​Find the linear regression equation for the following data pairs (x,y) given in the above table​

Correct option is B

Explanation-

Formula for Linear Regression (y = mx + c):
Where:

​$$\text{m = slope} = \frac{N \sum xy - \sum x \sum y}{N \sum x^2 - (\sum x)^2}$$

$$\text{c = intercept} = \frac{\sum y - m \sum x}{N}$$

Where N is the number of data points.

​Step 1: Calculate necessary sums:

$$\begin{aligned}\sum x &= 56 \\\sum y &= 184 \\\sum x^2 &= 560 \\\sum xy &= 1792 \\N &= 8\end{aligned}$$

​Step 2: Calculate slope (m):

$$\begin{aligned}m &= \frac{(8 \times 1792) - (56 \times 184)}{(8 \times 560) - (56^2)} \\m &= \frac{14336 - 10304}{4480 - 3136} \\m &= \frac{4032}{1344} = 3.0\end{aligned}$$

​Step 3: Calculate intercept (c):

 $$\begin{aligned}c &= \frac{184 - (3.0 \times 56)}{8} \\c &= \frac{184 - 168}{8} = \frac{16}{8} = 2.0\end{aligned}$$

​Final Linear Regression Equation: =3+2 (Option b)