Find the equation of the regression line for the given data. Round values to the thousandth x−5−341−1−2023−4y116−6−1341−4−58 1) y―=1.885x−0.755 2) y―=−0.758x−1.885 3) y―=−1.885x+0.758 4) y―=0.758x+1.885

Step 1 Solution: Number of counts (n)=10 xyxyx2−511−5525−36−1894−6−24161−1−11−13−31−24−8401002−4−843−5−159−48−3216Sum:−517−16485 Step 2 The regression line is given approximately by y―=mx+b Where, m=n∑xy−∑x∑yn∑x2−(∑x)2 m=10(−164)−(−5)⋅(17)(10⋅85)−(−5)2 m=−1640−(−85)850−25 m=−1640+85850−25 m=−1555825 m=−1.885 b=∑y−m∑xn b=17−(−1.885⋅−5)10 b=17−(9.425)10 b=7.57510 b=0.758 Therefore, y―=mx+b Plug in all the values in the formula, we get y―=−1.885x+0.758

Step by step solution to "Find the equation of the regression line for..."

Pearl Carney

Answered question

2021-11-26

Find the equation of the regression line for the given data. Round values to the thousandth

\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}

\overset{―}{y} = 1.885 x - 0.755

\overset{―}{y} = - 0.758 x - 1.885

\overset{―}{y} = - 1.885 x + 0.758

\overset{―}{y} = 0.758 x + 1.885

Answer & Explanation

James Etheridge

Beginner2021-11-27Added 16 answers

Step 1
Solution:
Number of counts

(n) = 10

\begin{array}{cc} x & y & x y & x^{2} \\ - 5 & 11 & - 55 & 25 \\ - 3 & 6 & - 18 & 9 \\ 4 & - 6 & - 24 & 16 \\ 1 & - 1 & - 1 & 1 \\ - 1 & 3 & - 3 & 1 \\ - 2 & 4 & - 8 & 4 \\ 0 & 1 & 0 & 0 \\ 2 & - 4 & - 8 & 4 \\ 3 & - 5 & - 15 & 9 \\ - 4 & 8 & - 32 & 16 \\ S u m : & - 5 & 17 & - 164 & 85 \end{array}

Step 2
The regression line is given approximately by

\overset{―}{y} = m x + b

Where,

m = \frac{n \sum x y - \sum x \sum y}{n \sum x^{2} - {(\sum x)}^{2}}

m = \frac{10 (- 164) - (- 5) \cdot (17)}{(10 \cdot 85) - {(- 5)}^{2}}

m = \frac{- 1640 - (- 85)}{850 - 25}

m = \frac{- 1640 + 85}{850 - 25}

m = \frac{- 1555}{825}

m = - 1.885

b = \frac{\sum y - m \sum x}{n}

b = \frac{17 - (- 1.885 \cdot - 5)}{10}

b = \frac{17 - (9.425)}{10}

b = \frac{7.575}{10}

b = 0.758

Therefore,

\overset{―}{y} = m x + b

Plug in all the values in the formula, we get

\overset{―}{y} = - 1.885 x + 0.758

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