NCERT Solutions Class 11, Economics, Statistics for Economics, Chapter- 6, Correlation
1. The unit of correlation coefficient between height in feet and weight in kgs is:
(i) kg/feet
(ii) percentage
(iii) non-existent
Solution:
(iii) non-existent
There is non-existence of correlation between the height in feet and weight in kilograms as both the figures have different measures. It is a situation of no relation. Hence, the unit of correlation is zero.
2. The range of simple correlation coefficient is
(i) 0 to infinity
(ii) minus one to plus one
(iii) minus infinity to infinity
Solution:
(ii) minus one to plus one
The value of correlation coefficient is between –1 and +1.
However, if the value of correlation is not inside this range, it indicates an error of calculation.
3. If rxy is positive the relation between X and Y is of the type:
(i) When Y increases X increases
(ii) When Y decreases X increases
(iii) When Y increases X does not change
Solution:
(i) When Y increases X increases
When the variables, say X and Y, share a positive correlation which means both X and Y increase simultaneously then the value of rxy is positive.
4. If rxy = 0 the variable X and Y are:
(i) linearly related
(ii) not linearly related
(iii) independent
Solution:
(ii) not linearly related
If Rxy = 0, the two variables X and Y are not correatled and there is no linear relation between them. It doesn’t mean that X and Y are completely independent, they might have other types of relationships.
5. Of the following three measures which can measure any type of relationship :
(i) Karl Pearson’s coefficient of correlation
(ii) Spearman’s rank correlation
(iii) Scatter diagram
Solution:
(iii) Scatter diagram
The scatter diagram is not just confined to linear relations. It is a useful technique for visually examining any form of relationship without calculating any mineral value.
6. If precisely measured data are available the simple correlation coefficient is
(i) more accurate than rank correlation coefficient
(ii) less accurate than rank correlation coefficient
(iii) as accurate as the rank correlation coefficient
Solution:
(ii) less accurate than rank correlation coefficient
Generally, all the properties of Karl Pearson’s coefficient of correlation are similar to that of the rank correlation. However, it is slightly less accurate because in rank correlation, ranks are used instead of the full set of observations.
7. Why is r preferred to covariance as a measure of association?
Solution:
Correlation coefficient r is preferred to covariance as a measure of variance because:
(i) The correlation coefficient is independent of scale.
(ii) The value of correlation coefficient (r) lies between –1 and 1.
i.e., –1 ≤ r ≤ 1.
8. Can r lie outside the – 1 and 1 range depending on the type of data?
Solution:
No, the value of r cannot lie outside the range of –1 to 1. If r = –1, there is a perfect negative correlation. If r = 1, there is a perfect positive correlation between the two variables. If the value of r is not within this range, there must be some mistake or error in the calculation.
9. Does correlation imply causation?
Solution:
No, correlation does not imply causation. Correlation measures covariation and not causation. The correlation between two variables does not signify that one variable causes the other. Hence correlation does not measure the cause and effect relationship between them.
10. When is rank correlation more precise than simple correlation coefficient?
Solution:
Rank correlation method is more percise than simple correlation coefficient due to the following reasons:
- When there is a reason to suspect the variables. Height and weight of people cannot be measured precisely but the people can be easily ranked in terms of height and weight.
- In case of qualitiative data, it is difficult to quantify qualities such as fairness, honesty, etc. Hence Ranking would be a better alternative for the quantifications of qualities.
11. Does zero correlation mean independence?
Solution:
No, zero correlation does not mean independence. If there is zero correlation, it shows that X and Y are not correlated and there is no linear relationship between the two.
12. Can simple correlation coefficient measure any type of relationship?
Solution:
No, the simple correlation coefficient cannot measure any type of relationship. It can measure only the direction and magnitude of linear relationship between the two variables.