The coefficient of correlation between two variables X and Y is 0.48. The covariance is 36. The variance of X is 16. The standard deviation of Y is:
18.75
σx=√16=4. From r=Cov(X,Y)/(σxσy), σy=36/(0.48×4)=18.75.
The correlation coefficient between two variables X and Y is 0.4. The correlation coefficient between 2X and (-Y) will be:
If a data set contains n paired values on two variables x(independent) and y(dependent), then their plot is called:
Suppose r xy is the correlation coefficient between two variables X and Y
where s.d.(X) = s.d.(Y). If θ is the angle between the two regression lines of Y on X and X on Y then:
For an experiment we have the following data set: n = 4, ∑x = a, ∑y = 10, ∑xy = 21, ∑x 2 = 30, ∑y 2 = 30. If the correlation coefficient is -0.8 then the value of a is:
The limit of multiple correlation coefficient R 1.23 are:
If the multiple correlation coefficient of X 1on X 2and X 3is zero, then:
If r 12 = +0.80, r 13 = -0.40 and r 23 = -0.56, then the square of multiple correlation coefficient (correct to four decimal places) \(R^2_1{.}{_2}{_3}\) is equal to:
For a trivariate distribution, if the correlation coefficients are r 12 = r 13 = r 23 = r, -1 < r < 1, then r 12.3 is:
If the regression line of Y on X is Y = 30 - 0.9X and the standard deviations are S x= 2 and S y= 9, then the value of the correlation coefficient r xy is :
The coefficients of the regression β X|y and β Y|x , are known, The coefficient of correlation equals:
If X ∼ N (0, 1) and Y = X2 then the correlation coefficient r (X, Y) is
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:
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