Find regression line equations if means \(\bar x\) = 20 and \(\bar y = 10\), \({\sigma _x} = 10\),\({\sigma _y} = 5\), r = 0.5.

Question

Question

Answer 1

CONCEPT:

\({b_{yx}} = r.\frac{{{\sigma _y}}}{{{\sigma _x}}}\)

Where \({\sigma _x}\) = standard deviation of x; \({\sigma _y}\) = standard deviation of y

Regression Line y on x is given as \(x - \bar x = {b_{xy}}\left( {y - \bar y} \right)\)

CALCULATION:

\({b_{yx}} = r.\frac{{{\sigma _y}}}{{{\sigma _x}}} = 0.5 \times \frac{5}{{10}} = 0.25\)

Regression Line y on x is given as \(x - \bar x = {b_{xy}}\left( {y - \bar y} \right)\)

y – 10 = 0.25(x - 20)

y – 10 = 0.25x - 5

y = 0.25x – 5 + 10

y = 0.25x + 5