Page 319 - DMTH404_STATISTICS

Unit 22: Correlation

(iii) If u + 3x = 5, 2y - v = 7 and r = 0.12, then r = 0.12. Notes
xy uv
(iv) If 2x - u = 8, y - 3v = 10 and r = 0.8, then r = 0.8.
xy uv
(v) If  d 2 i = 33 and n = 10 then r = 0.8.

22.13 Review Questions

1. (a) Define correlation between two variables. Distinguish between positive and
negative correlation. Illustrate by using diagrams.
(b) Define the concept of covariance. How do you interpret it?
2. Define correlation and discuss its significance in statistical analysis. Does it signify 'cause
and effect' relationship between the two variables?
3. (a) What do you understand by the coefficient of linear correlation? Explain the
significance and limitations of this measure in any statistical analysis.
(b) Write down an expression for the Karl Pearson's coefficient of linear correlation.
Why is it termed as the coefficient of linear correlation? Explain.

4. (a) Describe the method of obtaining the Karl Pearson's formula of coefficient of
linear correlation. What do positive and negative values of this coefficient indicate?
(b) Does a zero value of Karl Pearson's coefficient of correlation between two variables
X and Y imply that X and Y are not related? Explain.
5. Define product moment coefficient of correlation. What are the advantages of the study of
correlation?

6. Show that the coefficient of correlation, r, is independent of change of origin and scale.
7. Prove that the coefficient of correlation lies between - 1 and +1.
8. "If two variables are independent the correlation between them is zero, but the converse
is not always true". Explain the meaning of this statement.
9. What is Spearman's rank correlation? What are the advantages of the coefficient of rank
correlation over Karl Pearson's coefficient of correlation?

10. Distinguish between the Spearman's coefficient of rank correlation and Karl Pearson's
coefficient of correlation. Explain the situations under which Spearman's coefficient of
rank correlation can assume a maximum and a minimum value. Under what conditions
will Spearman's formula and Karl Pearson's formula give equal results?

11. Explain the method of calculating coefficient of correlation by Concurrent Deviation
Method.
12. Write short notes on:

(i) Positive and negative correlation.
(ii) Linear and non-linear correlation.
(iii) Probable error of correlation.
(iv) Scatter diagram.

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