Lecture compiled by Dr Parminder Kaur Assistant Professor Department of Commerce For BCom Prog II Sem Sec A SIMPLE LINEAR REGRESSION DEFINITION OF REGRESSION ID: 1020722
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1. Chapter – Simple Linear Regression Lecture compiled by Dr. Parminder Kaur Assistant Professor Department of Commerce For B.Com(Prog) II Sem Sec A
2. SIMPLE LINEAR REGRESSIONDEFINITION OF REGRESSION “Regression is the measure of the average relationship between two or more variables in terms of the original unit of the data.” Lines of Regression ( Least Squares Approach) By lines of regression we can estimate the values of a dependent variable from the known values of an independent variable
3. In this method the first line of equation is Y on XY = a + bXTo solve this we have to calculate values of a and b first, and to calculate these values we will use two equations.Y = na + b X---------------------------------1XY = aX + b X2 ---------------------------2Solving equation 1 and 2 simultaneously for a and b, we will getb(Regression Coefficient of Y on X) =
4. In this method the second line of equation is X on YX = a + bYTo solve this we have to calculate values of a and b first, and to calculate these values we will use two equations.X= na + b Y---------------------------------1XY = aY + b Y2 -----------------------------2Solving equation 1 and 2 simultaneously for a and b, we will getb (Regression Coefficient of X on Y )=
5. Example : Calculate the Regression Coefficients from the following information X = 50, , XY = 1000, 2 = 3000, Y2 = 1800, n= 10 Solution : Regression Coefficient of X on Y isbxy (Regression Coefficient )= = =0.497
6. byx (Regression Coefficient )= = =0.309
7. Regression Coefficients can be calculated by some more formulas likebyx = bxy = Example : The covariance between X and Y is -7.5 and the standard deviation of X is 5. Find the regression coefficient of Y on X.Solution : byx = byx = byx = -0.3
8. ThankyouLecture sourced fromBook “Business Mathematics and Statistics” by R. S. BhardwajBook “Business Mathematics and Statistics” by Dr. J. K. Thukral