🔵 1. What does correlation analysis primarily measure?
A) Causation between variables
B) Strength of association between variables
C) Variability in a single variable
D) Independence of variables
Answer: B) Strength of association between variables
Rationale: Correlation analysis quantifies the strength and direction of a linear relationship between two variables.
🔵 2. Which statistic is commonly used to measure correlation?
A) Mean
B) Median
C) Pearson's r
D) Mode
Answer: C) Pearson's r
Rationale: Pearson's correlation coefficient (r) is widely used to measure the linear relationship between two continuous variables.
🔵 3. The value of a correlation coefficient always lies between:
A) 0 to 1
B) –1 to 1
C) –1 to 0
D) 0 to ∞
Answer: B) –1 to 1
Rationale: The correlation coefficient ranges from –1 (perfect negative) to +1 (perfect positive).
🔵 4. A correlation coefficient of zero indicates:
A) A strong positive relationship
B) A weak negative relationship
C) No linear relationship
D) High variability
Answer: C) No linear relationship
Rationale: A zero correlation implies no linear relationship, though nonlinear relationships may still exist.
🔵 5. A correlation of –0.95 suggests:
A) Strong negative correlation
B) Weak positive correlation
C) No relationship
D) Perfect independence
Answer: A) Strong negative correlation
Rationale: Values close to –1 indicate a strong inverse (negative) relationship.
🔵 6. Which of the following is not a type of correlation?
A) Positive correlation
B) Negative correlation
C) Nonlinear correlation
D) Abstract correlation
Answer: D) Abstract correlation
Rationale: Abstract correlation is not a recognized type; the others describe actual correlation patterns.
🔵 7. Which graph is most commonly used to visualize correlation?
A) Bar chart
B) Pie chart
C) Scatter plot
D) Histogram
Answer: C) Scatter plot
Rationale: A scatter plot visually represents the relationship between two quantitative variables.
🔵 8. A perfect positive correlation is represented by:
A) r = 0
B) r = –1
C) r = 1
D) r = 0.5
Answer: C) r = 1
Rationale: A correlation coefficient of +1 indicates a perfect direct relationship.
🔵 9. Spearman’s rank correlation is used when:
A) Data are categorical
B) Data are normally distributed
C) Data are ranked or ordinal
D) Data have no variance
Answer: C) Data are ranked or ordinal
Rationale: Spearman’s rho measures the monotonic relationship between two ranked variables.
🔵 10. Correlation does not imply:
A) Direction
B) Association
C) Causation
D) Strength
Answer: C) Causation
Rationale: Correlation shows association but cannot confirm a cause-effect relationship.
🔵 11. Which of the following would likely have a positive correlation?
A) Temperature and woolen clothes sales
B) Age and number of teeth
C) Education level and income
D) Rainfall and sunscreen sales
Answer: C) Education level and income
Rationale: Typically, as education level increases, income also tends to increase — a positive correlation.
🔵 12. If the scatter plot points are widely scattered, it indicates:
A) Strong correlation
B) Weak correlation
C) No outliers
D) Perfect relationship
Answer: B) Weak correlation
Rationale: A loose scatter of data points reflects a weak correlation.
🔵 13. What does a negative correlation imply?
A) As one variable increases, the other increases
B) No relationship
C) As one variable increases, the other decreases
D) Both variables decrease
Answer: C) As one variable increases, the other decreases
Rationale: Negative correlation indicates an inverse relationship.
🔵 14. Which of the following best describes r = –1?
A) No correlation
B) Perfect negative linear correlation
C) Strong positive correlation
D) Nonlinear correlation
Answer: B) Perfect negative linear correlation
Rationale: r = –1 means a perfect linear inverse relationship.
🔵 15. Pearson's correlation coefficient is not appropriate for:
A) Ordinal data
B) Ratio scale data
C) Interval scale data
D) Normally distributed variables
Answer: A) Ordinal data
Rationale: Pearson's r requires continuous, normally distributed variables, not ranks.
🔵 16. The square of the correlation coefficient is known as:
A) Determination coefficient
B) Regression coefficient
C) T-statistic
D) Slope
Answer: A) Determination coefficient
Rationale: r² represents the proportion of variance in one variable predictable from the other.
🔵 17. A correlation coefficient of +0.8 indicates:
A) No relationship
B) Weak positive association
C) Strong positive association
D) Moderate negative relationship
Answer: C) Strong positive association
Rationale: Values closer to +1 represent strong direct relationships.
