An investor has found that company1 have an expected return on E(X) = 4% and variance for the return equal V(X) = 0.49. Company 2 has E(Y) = 6% and variance V(Y) = 0.64. The correlation between the companies return is ρ(X,Y) = 0.3. The investor wants to invest p (0
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An investor has found that company1 have an expected return on E(X) = 4% and variance for the return equal V(X) = 0.49. Company 2 has E(Y) = 6% and variance V(Y) = 0.64. The
The combined investment have a return: R = pX + (1-p)Y.
Let p=0.4 such that R= 0.4X +0.6Y. Find the Expectation and variance of R. how are these results in comparison with X and Y separatley?
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- I have some doubts regarding linear regression. if any 2 variables in X1, X2 AND Y have a positive correlation, then in the linear regression Y = b0 + b1X1 +b2X2 +e, will the sign of b1 and b2 both be positive? will the residuals that we get from linear regression will always be uncorrelated given X?In a typical multiple linear regression model where x1 and x2 are non-random regressors, the expected value of the response variable y given x1 and x2 is denoted by E(y | 2,, X2). Build a multiple linear regression model for E (y | *,, *2) such that the value of E(y | x1, X2) may change as the value of x2 changes but the change in the value of E(y | X1, X2) may differ in the value of x1 . How can such a potential difference be tested and estimated statistically?Two lines of regression are given by 5x+7y-22=0 and 6x+2y-22=0. If the variance of y is 15, find the standard deviation of x.
- If there is a positive correlation between X and Y, then the regression equation Y = bX + a will have _____.If other factors are held constant and the Pearson correlation value between X and Y is r = 0.80, then the regression equation will tend to produce more accurate predictions than would be obtained if the Pearson correlation value was r = 0.60. True or FalseIf the PDF of X is f(x)=2x/k2 for 0<x<k, for what value of k is the variance of X equal to 2?
- The slope of a regression line (y on x) is -0.24, we know that SDy=3.2 and SDx=4.0, then the correlation coefficient between the two variables is:A. 0.3B. -0.3C. 0.8D. -0.8If there is a positive correlation between X and Y then in the regression equation, Y = bX + a, ____.If other factors are held constant, if the Pearson correlation between X and Y is r = 0.50, then the regression equation will produce more accurate predictions than would be obtained if r = 0.70. True or false?
- There is a linear regression: Yi = B0+ B1(Xi^2)+ ei present, where Xi is squared. ei ∼ N(0,σ2). How would I derive LSE for B0 and B1 and their variance?Suppose that index model for Stocks A and B is estimated from excess returns with the following results : Ra 0.04 +0.6Rm+ea , Rb = - 0.04 + 1.3Rm + eb Risk on the market is 30% , R-squared of A is 30%R - squared of B is 40% , security A residual variance isAssume that variables xx and yy have a significant correlation, and that the line of best fit has been calculated as ˆy=1.4x+3.6y^=1.4x+3.6. One observation is (9,16.3)(9,16.3).What is the predicted value of yy for the value x=9x=9? What is the residual for the value x=9x=9? What is the best interpretation for the residual? The value 16.316.3 is below the average value for yy when x=9x=9 The value 99 is above the average value for yy when y=16.3y=16.3 The value 16.316.3 is above the average value for yy when x=9x=9. The value 16.316.3 is below the average value for xx when y=16.3