Expert: Ahmed Salami - 9/20/2010

Question
compute the two regression equations on the basis of the following data
mean of X and Y is 40 and 45 respectively, standard devation of X and Y is 10 and 9 respectively.Given that the coefficient of correlation between X and Y is 0.50.Also estimate the value of Y for X = 48?

Thank you

With Regards
Rehana

Answer
Hi Rehana,
The line of best fit relating X and Y has the equation
Y = a + bX
where a = y' - bx'  (x' and y' being the average values of X and Y respectively)
and b can be written as
b = r . [s(Y)/s(X)]
where s(Y) and s(X) are the standard deviations of X and Y values respectively and r is the correlation coefficient.
Therefore,
b = 0.50 (9/10)
  = 0.45

a = 45 - 0.45(40)
  = 45 - 18
  = 27
And
Y = 27 + 0.45X
When X = 48
Y = 27 + 0.45(48)
  = 27 + 21.6
  = 48.6

Regards