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It is given that $\overline{\mathrm{X}}=10, \overline{\mathrm{Y}}=90, \sigma_{\mathrm{X}}=3, \sigma_{\mathrm{Y}}=12$ and
$\mathrm{I}_{\mathrm{XY}}=0.8$. The regression equation of $\mathrm{X}$ on $\mathrm{Y}$ is
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$\mathrm{I}_{\mathrm{XY}}=0.8$. The regression equation of $\mathrm{X}$ on $\mathrm{Y}$ is
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Verified Answer
The correct answer is:
$\quad X=-8+0.2 Y$
$\overline{\mathrm{X}}=10, \overline{\mathrm{Y}}=90, \sigma_{\mathrm{x}}=3, \sigma_{\mathrm{y}}=12, \mathrm{r}_{\mathrm{xy}}=0.8$
Regression equation $\mathrm{x}$ on $\mathrm{y}$ is
$\mathrm{x}-10=\mathrm{r} \cdot \frac{\sigma_{\mathrm{x}}}{\sigma_{\mathrm{y}}}(\mathrm{y}-90)$
$\Rightarrow x-10=0.8 \times \frac{3}{12}(y-90)$
$\Rightarrow x-10=\frac{2.4}{12}(y-90)$
$10=0.2(\mathrm{y}-90)$
$\Rightarrow x-10=0.2 y-18$
$\Rightarrow x=0.2 y-8$
Regression equation $\mathrm{x}$ on $\mathrm{y}$ is
$\mathrm{x}-10=\mathrm{r} \cdot \frac{\sigma_{\mathrm{x}}}{\sigma_{\mathrm{y}}}(\mathrm{y}-90)$
$\Rightarrow x-10=0.8 \times \frac{3}{12}(y-90)$
$\Rightarrow x-10=\frac{2.4}{12}(y-90)$
$10=0.2(\mathrm{y}-90)$
$\Rightarrow x-10=0.2 y-18$
$\Rightarrow x=0.2 y-8$
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