60 Important Correlation and Covariance MCQs

Q: 1. What does covariance measure between two variables?

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Q: 2. The Pearson correlation coefficient assumes which type of relationship?

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Q: 3. What is the range of values for the correlation coefficient?

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Q: 4. Covariance can be positive, negative, or zero, but it is not standardized. What standardizes it to create correlation?

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Q: 5. Which correlation measure is non-parametric and suitable for ordinal data?

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Q: 6. A covariance matrix is a square matrix where the diagonal elements represent

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Q: 7. What does a correlation of -0.85 indicate?

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Q: 8. Kendall's tau measures the strength of

See the full post for the detailed answer.

Q: 9. The formula for sample covariance is

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Q: 10. Correlation does not imply

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Category: 1000 Data Analysis MCQDate: Published: November 8, 2025Posted by: MCQs Generator

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This set of 60 MCQs covers the fundamentals of correlation and covariance, including types like Pearson and Spearman, their calculations, interpretations, and applications in data analysis. Ideal for students and professionals exploring statistical relationships between variables.

1. What does covariance measure between two variables?

a) The direction and strength of linear relationship

b) How they vary together from their means

c) The difference in their means

d) The squared deviation from mean

Correct Answer: b) How they vary together from their means

Explanation:

Covariance indicates the direction of linear relationship: positive if variables move together, negative if oppositely.

2. The Pearson correlation coefficient assumes which type of relationship?

a) Non-linear

b) Monotonic

c) Linear

d) Quadratic

Correct Answer: c) Linear

Explanation:

Pearson's r measures the strength and direction of the linear association between two continuous variables.

3. What is the range of values for the correlation coefficient?

a) 0 to 1

b) -1 to 1

c) -∞ to ∞

d) 0 to ∞

Correct Answer: b) -1 to 1

Explanation:

Values close to 1 or -1 indicate strong positive or negative correlation; 0 indicates no linear relationship.

4. Covariance can be positive, negative, or zero, but it is not standardized. What standardizes it to create correlation?

a) Dividing by the product of standard deviations

b) Multiplying by the means

c) Taking the square root

d) Subtracting the variance

Correct Answer: a) Dividing by the product of standard deviations

Explanation:

Pearson's r = Cov(X,Y) / (SD_X * SD_Y), making it unitless and comparable.

5. Which correlation measure is non-parametric and suitable for ordinal data?

a) Pearson

b) Spearman

c) Kendall

d) Point-biserial

Correct Answer: b) Spearman

Explanation:

Spearman's rank correlation assesses monotonic relationships without assuming normality.

6. A covariance matrix is a square matrix where the diagonal elements represent

a) Variances of variables

b) Covariances between pairs

c) Means of variables

d) Standard deviations

Correct Answer: a) Variances of variables

Explanation:

Off-diagonals show pairwise covariances; diagonals are variances (Cov(X,X) = Var(X)).

7. What does a correlation of -0.85 indicate?

a) Weak positive relationship

b) Strong negative relationship

c) No relationship

d) Perfect positive relationship

Correct Answer: b) Strong negative relationship

Explanation:

Values between -0.7 and -1 suggest a strong inverse linear association.

8. Kendall's tau measures the strength of

a) Linear association

b) Monotonic association

c) Quadratic association

d) Causal relationship

Correct Answer: b) Monotonic association

Explanation:

It counts concordant and discordant pairs, suitable for small samples or ties.

9. The formula for sample covariance is

a) Σ(X_i - μ)(Y_i - ν) / n

b) Σ(X_i - x̄)(Y_i - ȳ) / (n-1)

c) ΣX_i Y_i / n

d) Σ(X_i^2 + Y_i^2) / n

Correct Answer: b) Σ(X_i - x̄)(Y_i - ȳ) / (n-1)

Explanation:

Uses n-1 for unbiased estimate; x̄ and ȳ are sample means.

