Page 205 - DMGT404 RESEARCH_METHODOLOGY

Unit 9: Correlation and Regression

11. From the data given below, find out: Notes
(i) Karl Pearson's coefficient of correlation.
(ii) The two regression equations.
(iii) The two regression coefficients.
(iv) The most likely value of X when Y = 41.

(v) The most likely value of Y when X = - 45.
X 52 60 58 39 41 53 47 34
Y 40 46 43 54 49 55 48 57
12. Find the multiple and partial correlation coefficients for the following data.

X 19 21 24 26 27 27 29 31 30 31
Y 24 28 29 39 30 31 34 35 36 37
Z 21 2- 26 30 27 32 31 36 33 38

13. Find the multiple correlation coefficient R , the partial correlation coefficient r and
1.23 23.1
the multiple regression equation of X on X X .
2 3 1
X1 55 59 63 68 56 73 82 76 64 74
Y1 58 60 53 52 61 70 76 77 63 80
Z1 63 55 51 56 59 74 74 81 61 84

14. Find the three multiple correlation coefficients for the following data.
X1 7 2 6 8 3 5 9 10 15 12
X2 1 5 8 4 9 3 6 7 13 10
X3 3 4 9 2 1 7 5 8 10 14

15. Find the regression equation of X on X , X for the following data.
2 3 1
X1 12 16 19 27 29 32 33 39 40 43
X2 7 9 11 13 16 19 24 31 33 37
X3 3 6 9 11 15 21 25 26 34 40

Answers: Self Assessment

1. ‘Spearman’s Rank Correlation 2. degree, direction

3. probable error 4. extreme
5. Rank 6. positive
7. mean 8. 0.3, small

9. cause and effect 10. uncorrelated
11. – 1 and + 1 12. origin, scale
13. avoid 14. multiple
15. simple 16. xk
17. Partial 18. dependent, independent

19. Multivariate Adaptive Regression Splines
20. kernel

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