Question

For the regression equations

y = 0.516x + 33.73

and

x = 0.512 y + 32.52

the means of x and y are nearly
1. 67.6 and 68.6
2. 68.6 and 68.6
3. 67.6 and 58.6
4. 68.6 and 58.6

Answer 1

Correct Answer - Option 1 : 67.6 and 68.6

The given regression equations are:

y = 0.516x + 33.73 ⇒ 0.516 x – y = -33.73

x = 0.512 y + 32.52 ⇒ x – 0.512 y = 32.52

By solving the above two equations, we get

x = 67.6, y = 68.6

Important Points:

The line of regression of y on x is

\(y - \bar y = r \cdot \left( {\frac{{{\sigma _y}}}{{{\sigma _x}}}} \right)\left( {x - \bar x} \right)\)

The line of regression of x on y is

\(x - \bar x = r \cdot \left( {\frac{{{\sigma _x}}}{{{\sigma _y}}}} \right)\left( {y - \bar y} \right)\)

\(r\left( {\frac{{{\sigma _y}}}{{{\sigma _x}}}} \right)\) is called the regression co-efficient of y on x and is denoted by b_yx

\(r\left( {\frac{{{\sigma _x}}}{{{\sigma _y}\;}}} \right)\) is called the regression co-efficient of x on y and is denoted by b_xy

If the line is in the form of y₁ = m₁ x₁ + c₁, then the regression co-efficient byx = m₁

If the line is in the form of x₂ = y₂ m₂ + c₃, then the regression co-efficient bxy = m₂

Correlation co-efficient \(\left( r \right) = \sqrt {{b_{yx}}{b_{xy}}}\)