Var X VVar X Cov X, Y 3. Cov X. Y Cor X, Y Algebraic Properties of Expected valu

Question

Var X VVar X Cov X, Y 3. Cov X. Y Cor X, Y Algebraic Properties of Expected value, Variance, and Covariance. 5. E ax a EX EX Y EY 7. Var a a var x) Var X k Var X var IX +Y] 10. Cov aX, bY abcov X, Y 11. Covlx k.Y Cov X. Y 12. Cov X Y. Z Cov X. Z Cov Y. Z Linear Models 14. Fitted Model: Y-A+ a, Y-A 13. Theoretical Model Y-A+A x e 15. Fitted values: i,- +B x, A 16. Residuals: e-y,- Least Squares Parameter Estimates 17. Normal Egns: o and YAa, 0 18. 19. 20. Corly, Y] Corly, x) Cov X, Y Var X SST, SSE, SSR, and R-Squared 24, ssR 25. ssTr 26, SST SSE SSR SSE SST SST MSE and RSE SSE 29, MSE 30, s- VMSET

Explanation / Answer

Answer to question)

R is the correlation coeffictiont. As per the definition it measures the strength of the relation between the two variables x and y.

is the regression parameter with the formula shown below:

= r . Sy/Sx

From the fromula above we get

= Cov(x,y) / Var(x)

Thus from the bove tw equations, we get:

Cov(x,y) / Var(x) = r . sy/ sx

[Var(x) = sx^2]

Cov(x,y) / Sx*Sy = r

.

From formula # 4 abvoe, we get:

Cor(x,y) = Cov(x,y) / sx sy

.

thus plugging the same in equation we got above we get:

Cor(x,y) = r

Thus on squaring the equation on both sides we get:

Cor(x,y)62 = r^2

or

r^2 = Cor*(x,y)

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