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Answer the following on regression and correlation.
Find the regression coefficients b_(yx), b_(xy) and correlation coefficient ‘r’ for the following…
Find the regression coefficients $b_{yx}$, $b_{xy}$ and correlation coefficient ‘$r$’ for the following data:
$(2, 8), \quad (6, 8), \quad (4, 5), \quad (7, 6), \quad (5, 2)$
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
$n = 5$, $\sum x = 24$, $\sum y = 29$, so $\bar x = \frac{24}{5}$ and $\bar y = \frac{29}{5}$.
$b_{yx} = -\frac{8}{37} \approx -0.216$ and $b_{xy} = -\frac{4}{31} \approx -0.129$.
$r = -\sqrt{b_{yx}\,b_{xy}} = -\sqrt{\frac{32}{1147}} \approx -0.167$ (the sign of $r$ is that of the regression coefficients).
Hence $b_{yx} = -\frac{8}{37}$, $b_{xy} = -\frac{4}{31}$ and $r \approx -0.167$.