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It is given that the means of x and y are 5 and 10. If the line of regression of y on x is parallel to the line $20y = 9x + 40,$ estimate the value of y for $x = 30. $

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It is given that the means of x and y are 5 and 10. If the line of regression of y on x is parallel to the line $20y = 9x + 40,$ estimate the value of y for $x = 30. $

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written 8.0 years ago by |

Given that means of x and y are 5 and 10

$\therefore \overline x=5$ and $\overline y=10$

Given line is $20y = 9x + 40$

$\therefore y=\dfrac {9x+40}{20}=\dfrac {9x}{20}+\dfrac {40}{20}$

Slope of the above line $(m_1) = \dfrac 9{20}$

Slope of the regression of y on x $(m_2) = byx$

Since two lines are parallel, $m_1 = m_2 $

$$\therefore byx=\dfrac 9{20}$$

Regression equation of y on x is $y-\overline y=byx (x-\overline x)\\ \therefore y-10=\dfrac 9{20}(x-5)\\ 20 y = 200 = 9x – 45 \\ 20y = 9x -45 + 200 \\ 20y = 9x + 155 \\ When \space \space x = 30\\ 20y = 9 (30) + 155\\ Y = 21.25$

Estimated value of y for $x = 30$ is $21.25.$

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