Question

Find the equation of the line of best fit for the following data.

$\begin{array}{cc}X& Y\\ 2& 5\\ 5& 7\\ 6& 8\\ 8& 11\\ 10& 12\\ 12& 16\\ 14& 17\end{array}$

• A. y=1.07x +2.15
• B. y =1.07x + 3.35
• C. y=2.07x +2.15
• D. y =2.07x + 3.35

Answer 1

The correct option is A

y=1.07x +2.15

$\begin{array}{cccccc}x& y& x-\overline{x}& (x-\overline{x}{)}^2& (y-\overline{y})& (x-\overline{x})(y-\overline{y})\\ 2& 5& -6.14& 37.7& -5.86& 35.98\\ 5& 7& -3.14& 9.86& -3.86& 12.12\\ 6& 8& -2.14& 4.58& -2.86& 6.12\\ 8& 11& -0.14& 0.02& 0.14& -0.02\\ 10& 1& 1.86& 3.46& 1.14& 2.12\\ 12& 16& 3.86& 14.9& 5.14& 19.84\\ 14& 17& 5.86& 34.34& 6.14& 35.98\\ \sum =57& \sum =76& & \sum =104.86& & \sum =112.14\end{array}$

$\overline{x}=\frac{\sum x}{n}=\frac{57}{7}=8.14$
$\overline{y}=\frac{\sum y}{n}=\frac{76}{7}=10.86$

$M=\frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{{\sum }_{i=1}^n(x_i-\overline{x}{)}^2}=\frac{112.14}{104.86}=1.07$
$B=\overline{y}-M\overline{x}=10.86-1.07\times 8.14=2.15$

$\therefore y=1.07x+2.15$