3. Suppose that (X, Y) is a Bivariate normal vector with mean vector (x, My) and Var(X) = ², Var(Y) =o and correlation coefficient 0 < p < 1 and p = 0. Then A. Var(Y|X) < Var (Y) B. Var (YX) > Var(Y) C. Var (Y|X) = Var(Y) D. None of the above is necessarily true.
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- Find the new data point (x,y) in which x=2 from the data points (1,3) and (4,12)Let the equations of the regression lines be expressed as 8X - 2Y = 0 and 3Y – 2X = 9 Then the correlation between X and Y is,Find the equation y = Bo + B1x of the least-squares line that best fits the given data points. (0,1), (1,1), (2,5), (3,5) The line is y =+ (Ox. (Type integers or decimals.)
- The equations of the regression line between two variables are expressed as 2x-3y=0 and 4y-5x-7=0 a) identify which of two can be called regression line of Y on X and X on Y b) find the correlation coefficient c) find mean value of X and mean value of Y2) Use Data Linearization technique to perform a fit in the form of y = (x^B)-¹ using the given data. x y 0.5 1.333 0.9 0.4115 0.333 1.5 0.231Suppose X and Y are two random variables with covariance Cov(X, Y) = 3 and Var(X) = 16. Find the correlation coefficient between X and Y.
- Find the least squares regression line for the points. (0, 5), (3, 3), (5, 1), (7, -4), (9, -5) 1.) y =Consider the points in the plane: (1,2) (2,3) (3,5) (4,4) (5,7) (7,8) (i) Compute the correlation coefficient. (ii) Compute the equation for the regression line.When the change in a variable 'x' directly causes the change in another variable y' that is an example of: O A. increasing O B. decreasing O C. causation O D. correlation
- Find the least-squares regression line ý = b + b₁ through the points (-2,0), (0,9), (5, 15), (8,20), (12,24). For what value of x is y = 0Two variables have the regression lines 3x + 2y = 26 and 6x + y = 31. Find the mean values, the correlation coefficient between x and y and the ratio of variances of the variables.a. Show that the regression R2 in the regression of Y on X is the squaredvalue of the sample correlation between X and Y. That is, show thatR2 = r2XY.b. Show that the R2 from the regression of Y on X is the same as the R2from the regression of X on Y. c. Show that ^β1 = rXY (sY/sX), where rXY is the sample correlationbetween X and Y, and sX and sY are the sample standard deviationsof X and Y.