The two-regression equation of variable \(\rm{x}\) and \(\rm{y}\) are \(\rm{y = 0.8x + 9.8}\) and \(\rm{x = 10.2 + 0.6y}\) The coefficient of correlation between \(\rm{x}\) and \(\rm{y}\) is
Given, \({\rm{y}} = 0.8{\rm{x}} + 9.8\)
∴ Regression coefficient of \(\rm{y}\) on \(\rm{x}\) is \({{\rm{b}}_{{\rm{YX}}}} = 0.8\)
\({\rm{x}} = 0.6{\rm{y}} + 10.2\)
∴ Regression coefficient of \(\rm{x}\) on \(\rm{y}\) is \({{\rm{b}}_{{\rm{XY}}}} = 0.6\)
∴ correlation coefficient \({\rm{\gamma }} = \sqrt {{{\rm{b}}_{{\rm{YX}}}}.{{\rm{b}}_{{\rm{XY}}}}} \)
\(\therefore {\rm{\gamma }} = \sqrt {0.8 \times 0.6} = 0.69\)
Important Questions from Correlation Analysis
Given below are two statements: One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): If the securities with less than perfect negative correlation between their price movements are combined, portfolio risk can be reduced significantly.
Reason (R): The term with negative correlation has the effect of reducing the computed value of total portfolio risk, given other terms that are positive.
In the light of the above statements, choose the most appropriate answer from the options given below:
X, Y and Z are three uncorrelated variables having variances \(\sigma_x^2, \sigma_y^2 \:and\:\sigma_z^2\) respectively, then the correlation between X + Y and Y + Z is:
If X ∼ N (0, 1) and Y = X2 then the correlation coefficient r (X, Y) is
Calculate the correlation coefficient between the following values :
x: 3, 5, 1, 7, 5
y: 4, 3, 0, 8, 2
Consider two exponentially distributed random variables X and Y, both having a mean of 0.50. Let Z = X + Y and r be the correlation coefficient between X and Y. If the variance of Z equals 0, then the value of r is _______ (round off to 2 decimal places).
