b$ $\sum xy=a\sum x+b\sum x^2⟹110=15a+55b$

Solving these simultaneous equations gives $a=0$ and $b=2$. Therefore, the best fit straight line is precisely $y=2x$.