Question

The following table contains the heights and weights of a sample of 5 women from a room. Find the line of best fit.

$\begin{array}{cc}Height(X,cm)& Weight(Y,kg)\\ 150& 54\\ 160& 58\\ 170& 63\\ 175& 65\\ 180& 70\end{array}$

• A. $y=0.42x-36.24$
• B. $y=0.51x-23.17$
• C. $y=0.63x-15.5$
• D. $y=0.36x-41.65$

Answer 1

The correct option is B

$y=0.51x-23.17$

$\begin{array}{cccccc}x& y& x-\overline{x}& (x-\overline{x}{)}^2& (y-\overline{y})& (x-\overline{x})(y-\overline{y})\\ 150& 54& -17& 289& -8& 136\\ 160& 58& -7& 49& -4& 28\\ 170& 63& 3& 9& 1& 3\\ 175& 65& 8& 64& 3& 24\\ 180& 70& 13& 169& 8& 104\\ & & & \sum =580& & \sum =295\end{array}$

$\overline{x}=\frac{\sum x}{n}=\frac{835}{5}=167$
$\overline{y}=\frac{\sum y}{n}=\frac{310}{5}=62$

$M=\frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{{\sum }_{i=1}^n(x_i-\overline{x}{)}^2}=\frac{295}{580}=0.51$
$B=\overline{y}-M\overline{x}=62-0.51\times 167=-23.17$

$\text{The line of best fit is}y=0.51x-23.17$