Page 220 - DMGT209_QUANTITATIVE_TECHNIQUES_II

Unit 10: Correlation

6. A ....................... rank correlation implies that a high (low) rank of an individual according Notes
to one characteristic is accompanied by its high (low) rank according to the other.
7. The regression equations are useful for predicting the value of ....................... variable for
given value of the ....................... variable.
8. When two or more individuals have the same rank, each individual is assigned a rank
equal to the ....................... of the ranks that would have been assigned to them in the event
of there being slight differences in their values.

10.5 Summary

 Researchers sometimes put all the data together, as if they were one sample.
 There are two simple ways to approach these types of data.
 We can use the technique of correlation to test the statistical significance of the association.
 In other cases we use regression analysis to describe the relationship precisely by means
of an equation that has predictive value.
 Straight-line (linear) relationships are particularly important because a straight line is a
simple pattern that is quite common.

 The correlation measures the direction and strength of the linear relationship.
10.6 Keywords

Correlation: It is an analysis of covariation between two or more variables.
Correlation Coefficient: It is a numerical measure of the degree of association between two or
more variables.
10.7 Review Questions

1. Obtain the two lines of regression from the following data and estimate the blood pressure
when age is 50 years. Can we also estimate the blood pressure of a person aged 20 years on
the basis of this regression equation? Discuss.

Age (X) (in years) 56 42 72 39 63 47 52 49 40 42 68 60
Blood Pressure (Y) 127 112 140 118 129 116 130 125 115 120 135 133

2. Show that the coefficient of correlation, r, is independent of change of origin and scale.
3. Prove that the coefficient of correlation lies between - 1 and + 1.
4. “If two variables are independent the correlation between them is zero, but the converse
is not always true”. Explain the meaning of this statement.
5. What is Spearman’s rank correlation? What are the advantages of the coefficient of rank
correlation over Karl Pearson’s coefficient of correlation?

Answers: Self Assessment

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

3. probable error 4. extreme

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