Chapter Simple Linear Regression Lecture compiled by Dr

Chapter – Simple Linear Regression Lecture compiled by Dr. Parminder Kaur Assistant Professor Department of Commerce For B. Com(Prog) II Sem Sec A

SIMPLE LINEAR REGRESSION DEFINITION 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

• In this method the first line of equation is Y on X • Y = a + b. X • To 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-----------------1 • XY = a. X + b X 2 --------------2 • Solving equation 1 and 2 simultaneously for a and b, we will get • b(Regression Coefficient of Y on X) =

• In this method the second line of equation is X on Y • X = a + b. Y • To 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-----------------1 • XY = a. Y + b Y 2 ---------------2 • Solving equation 1 and 2 simultaneously for a and b, we will get • b (Regression Coefficient of X on Y )=

Example : Calculate the Regression Coefficients from the following information X = 50, , XY = 1000, 2 = 3000, Y 2 = 1800, n= 10 Solution : Regression Coefficient of X on Y is bxy (Regression Coefficient )= = =0. 497

byx (Regression Coefficient )= = =0. 309

• Regression Coefficients can be calculated by some more formulas like • byx = • 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 = -0. 3

Thankyou Lecture sourced from • Book “Business Mathematics and Statistics” by R. S. Bhardwaj • Book “Business Mathematics and Statistics” by Dr. J. K. Thukral