FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.33Regression Equation of Y on X
Y
XY Y r (X X)− = σσ −Y - 30 = 0.8^45 (X - 20)
Y - 30 = 0.64 (X - 20)
Y - 30 = 0.64X - 12.8
Y = 0.64X +17.2
(iii) Estimate Y when X = 30
Put X = 30 in regression equation of Y on X.
Y = 0.64(30) + 17.2
Y = 17.2 + 19.2
Y = 36.4
Example22 :
The line of regression of marks in statistics (X) on marks in accountancy (Y) for a class of 50 students is
3Y - 5X + 180 = 0. Average marks in accountancy is 44 and variance of marks in statistics is 169 th of variance
of marks in accountancy. Find:
(i) Average marks in statistics
(ii) Coefficient of correlation between X and Y
Solution:
(i) Regression equation X on Y is
3Y - 5X +180 = 0
5x = 3Y + 180
X =^35 Y +^1805 = 0.6Y + 36
bXY =^35 = 0.6
given Y = 44, X can be obtained by putting Y = 44 in Regression Equation of X on Y
X = 0.6Y + 36
X = 0.6(44) + 36
X = 26.4 + 36
X = 62.4
X = 62.4 marks
Average marks in statistics are 62.4