Chapter 7 Correlation

Question 1.
The unit of correlation coefficient between height in feet and weight in kgs is
(a) kg/feet
(b) percentage
(c) non-existent
Answer:
(c) Correlation coefficient (r) has no unit. It is a pure number. It meansss units of measurement are not part of r.

Question 2.
The range of simple correlation coefficient is
(a) 0 to infinity
(b) minus one to plus one
(c) minus infinity to infinity
Answer:
(b) The value of the correlation coefficient lies between minus one and plus one, -1 ≤ r ≤ 1. If the value of r is outside this range it indicates error in calculation.

Question 3.
If rXY is positive the relation between X and Y is of the type
(a) when Y increases X increases
(b) when Y decreases X increases
(c) when Y increases X does not change
Answer:
(a) If r is positive the two variables move in the same direction. e.g., when the price of coffee rises, the demand for tea also rises as coffee is a substitute of tea. Therefore, the r between price of coffee and demand for tea will be positive.

Question 4.
If rXY = 0, the variable X and Y are
(a) linearly related
(b) not linearly related
(c) independent
Answer:
(b) If rXY = 0, it means the two variables are uncorrelated and there is no linear relation between them. However, other types of relation may be there and they may not be independent.

Question 5.
Of the following three measures which can measure any type of relationship?
(a) Karl Pearson’s coefficient of correlation
(b) Spearman’s rank correlation
(c) Scatter diagram
Answer:
(c) The scatter diagram gives a visual presentation of the relationship and is not confined to linear relations. Karl Pearson’s coefficient of correlation and Spearman’s rank correlation are strictly the measures of linear relationship.

Question 6.
If precisely measured data are available the simple correlation coefficient is
(a) more accurate than rank correlation coefficient
(b) less accurate than rank correlation coefficient
(c) as accurate as the rank correlation coefficient
Answer:
(a) Rank correlation should be used only when the variables cannot be measured precisely, generally it is not as accurate as the simple correlation coefficient as all the information concerning the data is not utilised in this.

Question 7.
Why is r preferred to covariance as a measure of association?
Answer:
Both, correlation coefficient and covariance measure the degree of linear relationship between two variables, but correlation coefficient is generally preferred to covariance due to the following reasons

Question 8.
Can r lie outside the -1 and 1 range depending on the type of data?
Answer:
No the value of the correlation coefficient lies between minus one and plus one, -1 ≤ r ≤ 1. If the value of r is outside this range in any type of data, it indicates error in calculation.

Question 9.
Does correlation imply causation?
Answer:
No, correlation measures do not imply causation. Correlation measures co-variation and not causation.
Correlation does not imply cause and effect relation. The knowledge of correlation only gives us an idea of the direction and intensity of change in a variable when the correlated variable changes. The presence of correlation between two variables X and Y simply means that when the value of one variable is found to change in one direction, the value of the other variable is found to change either in the same direction (i.epositive change) or in the opposite direction (i.e., negative change), in a definite way.

Question 10.
When is rank correlation more precise than simple correlation coefficient?
Answer:
Rank correlation is more precise than simple correlation coefficient in the following situations

Question 11.
Does zero correlation mean independence?
Answer:
No, zero correlation does not mean independence. If there is zero correlation (rXY = 0), it means the two variables are uncorrelated and there is no linear relation between them. However, other types of relation may be there and they may not be independent.

Question 12.
Can simple correlation coefficient measure any type of relationship?
Answer:
No, simple correlation coefficient can measure only linear relationship.

Question 13.
List some variables where accurate measurement is difficult.
Answer:
Accurate measurement is difficult in case of

Question 14.
Interpret the values of r as 1, -1 and 0.
Answer:

Question 15.
Why does rank correlation coefficient differ from Pearsonian correlation coefficient?
Answer:
Rank correlation coefficient differs from Pearsonian correlation coefficient in the following ways

Question 16.
Calculate the correlation coefficient between the heights of fathers in inches (X) and their sons (Y).

Statistics for Economics Class 11 NCERT Solutions Chapter 7 Correlation Q16
Answer:
Statistics for Economics Class 11 NCERT Solutions Chapter 7 Correlation Q16.1
Note Answer: printed in NCERT is incorrect.

Question 17.
Calculate the correlation coefficient between X and Y and comment on their relationship.
Statistics for Economics Class 11 NCERT Solutions Chapter 7 Correlation Q17
Answer:
Statistics for Economics Class 11 NCERT Solutions Chapter 7 Correlation Q17.1

Statistics for Economics Class 11 NCERT Solutions Chapter 7 Correlation Q17.2
As the value of r is zero, so there is no linear correlation between X and Y.

Question 18.
Calculate the correlation coefficient between X and Y and comment on their relationship.
Statistics for Economics Class 11 NCERT Solutions Chapter 7 Correlation Q18
Solution
Statistics for Economics Class 11 NCERT Solutions Chapter 7 Correlation Q18.1
As the correlation coefficient between the two variables is + 1, so the two variables are perfectly positive correlated.

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