🔵 18. When two variables move in opposite directions, their correlation is:
A) Zero
B) Positive
C) Negative
D) Undefined
Answer: C) Negative
Rationale: Opposing movements reflect negative correlation.
🔵 19. The method used to remove the effect of a third variable in correlation is:
A) Regression
B) Residual analysis
C) Partial correlation
D) Multiple regression
Answer: C) Partial correlation
Rationale: Partial correlation quantifies the relationship between two variables while controlling for a third.
🔵 20. What does the correlation matrix display?
A) T-values
B) Relationships among multiple variables
C) Frequency distribution
D) Variance values
Answer: B) Relationships among multiple variables
Rationale: A correlation matrix shows pairwise correlation coefficients among variables.
🔵 21. When r = 0.4, the coefficient of determination is:
A) 0.16
B) 0.40
C) 0.80
D) 0.64
Answer: A) 0.16
Rationale: r² = 0.4² = 0.16, meaning 16% of the variance is explained.
🔵 22. The assumption of Pearson correlation includes:
A) Binary variables
B) Heteroscedasticity
C) Linearity
D) Categorical data
Answer: C) Linearity
Rationale: Pearson's r assumes a linear relationship between variables.
🔵 23. Which of the following is true for correlation?
A) It depends on units
B) It is always positive
C) It is dimensionless
D) It requires unequal sample sizes
Answer: C) It is dimensionless
Rationale: Correlation is a unitless measure, making it universally comparable.
🔵 24. A perfect correlation suggests that:
A) Variables have no variation
B) One variable perfectly predicts the other
C) The dataset is biased
D) Regression is not possible
Answer: B) One variable perfectly predicts the other
Rationale: Perfect correlation implies a deterministic linear relationship.
🔵 25. The closer the points lie to a straight line in a scatter plot:
A) The weaker the correlation
B) The stronger the correlation
C) The higher the sample size
D) The more variance exists
Answer: B) The stronger the correlation
Rationale: Tightly clustered points indicate a strong relationship.
🔵 26. In correlation, the independent variable is:
A) Always required
B) Not necessary
C) Needed for prediction
D) Replaced by a dummy variable
Answer: B) Not necessary
Rationale: Correlation deals with the relationship, not causality or prediction.
🔵 27. If two variables are unrelated, their correlation is:
A) 1
B) –1
C) 0
D) 2
Answer: C) 0
Rationale: Zero correlation implies no linear association.
🔵 28. Spearman's rank correlation is appropriate when:
A) Data are not linear
B) Data are nominal
C) Data are interval-scaled
D) Data have high kurtosis
Answer: A) Data are not linear
Rationale: It captures monotonic relationships, even if not linear.
🔵 29. The test for significance of correlation involves:
A) F-test
B) Z-test
C) t-test
D) Chi-square test
Answer: C) t-test
Rationale: A t-test is used to assess the significance of the correlation coefficient.
🔵 30. What does a weak correlation imply?
A) Strong prediction
B) Low association
C) No causation
D) High error
Answer: B) Low association
Rationale: Weak correlation indicates minimal linear relationship.
🔵 31. Which of the following would result in a spurious correlation?
A) A direct cause-and-effect relationship
B) Random error
C) A third hidden variable influencing both
D) High sample variance
Answer: C) A third hidden variable influencing both
Rationale: A spurious correlation is caused by a lurking variable affecting both measured variables, giving a false sense of relationship.
🔵 32. What is the primary difference between correlation and regression?
A) Correlation uses more variables
B) Regression identifies causality
C) Correlation uses nonlinear models
D) Regression does not assume direction
Answer: B) Regression identifies causality
Rationale: While correlation measures association, regression estimates the causal effect of one variable on another.
🔵 33. A scatter plot showing a curve suggests:
A) Strong linear correlation
B) No correlation
C) Nonlinear correlation
D) Negative linear correlation
Answer: C) Nonlinear correlation
Rationale: A curved scatter indicates a nonlinear relationship that cannot be captured by Pearson’s r.
🔵 34. Which correlation coefficient is most suitable for nominal variables?
A) Pearson’s r
B) Spearman’s rho
C) Kendall’s tau
D) Phi coefficient
Answer: D) Phi coefficient
Rationale: The Phi coefficient is used to measure the association between two binary (nominal) variables.
🔵 35. A high positive correlation between rainfall and crop yield implies:
A) Rainfall causes crop failure
B) Increase in rainfall is associated with higher yield
C) Rainfall and yield are inversely related
D) Data is skewed
Answer: B) Increase in rainfall is associated with higher yield
Rationale: Positive correlation suggests that as rainfall increases, so does yield.