10. Correlation does not imply

a) Association

b) Causation

c) Linearity

d) Strength

Correct Answer: b) Causation

Explanation:

Spurious correlations can occur without causal links; further analysis needed.

11. Which is affected by outliers more: covariance or correlation?

a) Correlation

b) Covariance

c) Both equally

d) Neither

Correct Answer: b) Covariance

Explanation:

Covariance has units and scales with data; correlation is standardized and more robust.

12. Partial correlation measures the relationship between two variables while controlling for

a) All other variables

b) One or more other variables

c) Outliers

d) Non-linearity

Correct Answer: b) One or more other variables

Explanation:

It removes the effect of confounders to isolate direct association.

13. In a scatter plot, a tight cluster around the line y = x indicates

a) r ≈ 0

b) r ≈ 1

c) r ≈ -1

d) Undefined r

Correct Answer: b) r ≈ 1

Explanation:

Points aligned with positive slope show strong positive linear correlation.

14. The point-biserial correlation is used for

a) Two continuous variables

b) One continuous and one binary variable

c) Two binary variables

d) Ordinal and nominal

Correct Answer: b) One continuous and one binary variable

Explanation:

It's a special case of Pearson for dichotomous predictors.

15. What is the covariance of a variable with itself?

a) Mean

b) Standard deviation

c) Variance

d) Correlation

Correct Answer: c) Variance

Explanation:

Cov(X,X) = Var(X), the spread of the variable.

16. Spearman's rho is calculated using

a) Raw data

b) Ranked data

c) Log-transformed data

d) Z-scores

Correct Answer: b) Ranked data

Explanation:

It applies Pearson correlation to ranks, handling non-normal data.

17. A correlation matrix diagonal is always

a) 1

b) 0

c) Mean

d) Variance

Correct Answer: a) 1

Explanation:

Correlation of a variable with itself is perfect (r=1).

18. Polychoric correlation is appropriate for

a) Continuous variables

b) Ordinal variables assuming latent continuity

c) Binary variables

d) Nominal variables

Correct Answer: b) Ordinal variables assuming latent continuity

Explanation:

It estimates correlation from underlying normal variables.

19. If two variables have zero covariance, their correlation is

a) 1

b) 0

c) -1

d) Undefined

Correct Answer: b) 0

Explanation:

No linear co-variation implies uncorrelated variables.

20. The sign of covariance matches the sign of

a) Correlation

b) Variance

c) Mean

d) Standard deviation

Correct Answer: a) Correlation

Explanation:

Both indicate direction: positive or negative association.

21. Biserial correlation assumes the binary variable is

a) Continuous

b) From an underlying continuous distribution

c) Nominal

d) Ordinal

Correct Answer: b) From an underlying continuous distribution

Explanation:

Used when the dichotomy is artificial, like pass/fail.

22. In hypothesis testing for correlation, the null hypothesis is usually

a) ρ = 0

b) ρ = 1

c) ρ > 0

d) ρ < 0

Correct Answer: a) ρ = 0

Explanation:

Tests if the true population correlation is zero (no association).

23. Tetrachoric correlation is for

a) Two continuous variables

b) Two binary variables

c) Ordinal and continuous

d) Nominal and binary

Correct Answer: b) Two binary variables

Explanation:

Assumes underlying bivariate normal distribution.

24. Covariance is sensitive to

a) Units of measurement

b) Scale invariance

c) Normality only

d) Monotonicity

Correct Answer: a) Units of measurement

Explanation:

Changing units (e.g., cm to m) scales covariance, unlike correlation.

25. Phi coefficient measures correlation for

a) Two continuous variables

b) Two binary variables

c) One binary and one continuous

d) Ordinal variables

Correct Answer: b) Two binary variables

Explanation:

It's Pearson's r applied to 2x2 contingency tables.

26. A high positive covariance means variables tend to be

a) Both high or both low

b) One high, one low

c) Independent

d) Constant

Correct Answer: a) Both high or both low

Explanation:

They deviate from means in the same direction.

