Regression equation of Yon X Y = a + bx To find the values of a and b, the following two equations are to be solved = na +bEX ...) EXY = AEX + BEX (6) By putting the values we get 67 = 5a + 45b 655 = 45a + 455b ... (iv) Multiplying equation (in) 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 b= 52 - = 1.04 or or By putting the value of b in equation (i), we get 67 = 5a +45* 1.04 67 = 5a + 46.80 67-46.80 = 5a 5a 20.20 20.20 or 5 or a = 4.04 Now by putting the values of a and b the required regression equation of Yon X, is Y = a + bx or. Y = 4.04+1.04X or x24 a or. When X = 10 lakhs than Y = 4.04 + 1.04 (10) 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 wil 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 Y on X and estimate the number of scooters to be found in a town with a population of 16 lakhs