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

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

    A.

    y=4x+0

    B.

    y=3x+2

    C.

    y=6x+2

    D.

    y=0.33+2

    Correct option is B

    Explanation-

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

    m = slope=NxyxyNx2(x)2\text{m = slope} = \frac{N \sum xy - \sum x \sum y}{N \sum x^2 - (\sum x)^2}

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

    Where N is the number of data points.

    ​Step 1: Calculate necessary sums:

    x=56y=184x2=560xy=1792N=8\begin{aligned}\sum x &= 56 \\\sum y &= 184 \\\sum x^2 &= 560 \\\sum xy &= 1792 \\N &= 8\end{aligned}

    ​Step 2: Calculate slope (m):

    m=(8×1792)(56×184)(8×560)(562)m=143361030444803136m=40321344=3.0\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):

     c=184(3.0×56)8c=1841688=168=2.0\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)

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