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Answer the following on regression and correlation.
If x̅ = 18, y̅ = 100, σ_x = 14, σ_y = 20 and correlation coefficient r_(xy) = 0.8, find the…
If $\bar{x} = 18$, $\bar{y} = 100$, $\sigma_x = 14$, $\sigma_y = 20$ and correlation coefficient $r_{xy} = 0.8$, find the regression equation of $y$ on $x$.
Answer
Answer
Line of y on x: y = (8/7)x + 556/7
$b_{yx} = r\frac{\sigma_y}{\sigma_x} = 0.8\times\frac{20}{14} = \frac{8}{7}$
Regression line of $y$ on $x$: $y-\bar y = b_{yx}(x-\bar x)$, so $y-100 = \frac87(x-18)$
$7y-700 = 8x-144$
Hence the regression equation of $y$ on $x$ is $y = \frac{8}{7}x+\frac{556}{7}$, that is, $8x-7y+556=0$.