Question

Shreya was doing an experiment to find out the relationship between voltage (X) and current (Y). The values obtained by Shreya are tabulated below.

$\begin{array}{cc}Voltage\left(X\right)& Current\left(Y\right)\\ 2& 3.5\\ 3& 5.5\\ 4& 8\\ 5& 9.5\\ 6& 12\\ 7& 14.5\\ 8& 16\end{array}$

Find the line of best fit for this data.

• A. y = 2x
• B. y= 1.95x +0.65
• C. y = 2.05x -0.45
• D. y = 2.125x - 0.765

Answer 1

The correct option is D

y = 2.125x - 0.765

$\begin{array}{cccccc}x& y& x-\overline{x}& (x-\overline{x}{)}^2& (y-\overline{y})& (x-\overline{x})(y-\overline{y})\\ 2& 3.5& -3& 9& -6.36& 19.08\\ 3& 5.5& -2& 4& -4.36& 8.72\\ 4& 8& -1& 1& -1.86& 1.86\\ 5& 9.5& 0& 0& -0.36& 0\\ 6& 12& 1& 1& 2.14& 2.14\\ 7& 14.5& 2& 4& 4.64& 9.28\\ 8& 16& 3& 9& 6.14& 18.42\\ & & & \sum =28& & \sum =59.5\end{array}$

$\overline{x}=\frac{\sum x}{n}=\frac{35}{7}=5$
$\overline{y}=\frac{\sum y}{n}=\frac{69}{7}=9.86$

$M=\frac{{\sum }_{i=1}^n(x_i-\overline{x})(y_i-\overline{y})}{{\sum }_{i=1}^n(x_i-\overline{x}{)}^2}=\frac{59.5}{28}=2.125$
$B=\overline{y}-M\overline{x}=9.86-2.125\times 5=-0.765$

The equation of the line is y = 2.125x - 0.765