Expert Answer to "Provide an appropriate response. Find the equation of..."

uneskovogl5

Answered question

2021-11-29

Provide an appropriate response.
Find the equation of the regression line for the given data.

\begin{array}{cc} x & - 5 & - 3 & 4 & 1 & - 1 & - 2 & 0 & 2 & 3 & - 4 \\ y & 11 & 6 & - 6 & - 1 & 3 & 4 & 1 & - 4 & - 5 & 8 \end{array}

Answer & Explanation

Richard Cheatham

Beginner2021-11-30Added 16 answers

Step 1:
The regression line is given by,

Y = a + b X

b = \frac{N \sum X Y - (\sum X) (\sum Y)}{N \sum X^{2} - {(\sum X)}^{2}}

a = \frac{\sum Y - b \sum X}{N}

Step 2:

\sum X = (- 5 - 3 + 4 + 1 - 1 - 2 + 2 + 3 - 4) = - 5

\sum 4 = (11 + 6 - 6 - 1 + 3 + 4 + 1 - 4 - 5 + 8) = 17

\sum x^{2} = (5^{2} + 3^{2} + 4^{2} + 1^{2} + 1^{2} + 2^{2} + 2^{2} + 3^{2} + 4^{2}) = 85

\sum x 4 = (- 55 - 18 - 24 - 1 - 3 - 8 - 15 - 32) = - 156

Here

n = 10

b = \frac{10 x (- 156) - (- 5) \times (17)}{10 \times 85 - {(- 5)}^{2}}

= \frac{- 1475}{825}

b = - 1.788

a = \frac{\sum 4 - b \sum x}{N}

= \frac{17 + 1.788 x (- 5)}{10}

a = 0.806

\Rightarrow 4 = 0.806 - 1.788 x

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