Multiple Choice Questions
Q1: If all the points lie on the same downward sloping line, the correlation is said to be
(a) perfect correlation
(b) perfect positive correlation
(c) perfect negative correlation
(d) negative correlation
Ans: c
Q2: Correlation is an analysis of ____ between two or more variables.
(a) relationship
(b) covariation
(c) determination
(d) calculation
Ans: b
Q3: Scatter diagram can be used to indicate which of the following degrees of correlation?
(a) Perfect positive correlation
(b) Perfect negative correlation
(c) No correlation
(d) All of the above
Ans: d
Q4: Which of the following techniques deals with the association between two or more variables?
(a) Index number
(b) Correlation
(c) Dispersion
(d)None of these
Ans: b
Q5: When the mean of series is a decimal number, then which method should be used for computing Karl Pearson’s coefficient of correlation?
(a) Direct Method
(b) Short-cut Method
(c) Step Deviation Method
(d) None of these
Ans: b
Q6: When two variables move together in the same direction, it is said to be
(a) no correlation
(b) negative correlation
(c) positive correlation
(d) zero correlation
Ans: c
Q7: The coefficient of correlation is independent of
(a) change of scale only
(b) change of origin only
(c) both change of scale and origin
(d) None of the above
Ans: c
Q8: A modified version of Karl Pearson’s formula is
(a) r=∑xy/∑x2.∑y2
(b) r= ∑xy/√∑x2x∑y2
(c) r= ∑xy/n∑x2·∑y2
(d) r= ∑xy/nδx·δy
Ans: b
Q9: Karl Pearson’s coefficient of correlation indicates the ...... and also the degree of relationship between the two variables.
(a) direction
(b) relation
(c) interpretation
(d) None of these
Ans: a
Q10: Which of the following pair is correctly matched?
Codes
(a) A–(i)
(b) B–(ii)
(c) C–(iii)
(d) None of these
Ans: c
Q11: Statement I Correlation is a multivariate analysis.
Statement II Partial correlation considers all other variables to be constant.
Alternatives
(a) Statement I is correct and Statement II is incorrect
(b) Statement II is correct and Statement I is incorrect
(c) Both the statements are correct
(d) Both the statements are incorrect
Ans: c
Q12: The minimum limit of correlation under Karl Pearson’s method is
(a) −1
(b) 0
(c) 1
(d) None of these
Ans: a
Q13: If the dots in a scatter diagram fall on a narrow band, it indicates a ..........degree of correlation.
(a) zero
(b) high
(c) low
(d) None of these
Ans: c
Q14: Statement I Non-linear correlation is also called curvy linear correlation.
Statement II Numerical measure of correlation is called coefficient of determination.
Alternatives
(a) Statement I is correct and Statement II is incorrect
(b) Statement II is correct and Statement I is incorrect
(c) Both the statements are correct
(d) Both the statements are incorrect
Ans: a
Q15: Coefficient of correlation lies between
(a) 0 and +1
(b) 0 and –1
(c) –1 and +1
(d) – 3 and +3
Ans: c
Assertion–Reasoning based MCQs
(a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
(b) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A)
(c) Assertion (A) is false, but Reason (R) is true
(d) Both Assertion (A) and Reason (R) are false
Q1: Assertion (A) Correlation analysis is a means for examining inter relationships systematically.
Reason (R) Causation explain the cause and effect relationship between variables.
Ans: b
Q2: Assertion (A) Sale of ice-cream increases during summer, shows positive correlation.
Reason (R) When two variables move in same direction, it shows positive correlation.
Ans: b
Q3: Assertion (A) Broadly, there only two types of correlation i.e., positive and negative.
Reason (R) The correlation is said to be positive when the variables move together in the same direction, the correlation is negative when they move in opposite directions.
Ans: b
Q4: Assertion (A) Karl Pearson’s method is non-mathematical in nature.
Reason (R)Degree of correlation helps in identifying the nature of correlation between variables.
Ans: c
Case Study Questions Measures of Correlation
Coefficient of correlation is an important statistical tool which is used to measure the relationship between two variables. This is not only useful in the field of statistics but also used in other disciplines like Economics, Geography, Psychology.
