FUNDAMENTALS OF BUSINESS MATHEMATICS AND STATISTICS I 6.41SELF EXAMINATION QUESTION
Problem 1. For a given set of data, the following result are available-
X 53,Y 28,b 1.5b 0.2= = XY= − YX= −
Find
(1) The two regression equations
(2) The coefficient of correlation
(3) The most likely value of Y when X = 60
(4) The most likely value of X when Y = 20
[Ans. : Reg. equation of X on Y : X = 58.6 - 0.2Y, equation of Y on X : Y = 107.5 1.5 - X, r = -0.548; 17.5; 54.6]
Problem 2. From the following data find:
(a) two regression equations
(b) the coefficient of correlation between the marks in economics and statistics
(c) the most likely marks in stastistics when marks in economics are 30
Marks in Economics 25 28 35 32 31 36 29 38 34 32
Marks in statistic 43 46 49 41 36 32 31 30 33 39
[Ans. : X = 0.23Y + 40.74, Y = 0.66X + 59.12; r = -0.389, marks in stats: 39.3]
Problem 3. Using the following data obtain two regression equations:
X 16 21 26 23 28 24 17 22 21
Y 33 38 50 39 52 47 35 43 41
[Ans. : X = -1.39+0.557Y, Y = 6.624+1.608X]
Problem 4. The following data about the sale and advertisement expenditure of a firm are given below:
Sales Expenditure
(crores) ( crores)
Mean 40 6
S.D. 10 1.5
Coefficient of correlation r = 0.9
(1) Find the likely sales for a proposed expenditure of 10 crores. (2) What should be the advertisement expenditure if the firm proposes a sales target of 60 crores.
[Ans.: 64 crores, 8.7 crores]
Problem 5. Find the mean of X and Y variables and the coefficient of correlation between them from the
following regression equations:
2Y - X = 50, 3Y - 2X = 10
[Ans. 130, 90. r = 0.86]
Problem 6. The equations of regression lines between two variables are expressed as 2X - 3Y = 0 and
4Y - 5X - 8 = 0. Find X and Y, the regression coefficients and the correlation coefficient between X and Y.
[Ans. (i) X = -3.42, Y= -2.28, bYX = 0.67, bXY = 0.8, r = 0.73]
Problem 7. Given the mean of X and Y are 35 and 67. Their standard deviations are 2.5 and 3.5 respectively
and the coefficient of correlation between them is 0.8.