How do you find the slope of the regression line for the following set of data?

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How do you find the slope of the regression line for the following set of data?

X values –3 0 3 5 3
Y values 7 4 –2 2 –3

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Answer 1 · 2017-10-05T19:33:43

The slope is $- \frac{97}{98} \approx - 0.989796$ $-97/98approx -0.989796$ .

Explanation:

You can use the formula that the slope is $b_{1} = \frac{S S_{x y}}{S S_{x x}}$ $b_{1}=(SS_{xy})/(SS_{x x})$ , where $S S_{x x} = n \sum i = 1 {(x_{i} - ¯ x)}_{i}^{2} = n \sum i = 1 x_{i}^{2} - \frac{{(\sum_{i = 1}^{n} x_{i})}_{i}^{2}}{n}$ $SS_{x x}=sum_{i=1}^{n}(x_{i}-bar{x})^{2}=sum_{i=1}^{n}x_{i}^{2}-((sum_{i=1}^{n}x_{i})^{2})/n$ and $S S_{x y} = n \sum i = 1 (x_{i} - ¯ x) \cdot (y_{i} - ¯ y)$ $SS_{x y}=sum_{i=1}^{n}(x_{i}-bar{x})*(y_{i}-\bar{y})$

$= n \sum i = 1 x_{i} y_{i} - \frac{(\sum_{i = 1}^{n} x_{i}) \cdot (\sum_{i = 1}^{n} y_{i})}{n}$ $=sum_{i=1}^{n}x_{i}y_{i}-((sum_{i=1}^{n}x_{i})*(sum_{i=1}^{n}y_{i}))/n$

In the given situation $n = 5$ $n=5$ and we have

$n \sum i = 1 x_{i} = - 3 + 0 + 3 + 5 + 3 = 8$ $sum_{i=1}^{n}x_{i}=-3+0+3+5+3=8$ , $n \sum i = 1 y_{i} = 7 + 4 - 2 + 2 - 3 = 8$ $sum_{i=1}^{n}y_{i}=7+4-2+2-3=8$ , $n \sum i = 1 x_{i}^{2} = 9 + 0 + 9 + 25 + 9 = 52$ $sum_{i=1}^{n}x_{i}^{2}=9+0+9+25+9=52$ , $n \sum i = 1 y_{i}^{2} = 49 + 16 + 4 + 4 + 9 = 82$ $sum_{i=1}^{n}y_{i}^{2}=49+16+4+4+9=82$ , and $n \sum i = 1 x_{i} y_{i} = - 21 + 0 - 6 + 10 - 9 = - 26$ $sum_{i=1}^{n}x_{i}y_{i}=-21+0-6+10-9=-26$ .

Therefore, $S S_{x x} = 52 - \frac{8^{2}}{5} = \frac{260 - 64}{5} = \frac{196}{5} = 39.2$ $SS_{x x}=52-(8^2)/5=(260-64)/5=196/5=39.2$ and $S S_{x y} = - 26 - \frac{8 \cdot 8}{5} = \frac{- 130 - 64}{5} = - \frac{194}{5} = - 38.8$ $SS_{x y}=-26-(8*8)/5=(-130-64)/5=-194/5=-38.8$ .

This leads to a slope of $b_{1} = \frac{- 38.8}{39.2} = - \frac{97}{98} \approx - 0.989796$ $b_{1}=(-38.8)/39.2=-97/98approx -0.989796$ .

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How do you find the slope of the regression line for the following set of data?

X values –3 0 3 5 3
Y values 7 4 –2 2 –3

1 Answer

Explanation:

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Science

Math

Humanities

... and beyond

How do you find the slope of the regression line for the following set of data?

X values –3 0 3 5 3 Y values 7 4 –2 2 –3

1 Answer

Explanation:

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Impact of this question

X values –3 0 3 5 3
Y values 7 4 –2 2 –3