27. Multiple correlation coefficient R measures

a) Pairwise correlations

b) Relationship between one variable and multiple others

c) Covariance matrix determinant

d) Partial associations

Correct Answer: b) Relationship between one variable and multiple others

Explanation:

R is the correlation between observed and predicted values in regression.

28. Intraclass correlation assesses

a) Between-group similarity

b) Within-group reliability

c) Linear trends

d) Causal effects

Correct Answer: b) Within-group reliability

Explanation:

Used for clustered data, like inter-rater agreement.

29. If X and Y are independent, their covariance is

a) Positive

b) Negative

c) Zero

d) Variance of X

Correct Answer: c) Zero

Explanation:

Independence implies uncorrelatedness (for linear relationships).

30. Cramér's V is a measure of association for

a) Continuous variables

b) Nominal categorical variables

c) Ordinal variables

d) Binary only

Correct Answer: b) Nominal categorical variables

Explanation:

Derived from chi-square, ranges 0-1 for contingency tables.

31. The sample correlation formula uses

a) n in denominator

b) n-1 in denominator

c) n-2 in denominator

d) Population size

Correct Answer: a) n in denominator

Explanation:

For r, it's Σ deviations product divided by (n * SD_X * SD_Y), but consistent with covariance's n-1 adjustment.

32. Canonical correlation analyzes relationships between

a) Two sets of variables

b) Single pairs

c) Time series

d) Spatial data

Correct Answer: a) Two sets of variables

Explanation:

Finds linear combinations maximizing correlation between groups.

33. A correlation of 0 does not mean

a) No linear relationship

b) No relationship at all

c) Independence

d) Variables are unrelated

Correct Answer: b) No relationship at all

Explanation:

Non-linear relationships (e.g., quadratic) can exist with r=0.

34. Variance-covariance matrix is used in

a) PCA for dimensionality reduction

b) Only regression

c) Histogram plotting

d) Data cleaning

Correct Answer: a) PCA for dimensionality reduction

Explanation:

Eigen decomposition reveals principal components.

35. Kendall's tau-b accounts for

a) Ties in data

b) Only linear ties

c) No ties

d) Outliers only

Correct Answer: a) Ties in data

Explanation:

Adjusts for tied ranks in ordinal comparisons.

36. Negative covariance indicates

a) Variables move in same direction

b) Variables move in opposite directions

c) No movement

d) Constant values

Correct Answer: b) Variables move in opposite directions

Explanation:

One increases as the other decreases from means.

37. Theil's U is an asymmetric measure for

a) Categorical prediction uncertainty

b) Continuous correlation

c) Ordinal ranks

d) Binary phi

Correct Answer: a) Categorical prediction uncertainty

Explanation:

Measures how one variable reduces uncertainty in another.

38. In time series, autocorrelation is

a) Covariance with lagged self

b) Cross-correlation with another series

c) Static variance

d) Trend removal

Correct Answer: a) Covariance with lagged self

Explanation:

Normalized to detect patterns like seasonality.

39. Pearson correlation requires

a) Linearity and homoscedasticity

b) Only monotonicity

c) No assumptions

d) Categorical data

Correct Answer: a) Linearity and homoscedasticity

Explanation:

Assumes bivariate normality for significance tests.

40. Cross-correlation measures

a) Similarity between two series at lags

b) Self-similarity

c) Static pairs

d) Spatial links

Correct Answer: a) Similarity between two series at lags

Explanation:

Used in signal processing for time shifts.

41. A value of covariance close to zero suggests

a) Strong association

b) Little linear co-variation

c) Perfect opposition

d) High variance

Correct Answer: b) Little linear co-variation

Explanation:

But magnitude depends on scales; check correlation for standardization.

42. Sommer's d is a correction for

a) Ties in Kendall's tau

b) Outliers in Pearson

c) Small samples

d) Non-normality

Correct Answer: a) Ties in Kendall's tau

Explanation:

Adjusts tau-a for tied observations.

