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If the tangent of the angle made by the line of regression of y on x is 0.6 and $\sigma_{y} = 2\sigma_{x}$. Find the correlation coefficient between x and y.

Mumbai University > Mechanical Engineering > Sem 4 > Applied Mathematics IV

Marks: 5M

Year: May 2015

1 Answer
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Let $L_{yx}\ $be the line of regression of y on x.

Let the angle made by $L_{yz}\ $with X-axis be $\mathrm{\theta}$

$\mathrm{\therefore }$ Tangent of the angle made by $L_{yz}$ with X- axis = tan $\mathrm{\theta}$ = 0.6

But , slope of any line with X-axis = tan $\mathrm{\theta}$

However, slope of $L_{yx}=\ b_{yx}$

$\mathrm{\therefore }$ $b_{yx}$ = tan $\mathrm{\theta}$ = 0.6

But $b_{yx}=r\ \frac{{\sigma }_y}{{\sigma }_x}$

$$\mathrm{\therefore } 0.6 = r\ \frac{2{\sigma }_x}{{\sigma }_x} --------(given)$$ $$\mathrm{\therefore } 0.6 = 2 r$$ $$r=0.3$$

$\boldsymbol{\mathrm{\therefore }}$ The correlation coefficient between x and y(r) = 0.3

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