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If $\mathrm{X}$ is changed to $+\mathrm{hU}$ and $\mathrm{Y}$ to $\mathrm{b}+\mathrm{kV}$, then which one of the following is the correct relation between the regression coefficients $\mathrm{b}_{\mathrm{XY}}$ and $\mathrm{b}_{\mathrm{UV}}$ ?
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The correct answer is:
$\mathrm{k} \mathrm{b}_{\mathrm{XY}}=\mathrm{h} \mathrm{b}$
If $\mathrm{X}$ is changed to $\mathrm{a}+\mathrm{hU}$ and $\mathrm{Y}$ to $\mathrm{b}+\mathrm{k} \mathrm{V}$, then
$\mathbf{b}_{\mathrm{XY}}=\left|\frac{\mathrm{h}}{\mathrm{k}}\right| \mathrm{b}_{\mathrm{UV}}$
$\Rightarrow \mathrm{kb}_{\mathrm{XY}}=\mathrm{h} \cdot \mathrm{b}_{\mathrm{UV}}$
$\mathbf{b}_{\mathrm{XY}}=\left|\frac{\mathrm{h}}{\mathrm{k}}\right| \mathrm{b}_{\mathrm{UV}}$
$\Rightarrow \mathrm{kb}_{\mathrm{XY}}=\mathrm{h} \cdot \mathrm{b}_{\mathrm{UV}}$
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