X | Y | ||
3 | 23.58 | 3.233 | 16 |
4 | 23.29 | 2.274 | 9 |
5 | 23.33 | 2.396 | 4 |
6 | 24.05 | 5.144 | 1 |
7 | 20.68 | 1.214 | 0 |
8 | 21.22 | 0.316 | 1 |
9 | 20.65 | 1.281 | 4 |
10 | 19.88 | 3.618 | 9 |
11 | 19.36 | 5.866 | 16 |
= 63 | = 196.04 | 25.342 | 60 |
=21.782 , = 7
The regression line is given by,
y = a + b x,
where, , and
where, r is the correlation coefficient. and Sy and Sx are the standard deviation of y and x respectively.
= 1.678
= 2.582
cov(x,y) = -1.14
r = -0.263
Therefore, the slope is given by, = (-0.263)*(1.678/2.582) = -0.2
and the intercept is given by, = 21.782 - (-0.2)*7 = 23.2
therefore, the regression equation is given by,
y = 23.2 -0.2x
y+0.2 x = 23.2 (ans)
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