bus-stat-book1

That is to say for the given values of x we can find

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Unformatted text preview: ient of correlation. Symbolically ≥r 2 225 7. If r=0, the variables are uncorrelated , the lines of regression become perpendicular to each other. 8. If r= +1, the two lines of regression either coincide or parallel to each other m − m2 9. Angle between the two regression lines is θ = t an-1 1 1 + m1m2 where m1 and,m2 are the slopes of the regression lines X on Y and Y on X respectively. 10.The angle between the regression lines indicates the degree of dependence between the variables. Example 2: If 2 regression coefficients are b1= 4 9 and b2 = .What would be 5 20 the value of r? Solution: The correlation coefficient , r = ± b1b2 49 x 5 20 = = 36 6 = = 0.6 100 10 Example 3: 15 3 and b2 = , Find r Given b1 = 8 5 Solution: r = ± b1b2 = 15 3 x 85 9 =1.06 8 It is not possible since r, cannot be greater than one. So the given values are wrong = 226 9.6 Why there are two regression equations? The regression equation of Y o n X is σ Ye = Y + r y ( X − X ) σx (1) (or) Ye = Y + b1 ( X − X ) The regression equation of X on Y is σ X e = X + r x (Y − Y ) σy X e = X + b2 (Y − Y ) These two regression equations represent entirely two different lines. In other words, equation (1) is a function of X, which can be written as Ye = F(X) and equation (2) is a function of Y, which can be written as Xe = F(Y). The variables X and Y are not inter changeable. It is mainly due to the fact that in equation (1) Y is the dependent variable, X is the independent variable. That is to say for the given values of X we can find the estimates of Ye of Y only from equation (1). Similarly, the estimates Xe of X for the values of Y can be obtained only from equation (2). Example 4: Compute the two regression equations from the following data. X 1 2 34 5 Y 2 3 5 4 6 If x =2.5, what will be the value of y? Solution: X Y x2 y2 xy x = X − X y = Y −Y 1 2 -2 -2 4 4 4 2 3 -1 -1 1 1 -1 3 5 0 1 0 1 0 4 4 1 0 1 0 0 5 6 2 2 4 4 4 15 20 20 10 10 9 227 ∑ X 15 = =3 n 5 ∑ Y 20 Y= = =4 n 5...
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This note was uploaded on 01/18/2014 for the course BUS 100 taught by Professor Moshiri during the Winter '08 term at UC Riverside.

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