🔵 36. Which of the following values of r shows the weakest relationship?
A) r = –0.85
B) r = 0.50
C) r = 0.05
D) r = –0.60
Answer: C) r = 0.05
Rationale: Correlation close to 0 indicates very weak or no linear relationship.
🔵 37. What is the main limitation of correlation analysis?
A) It can’t be used for more than two variables
B) It requires ordinal data
C) It does not imply causality
D) It uses only categorical variables
Answer: C) It does not imply causality
Rationale: Correlation only measures association, not cause and effect.
🔵 38. Kendall’s tau is preferred when:
A) Data have many ties or are ordinal
B) Data are continuous
C) Sample size is above 10,000
D) Nominal data is involved
Answer: A) Data have many ties or are ordinal
Rationale: Kendall’s tau is robust in handling tied ranks and ordinal data.
🔵 39. Which of the following is not an assumption of Pearson correlation?
A) Linearity
B) Normality of variables
C) Homoscedasticity
D) Data measured on nominal scale
Answer: D) Data measured on nominal scale
Rationale: Pearson’s r requires continuous interval or ratio scale variables.
🔵 40. A non-significant correlation suggests that:
A) There is no trend at all
B) The relationship is not strong enough to be statistically valid
C) The data is incorrect
D) Sample size is too small to conduct the test
Answer: B) The relationship is not strong enough to be statistically valid
Rationale: Statistical significance helps assess whether an observed correlation likely exists in the population.
🔵 41. Multicollinearity in regression analysis is detected using:
A) Pearson correlation
B) Variance Inflation Factor (VIF)
C) Covariance
D) Scatter plot
Answer: B) Variance Inflation Factor (VIF)
Rationale: VIF detects how much a variable is linearly related to others, helping identify multicollinearity.
🔵 42. Which of the following correlation tests is least sensitive to outliers?
A) Pearson's correlation
B) Spearman's rank correlation
C) Point-biserial correlation
D) Phi coefficient
Answer: B) Spearman's rank correlation
Rationale: Being based on ranks, Spearman's rho is less affected by extreme values.
🔵 43. What type of correlation is used when one variable is binary and the other is continuous?
A) Pearson’s correlation
B) Point-biserial correlation
C) Phi coefficient
D) Kendall’s tau
Answer: B) Point-biserial correlation
Rationale: This correlation is used for one continuous and one dichotomous variable.
🔵 44. What is the effect of a large sample size on correlation analysis?
A) Reduces correlation
B) Reduces variability
C) Increases statistical power
D) Makes interpretation difficult
Answer: C) Increases statistical power
Rationale: A larger sample improves the accuracy of the estimate and likelihood of finding a significant relationship.
🔵 45. A correlation coefficient of –0.01 indicates:
A) Strong negative correlation
B) Weak negative correlation
C) No linear correlation
D) High inverse correlation
Answer: C) No linear correlation
Rationale: This value is too close to zero to suggest any meaningful relationship.
🔵 46. If all points lie exactly on a straight downward slope in a scatter plot, then:
A) r = 0
B) r = 1
C) r = –1
D) r = 0.5
Answer: C) r = –1
Rationale: This represents a perfect negative linear correlation.
🔵 47. Which of these is most sensitive to extreme values?
A) Spearman’s rho
B) Kendall’s tau
C) Pearson’s r
D) Point-biserial
Answer: C) Pearson’s r
Rationale: Pearson’s r is based on actual values, so outliers can heavily distort it.
🔵 48. What does a high correlation imply about prediction accuracy?
A) Low predictive accuracy
B) High predictive accuracy
C) No impact
D) High causality
Answer: B) High predictive accuracy
Rationale: A strong correlation indicates that one variable can predict the other with reasonable accuracy.
🔵 49. Which method adjusts for the presence of multiple influencing variables?
A) Zero-order correlation
B) Simple correlation
C) Partial correlation
D) Non-parametric correlation
Answer: C) Partial correlation
Rationale: Partial correlation removes the effect of additional variables.
🔵 50. What does it mean if r² = 0.81?
A) 81% of variation in one variable is explained by the other
B) 81% prediction error
C) 19% correlation strength
D) No correlation exists
Answer: A) 81% of variation in one variable is explained by the other
Rationale: The coefficient of determination (r²) explains the proportion of variance accounted for in the dependent variable.
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