In the present time due to the outbreak of Covid-19 corona virus, demand has gradually come down in almost all areas. As per the latest estimates, demand for car has decreased after the nationwide lockdown is lifted in phased manner.
Q1: If one variable change exactly in the reverse direction of the other variable, ........... should be the degree of correlation.
(a) positive correlation
(b) negative correlation
(c) perfect positive correlation
(d) perfect negative correlation
Ans: d
Q2: Which method of calculating correlation uses actual mean?
(a) Karl Pearson’s coefficient of correlation
(b) Scatter diagram method
(c) Spearman’s rank correlation method
(d) Both (a) and (c)
Ans: a
Q3: In perfect positive correlation, the value of ‘r’ is____.
(a) –1
(b) 0
(c) 1
(d) infinity
Ans: c
Q4: Which of the following tools can be used to know the pattern of demand during lockdown?
(a) Correlation
(b) Causation
(c) Both (a) and (b)
(d) Neither (a) nor (b)
Ans: b
Q5: What will be the coefficient of correlation between demand for car and varied level of income due to nationwide lockdown?
(a) Positive correlation
(b) Negative correlation
(c) Perfect positive correlation
(d) No correlation
Ans: a
Q6: The correlation between using mask and being injected by the virus will be
(a) positive
(b) negative
(c) Not correlated
(d) Either (a) or (b)
Ans: b
Short Answer Type Questions
Q1: Why is ‘r’ preferred to covariance as a measure of association?
Ans: Both, correlation coefficient and covariance measure the degree of linear relationship between two variables but correlation coefficient is generally preferred to covariance.
It is due to the following reasons
(i) The correlation coefficient (r ) has no unit.
(ii) The correlation coefficient is independent of origin as well as scale.
Q2: What do you understand by ‘spurious’ or ‘non-sense’ correlation?
Ans: If there is no evident or sensible connection between two variables, then the correlation between these variables is said to be spurious, non-sense or chance correlation. For example, correlation between rainfall recorded and production of steel.
These two variables are not connected by any way. So,the correlation between these variables is said to be spurious.
Q3: Give the advantages of Karl Pearson’s coefficient of correlation.
Ans: The advantages of Karl Pearson’s coefficient of correlation are
(i) Karl Pearson’s coefficient of correlation indicates the relationship as positive or negative and thus direction of the relationship can be ascertained.
(ii) This measure gives summarised and precise quantitative figure of correlation which can be interpreted easily and can provide meaningful results.
(iii) This coefficient of correlation indicates the direction and also the degree of relationship between the two variables. It shows whether the relationship is high, moderate or low.
Q4: List some variables where accurate measurement is difficult.
Ans: Accurate measurement is difficult in case of
(i) Qualitative variables such as beauty, intelligence,honesty, etc.
(ii) It is also difficult to measure subjective variables such as poverty, development, etc, which are
(iii) Where the cause and effect relationship is not known.
Q5: Interpret the values of r as 1, –1 and 0.
Ans: (i) If r = 0, the two variables are uncorrelated. There is no linear relation between them. However, other types of relation may be there and hence thevariables may not be independent.
(ii) If r = 1, the correlation is perfectly positive. The relation between them is exact in the sense that if one increases,the other also increases in the same proportion and if one decreases, the other also decreases in the same proportion.
(iii) If r = –1, the correlation is perfectly negative. The relation between them is exact in the sense that if one increases, the other decreases in the same proportion and if one decreases, the other increases in the same proportion.
Q6: Can r lie outside the −1 and 1 range depending on the type of data?
Ans: No, the value of the correlation coefficient lies between minus one and plus one i.e., −1 £ r £ 1. If the value of r is outside this range in any type of data, it indicates error in calculation as in between two or more variables, there can be either a perfect or an imperfect relationship. A perfect relationship is indicated by –1 or 1 and imperfect relationships are indicated by a value between –1 and 1,excluding 0.
Q7: Give the disadvantages of Karl Pearson’s coefficient of correlation.
Ans: The disadvantages of Karl Pearson’s coefficient of correlation are
(i) The value of coefficient is affected by extreme items.
(ii) The calculation process consumes a lot of time.
(iii) Correlation coefficient needs very careful interpretation, otherwise it may be misinterpreted.