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  • Why is a regression coefficient covariance variance - Cross . . .
    Why $$\frac{cov(x,y)}{var(x)}$$ gives a regression coefficient for dependent variable y and independent variable x? A linear regression coefficient tells us: If predictor variable $x$ increases by 1, what is the expected increase in outcome variable $y$ ?
  • Chapter 4 Variances and covariances - Yale University
    var(X+C) = var(X) for every constant C, because (X+C) E(X+C) = X EX, the C’s cancelling It is a desirable property that the spread should not be a ected by a change in location However, it is also desirable that multiplication by a constant should change the spread: var(CX) = C2var(X) and sd(CX) = jCjsd(X), because (CX E(CX))2 = C2(X EX)2
  • STAT 234 Lecture 10B Expected Values, Covariance,and . . .
    The covariance of X and Y, denoted as Cov(X, ) or σ XY, is defined as Cov(X,Y) = σ XY = E[(X −µ X)(Y −µ Y)], in which µ X = E(X), Y = E(Y) • Covariance is a generalization of variance: Var(X) = Cov(X,X) = E[(X −µ X)2] • Covariance can be positive or negative: • Cov( X,Y) >0 means positive association between , Y
  • Random Variability: Covariance and Correlation
    Var[X+Y] = Var[X] + Var[Y]+ 2 (E[XY] - E[X] E[Y]) This means that variances add when the random variables are independent, but not necessarily in other cases The covariance of two random variables is Cov[X,Y] = E[ (X-E[X]) (Y-E[Y]) ] = E[XY] - E[X] E[Y] We can restate the previous equation as Var[X+Y] = Var[X] + Var[Y] + 2 Cov[X,Y]
  • 5. 4. 1 Covariance and Properties - University of Washington
    1 If X?Y, then Cov(X;Y) = 0 (but not necessarily vice versa, because the covariance could be zero but Xand Y could not be independent) 2 Cov(X;X) = Var(X) (Just plug in Y = X) 3 Cov(X;Y) = Cov(Y;X) (Multiplication is commutative) 4 Cov(aX;Y) = aCov(X;Y) for scalar a 5 Cov(X+ c;Y) = Cov(X;Y) for scalar c
  • Expected Value, Variance and Covariance (Sections 3. 1-3. 3)1
    Variance of a random variable X Let E(X) = (The Greek letter \mu") Var(X) = E (X )2 The average (squared) di erence from the average It’s a measure of how spread out the distribution is Another measure of spread is the standard deviation, the square root of the variance 22 31
  • Covariance and correlation - University of California, Los . . .
    Let random variables X, Y with means X; Y respectively The covariance, denoted with cov(X;Y), is a measure of the association between Xand Y De nition: cov(X;Y) = E(X X)(Y Y) This can be simpli ed as follows: cov(X;Y) = E(X X)(Y Y) = E(XY) Y E(X) XE(Y) + X Y Therefore, cov(X;Y) = E(XY) (EX)(EY)





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