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Maths-

General

Easy

Question

If regression coefficient of y on x is $fraction numerator 8 over denominator 5 end fraction$ and that of x on y is $fraction numerator 2 over denominator 5 end fraction$ and the acute angle between the two lines is $alpha$ , then the value of $tan invisible function application alpha$ is

9/25
$9 / 2 \sqrt{5}$
3/25
9/50

The correct answer is: 9/50

Here $b subscript y x end subscript equals fraction numerator 8 over denominator 5 end fraction$ and $b subscript x y end subscript equals fraction numerator 2 over denominator 5 end fraction$
Hence $m subscript 1 end subscript equals fraction numerator 8 over denominator 5 end fraction$ and $m subscript 2 end subscript equals fraction numerator 1 over denominator b subscript x y end subscript end fraction equals fraction numerator 5 over denominator 2 end fraction$
Þ $tan invisible function application theta equals plus-or-minus open parentheses fraction numerator m subscript 1 end subscript minus m subscript 2 end subscript over denominator 1 plus m subscript 1 end subscript m subscript 2 end subscript end fraction close parentheses equals plus-or-minus fraction numerator fraction numerator 8 over denominator 5 end fraction minus fraction numerator 5 over denominator 2 end fraction over denominator 1 plus fraction numerator 8 over denominator 5 end fraction cross times fraction numerator 5 over denominator 2 end fraction end fraction equals fraction numerator 9 over denominator 50 end fraction$ .

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