Answer to Question #140751 in Statistics and Probability for Esther Gathenya

Question

The managing director of a company wants to find whether there is a relationship between units of a
product produces and the profits in a period of ten months
Month Jan Feb Mar Apr May June July Aug Sept Oct
Units produced (X)‘000 12 18 21 14 12 10 16 25 20 23
Profits (Y) ‘000 25 31 29 24 28 23 27 36 32 34
Calculate the regression equation of the form Y = a + bX and hence estimate the value of the profits when 12
units are produced. Clearly explain how this result compares to that given above as 28,000.

Answer 1

Sum of X = 171

Sum of Y = 289

Mean X = 17.1

Mean Y = 28.9

Sum of squares (SS_X) = 234.9

Sum of products (SP) = 181.1

Regression Equation = ŷ = bX + a

b = SP/SS_X = 181.1/234.9 = 0.77097

a = M_Y - bM_X = 28.9 - (0.77*17.1) = 15.71648

ŷ = 0.77097X + 15.71648

for 12 y(12)=0.77097*12+15.71648=24.96812

given value almost repeats the table value