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Answer the following on regression and correlation.
Find the regression coefficient b_(yx) and b_(xy) and the two lines of regression for the following…
Find the regression coefficient $b_{yx}$ and $b_{xy}$ and the two lines of regression for the following data:
Also, compute the correlation coefficient.
| X | 2 | 6 | 4 | 7 | 5 |
| Y | 8 | 8 | 5 | 6 | 2 |
Answer
Answer
Mean of x: 24/5
Mean of y: 29/5
Regression coefficient of y on x: -8/37
Regression coefficient of x on y: -4/31
Correlation coefficient r: -0.167
Line of y on x: y = (-8/37)x + 253/37
Line of x on y: x = (-4/31)y + 172/31
$n = 5$, $\bar{x} = \frac{24}{5} = 4.8$, $\bar{y} = \frac{29}{5} = 5.8$.
$b_{yx} = -\frac{8}{37} \approx -0.216$, $b_{xy} = -\frac{4}{31} \approx -0.129$.
Line of $y$ on $x$: $y - 5.8 = -\frac{8}{37}(x - 4.8)$, i.e. $y = -\frac{8}{37}x + \frac{253}{37}$.
Line of $x$ on $y$: $x - 4.8 = -\frac{4}{31}(y - 5.8)$, i.e. $x = -\frac{4}{31}y + \frac{172}{31}$.
$r = -\sqrt{b_{yx}b_{xy}} = -\sqrt{\frac{32}{1147}} \approx -0.167$.
Hence $r \approx -0.167$.