Question

You are given the following data:

Details	X	Y
Arithmetic Mean	36	85
Standard Deviation	11	8

If the Correlation coefficient between X and Y is 0.66, then find 

(i) the two regression coefficients, 

(ii) the most likely value of Y when X = 10.

Answer 1

\(\bar{X}\) = 36, \(\bar{Y}\) = 85, σ_x = 11, σ_y = 8, r = 0.66

(i) The two regression coefficients are,

(ii) Regression equation of X on Y:

X - \(\bar{X}\) = b_xy(Y - \(\bar{Y}\))

X – 36 = 0.91(Y – 85)

X – 36 = 0.91Y – 77.35 

X = 0.91Y – 77.35 + 36 

X = 0.91Y – 41.35 

Regression line of Y on X:

Y - \(\bar{Y}\) = b_yx(X - \(\bar{X}\))

Y – 85 = 0.48(X – 36) 

Y = 0.48X – 17.28 + 85 

Y = 0.48X + 67.72 

The most likely value of Y when X = 10 is 

Y = 0.48(10) + 67.72 

= 72.52