Page 203 - DCOM203_DMGT204_QUANTITATIVE_TECHNIQUES_I

Quantitative Techniques – I

Notes 9. Show that, in principle, there are always two lines of regression for a bivariate data. Prove
that the coefficient of correlation between two variables is either + 1 or –1 when the two
lines are identical and is zero when they are perpendicular.
10. Fit a linear regression of Y on X to the following data:
X : 1 2 3 4 5 6 7 8
Y : 65 80 45 86 178 205 200 250
11. The following table gives the data relating to purchases and sales. Obtain the two regression
equations by the method of least squares and estimate the likely sales when purchases
equal 100.
Purchases : 62 72 98 76 81 56 76 92 88 49
Sales : 112 124 131 117 132 96 120 136 97 85
12. The following table gives the marks of ten students in economics (X) and statistics (Y).
Compute the appropriate regression equation to estimate the marks in statistics of a
student who scored 65 marks in economics.
X : 54 50 63 65 50 65 54 55 61 60
Y : 65 58 78 72 62 72 60 63 66 70
13. In a partially destroyed record the following data are available:
The two regression lines are 5X + 3Y = 290 and 3X + 2Y = 180. The variance of X = 16.
Find (a) Mean values of X and Y
(b) Standard deviation of Y
(c) Coefficient of correlation between X and Y.
14. The two regression lines obtained by a student were as given below:
3X - 4Y = 5
8X + 16Y = 15
Do you agree with him? Explain with reasons.
15. Obtain the lines of regression of Y on X and X on Y for the data given below:

2 2
X 50, Y 60, XY 350,n 10, X 4 and Y 9
Answers: Self Assessment

1. 'Regression’ 2. regression equation

3. linear association 4. dependent
5. different from 6. (c)
7. (d) 8. (c)
9. (b) 10. (b)

11. False 12. True
13. False 14. True
15. False 16. True
17. False 18. True

19. False 20. True

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