43. In multivariate analysis, the correlation between residuals checks for

a) Multicollinearity

b) Independence assumptions

c) Homoscedasticity

d) Normality

Correct Answer: b) Independence assumptions

Explanation:

Non-zero residual correlations violate model assumptions.

44. Covariance in portfolio theory measures

a) Risk diversification

b) Asset co-movement

c) Expected returns

d) Volatility alone

Correct Answer: b) Asset co-movement

Explanation:

Low or negative covariance reduces overall portfolio risk.

45. Gamma coefficient is for

a) Ordinal data, ignoring ties

b) Nominal data

c) Continuous data

d) Binary data

Correct Answer: a) Ordinal data, ignoring ties

Explanation:

Proportion of concordant minus discordant pairs.

46. The determinant of a correlation matrix indicates

a) Multicollinearity severity

b) Overall association strength

c) Average r

d) No meaning

Correct Answer: a) Multicollinearity severity

Explanation:

Near zero suggests singular matrix, high redundancy.

47. Spearman correlation equals Pearson when data is

a) Ranked

b) Linear

c) Monotonic

d) Normal

Correct Answer: c) Monotonic

Explanation:

Ranks preserve monotonic relationships exactly.

48. Zero correlation can occur with

a) Perfect linear trend

b) Unrelated variables

c) Quadratic relationship

d) Causal link

Correct Answer: c) Quadratic relationship

Explanation:

Curvilinear patterns cancel linear signal.

49. In R, cor() function defaults to

a) Spearman

b) Kendall

c) Pearson

d) Polychoric

Correct Answer: c) Pearson

Explanation:

Use method='spearman' for ranks.

50. Covariance stationarity in time series requires constant

a) Mean and variance over time

b) Only mean

c) Only covariance

d) Trends

Correct Answer: a) Mean and variance over time

Explanation:

Covariances depend only on lag, not time.

51. Yule's Q measures association in

a) 2x2 tables

b) Larger contingency

c) Ordinal

d) Continuous

Correct Answer: a) 2x2 tables

Explanation:

Based on odds ratio for dichotomous variables.

52. Bivariate correlation is

a) Univariate analysis

b) Pairwise relationship

c) Multivariate

d) Unconditional

Correct Answer: b) Pairwise relationship

Explanation:

Focuses on two variables at a time.

53. In Excel, CORREL function computes

a) Covariance

b) Pearson correlation

c) Spearman

d) Variance

Correct Answer: b) Pearson correlation

Explanation:

For two ranges of data.

54. Heteroscedasticity affects correlation by

a) No impact

b) Biasing toward zero

c) Inflating values

d) Changing sign

Correct Answer: a) No impact

Explanation:

Correlation is scale-invariant but assumes homoscedasticity for inference.

55. Lambda coefficient is for

a) Asymmetric nominal association

b) Symmetric ordinal

c) Binary symmetric

d) Continuous

Correct Answer: a) Asymmetric nominal association

Explanation:

Reduces prediction error using one variable to predict another.

56. The squared correlation r² represents

a) Variance explained

b) Total variance

c) Residual variance

d) Covariance ratio

Correct Answer: a) Variance explained

Explanation:

Proportion of variance in Y predictable from X.

57. In Python pandas, df.corr() returns

a) Covariance matrix

b) Correlation matrix

c) Means

d) Variances

Correct Answer: b) Correlation matrix

Explanation:

Default is Pearson; specify method for others.

58. Concordant pairs in Kendall's tau are those where

a) Ranks agree in order

b) Ranks disagree

c) Tied

d) Equal

Correct Answer: a) Ranks agree in order

Explanation:

Both pairs increase or decrease together.

59. Covariance of standardized variables is

a) Variance

b) Correlation

c) Mean

d) Zero

Correct Answer: b) Correlation

Explanation:

Z-scores have SD=1, so Cov(Zx, Zy) = r.

