Q1 The following results were obtained with respect to two variables x and y : ∑x = 30, ∑y = 42, ∑xy = 199, ∑x² = 184, ∑x² = 318, n = 6, Find the following :
(i) the regression coefficients.
(ii) correlation coefficient between x and y.
(iii) the regression equation of y on x.
(iv) the likely value of y when x = 10.

Solution

Q2 (i) Out of the two regression lines, find the line of regression of Y on X : 3x + 12y = 8, 9x + 3y = 46
(ii) Two regression lines are represented by 2x + 3y—10 = 0 and 4x + y —5 =0. Find the line of regression of y on x.
(iii) Two regression lines are represented by 4x + 10y = 9 and 6x + 3y = 4. Find the regression line of y on x.

Solution

Q3 Find the coefficient of correlation from the following regression lines
(i) x - 2y + 3 = 0 , 4x - 5y + 1 = 0
(ii) 3x + 4y - 7 = 0, 4x + y - 5 = 0.

Solution

Q4 Following table shows the sales and advertisement expenditure of a firm

	Sales (₹ in crores)	Advertisement Expenditure ( ₹ in crores)
Mean Standard deviation	40 10	6 1.5

Correlation of coefficient = r = 0.9
Estimate the likely sales for a proposed expenditure of ₹10 crores

Solution

Q5 The following table shows the mean and standard deviation of the marks of Mathematics and Physics scored by the students of a school:

	Mathematics	Physics
Mean Standard deviation	84 7	81 4

The correlation coefficient between the given marks is 0.86. Estimate the likely marks in Physics if the marks in Mathematics are 92.

Solution

Q6 There are two series of index numbers : P for price index and S for stock of a commodity. The mean and standard deviation of P are 100 and 8 and of S are 103 and 4 respectively. The correlation coefficient between the two series is 0.4. With these data, obtain the regression lines of P on S and S on P.

Solution

Q7 From the equations of the two regression lines, 4x + 3y +7 =0 and 3x + 4y + 8 =0, find:
(i) the means of x and y.
(ii) the regression coefficients.
(iii) the coefficient of correlation.

Solution

Q8 Find the equations of the lines of regression on the basis of following data

x	1	2	3	4	5
y	166	184	142	180	338

Solution

Q9 A manufacturer of optical lenses has the following data on the cost per unit (in ₹) of a certain quality of lens and the number of units made in each order:

Order number	No. of units (x)	Cost per unit (y)
1 2 3 4 5 6	1 3 5 7 10 15	58 52 46 40 37 22

Find the correlation coefficient. Also determine the two regression equations.

Solution

Q10 The following observations are given : (1, 4), (2, 8), (3, 2), (4, 12), (5, 10), (6, 14), (7, 16), (8, 6), (9, 18) Estimate the values of y when the value of x is 10 and also estimate the value of x when the value of y is 5.

Solution