In a laboratory experiment on correlation research study the equation of the two regression lines were found to be 2X– Y+1=0 and 3 X–2 Y+7=0. The two regression lines are 3 X+2 Y=26 and 6 X+3 Y=31.
#SIX SIGMA MATH FORMULAS SERIES#
The correlation coefficient between the series is r ( X, Y )=0.4įor 5 pairs of observations the following results are obtained ∑ X=15, ∑ Y=25, ∑ X2 =55, ∑ Y2 =135, ∑ XY=83 Find the equation of the lines of regression and estimate the value of X on the first line when Y=12 and value of Y on the second line if X=8. respectively and the mean and SD of S is considered as Y -Bar =103 and σ y =4. Then the mean and SD for P is considered as X-Bar = 100 and σ x =8. Let us consider X for price P and Y for stock S. With these data obtain the regression lines of P on S and S on P. The correlation coefficient between the two series is 0.4. The mean and standard deviation of P are 100 and 8 and of S are 103 and 4 respectively. There are two series of index numbers P for price index and S for stock of the commodity. When advertisement expenditure is 10 crores i.e., Y=10 then sales X=6(10)+4=64 which implies sales is 64. Estimate the likely sales for a proposed advertisement expenditure of Rs. The following table shows the sales and advertisement expenditure of a formĬoefficient of correlation r= 0.9. Therefore treating equation (1) has regression equation of Y on X and equation (2) has regression equation of X on Y . Let us assume equation (2) be the regression equation of Y on Xīut this is not possible because both the regression coefficient are greater than
Let us assume equation (1) be the regression equation of X on Y Therefore our assumption on given equations are correct. It may be noted that in the above problem one of the regression coefficient is greater than 1 and the other is less than 1. Let us assume equation (1) be the regression equation of Y on X The regression equation of Y on X is Y= 0.942 X+6.08 Estimation of Y when X= 55įind the means of X and Y variables and the coefficient of correlation between them from the following two regression equations: Obtain regression equation of Y on X and estimate Y when X=55 from the following The regression equation of Y on X is Y= 0.929 X + 7.284Ĭalculate the two regression equations of X on Y and Y on X from the data given below, taking deviations from a actual means of X and Y.Įstimate the likely demand when the price is Rs.20. Calculate the regression coefficient and obtain the lines of regression for the following data
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