( Y) of a random sample of 10 students from a large group of students of age 17 years:Įstimate weight of the student of a height 69 inches.Ĥ. The following data give the height in inches ( X) and the weight in lb. The heights ( in cm.) of a group of fathers and sons are given belowįind the lines of regression and estimate the height of son when the height of the father is 164 cm.ģ. Since the two regression coefficients are positive then the correlation coefficient is also positive and it is given byįind (a) The two regression equations, (b) The coefficient of correlation between marks in Economics and statistics, (c) The mostly likely marks in Statistics when the marks in Economics is 30.Ģ. (i) First convert the given equations Y on X and X on Y in standard form and find their regression coefficients respectively. Solving the two regression equations we get mean values of X and Yįor the given lines of regression 3 X–2 Y=5and X–4 Y=7. Also work out the values of the regression coefficient and correlation between the two variables X and Y. 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. 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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