60. Spurious correlation example is

a) Height and weight

b) Ice cream sales and drownings

c) Temperature and plant growth

d) Age and experience

Correct Answer: b) Ice cream sales and drownings

Explanation:

Both correlated with summer heat, not causally.

61. In confirmatory factor analysis, correlations inform

a) Factor loadings

b) Latent structure

c) Observed means

d) Error terms

Correct Answer: b) Latent structure

Explanation:

High inter-correlations suggest common factors.

62. The eta coefficient measures

a) Nominal predictor on continuous outcome

b) Ordinal on ordinal

c) Continuous on binary

d) Spatial correlation

Correct Answer: a) Nominal predictor on continuous outcome

Explanation:

Non-linear analog of point-biserial.

63. Autocovariance at lag 0 is

a) Variance

b) Mean

c) Zero

d) Covariance with lag 1

Correct Answer: a) Variance

Explanation:

Cov(Y_t, Y_t) = Var(Y).

64. Fisher's z-transformation is used to

a) Stabilize variance of r for inference

b) Compute covariance

c) Rank data

d) Test normality

Correct Answer: a) Stabilize variance of r for inference

Explanation:

z = 0.5 ln((1+r)/(1-r)) for hypothesis tests.

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60 Important Correlation and Covariance MCQs

1. What does covariance measure between two variables?

2. The Pearson correlation coefficient assumes which type of relationship?

3. What is the range of values for the correlation coefficient?

4. Covariance can be positive, negative, or zero, but it is not standardized. What standardizes it to create correlation?

5. Which correlation measure is non-parametric and suitable for ordinal data?

6. A covariance matrix is a square matrix where the diagonal elements represent

7. What does a correlation of -0.85 indicate?

8. Kendall's tau measures the strength of

9. The formula for sample covariance is

10. Correlation does not imply

11. Which is affected by outliers more: covariance or correlation?

12. Partial correlation measures the relationship between two variables while controlling for

13. In a scatter plot, a tight cluster around the line y = x indicates

14. The point-biserial correlation is used for

15. What is the covariance of a variable with itself?

16. Spearman's rho is calculated using

17. A correlation matrix diagonal is always

18. Polychoric correlation is appropriate for

19. If two variables have zero covariance, their correlation is

20. The sign of covariance matches the sign of

21. Biserial correlation assumes the binary variable is

22. In hypothesis testing for correlation, the null hypothesis is usually

23. Tetrachoric correlation is for

24. Covariance is sensitive to

25. Phi coefficient measures correlation for

26. A high positive covariance means variables tend to be

27. Multiple correlation coefficient R measures

28. Intraclass correlation assesses

29. If X and Y are independent, their covariance is

30. Cramér's V is a measure of association for

31. The sample correlation formula uses

32. Canonical correlation analyzes relationships between

33. A correlation of 0 does not mean

34. Variance-covariance matrix is used in

35. Kendall's tau-b accounts for

36. Negative covariance indicates

37. Theil's U is an asymmetric measure for

38. In time series, autocorrelation is

39. Pearson correlation requires

40. Cross-correlation measures

41. A value of covariance close to zero suggests

42. Sommer's d is a correction for

43. In multivariate analysis, the correlation between residuals checks for

44. Covariance in portfolio theory measures

45. Gamma coefficient is for

46. The determinant of a correlation matrix indicates

47. Spearman correlation equals Pearson when data is

48. Zero correlation can occur with

49. In R, cor() function defaults to

50. Covariance stationarity in time series requires constant

51. Yule's Q measures association in

52. Bivariate correlation is

53. In Excel, CORREL function computes

54. Heteroscedasticity affects correlation by

55. Lambda coefficient is for

56. The squared correlation r² represents

57. In Python pandas, df.corr() returns

58. Concordant pairs in Kendall's tau are those where

59. Covariance of standardized variables is

60. Spurious correlation example is

61. In confirmatory factor analysis, correlations inform

62. The eta coefficient measures

63. Autocovariance at lag 0 is

64. Fisher's z-transformation is used to

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