Question

Construct two regression equations for the following data and estimate the value of x when y = 70 and y when x = 650.

Answer 1

The two regression equations are: 

Regression equation of x on y : (x – x̄) = b_xy (y – ȳ) 

Regression equation of y on x : (y – ȳ) = b_xy (x – x̄) 

Both variables having common differences, so use step deviation methods.

Here i_x common width in x = 100

i_y common width in v = 10 and n = 7;

Regression equation of x on y:

x – 400 = 6.05 (y-80) = 6.05y-605 × 80

x = 6.05y – 48.4+ 400

Regression equation of x on y : (x – x̄) = b_xy (y – ȳ)

x – 14 = 1(y – 8)

x = y – 8 + 14

∴ x = y + 6

and regression equation y on x is : (y – ȳ) = b_xy (x – x̄)

y – 8 = 0.8695 (x – 14)

y = 0.8695x – 12.173 + 8

∴ y = 0.8695x -4.173

Estimation of x when y = 20

∴ From the Regression equation of x on y:

x = 20 + 6 = 26

We know that the coeffiicent of correlation: