88 165 266 EXY = 655 8 11 64 11 15 121 14 19 196 = 45 y = 67 2 = 455 Regression equation of Y on X Y = a + bx To find the values of a and b, the following two equations are to be solved = na + bex ... (0) = X + 2 By putting the values we get 67 = 5a + 45b . (ii) 655 = 45a + 455b ... (iv) Multiplying equation (ii) by 9 and putting it as no. (v) we get, 603 = 45a + 405b ... (V) By deducting equation (V) from equation (iv): we get 52 - 50b 52 b = 1.04 50 By putting the value of b in equation (iii), we get 67 = 50 + 45 x 1.04 or 67 5a + 46.80 = or 67-46.80 5a or 5a 20.20 20.20 or a 5 or a = 4.04 Now by putting the values of a and b the required regression equation of Y on X, is Y = a + bx or. Y = 4.04 +1.04X v2 When X = 10 lakhs than Y = 4.04 + 1.04 (10) or, Y = 4.04 + 10.40 or 14,44 thousand CTV sets. Similarly for town having population of 20 lakhs, by putting the value of X = 20 lakhs in regression equation Y = 4.04 + 1.04 (20) = 4.04 + 20.80 = 24.84 thousands CTV sets. . Hence expected demand for CTV for two towns will be 14.44 thousand and 24.84 thousand CTV sets. Illustration 4. An investigation into the use of scooters in 5 towns has resulted in the following data: Population in town Population in town in lakhs) (X) 4 6 7 10 13 No. of scooters (Y) 4,400 6,600 5,700 8.000 10,300 Fit a linear regression of Yon X and estimate the number of scooters to be found in a town with a population of 16 lakhs