TRB BT Assistant - Correlation, Regression and Index Numbers Online Test (MCQ Quiz)

1. What does a correlation coefficient of +1 indicate?

A) Perfect negative linear correlation B) No linear correlation C) Perfect positive linear correlation D) Weak positive linear correlation

2. Which of the following is a measure of the strength and direction of a linear relationship between two quantitative variables?

A) Standard Deviation B) Mean C) Correlation Coefficient D) Variance

3. A correlation coefficient of -0.8 suggests:

A) A weak positive linear relationship B) A strong negative linear relationship C) No linear relationship D) A strong positive linear relationship

4. If the correlation coefficient between two variables is 0, it implies:

A) A perfect positive linear relationship B) A perfect negative linear relationship C) There is no linear relationship between the variables D) The variables are identical

5. What is the range of possible values for the Pearson correlation coefficient?

A) 0 to 1 B) -1 to 0 C) -1 to +1 D) 0 to 100

6. The Spearman rank correlation coefficient is used when:

A) Variables are continuous and linearly related B) Variables are ordinal or non-normally distributed C) Only one variable is quantitative D) There is no relationship between variables

7. Which statistical method is used to model the relationship between a dependent variable and one or more independent variables?

A) Correlation Analysis B) Hypothesis Testing C) Regression Analysis D) Time Series Analysis

8. In a simple linear regression equation, Y = a + bX, what does 'b' represent?

A) The intercept B) The dependent variable C) The independent variable D) The slope (or regression coefficient)

9. The 'a' in the simple linear regression equation Y = a + bX represents:

A) The slope B) The predicted value of Y when X is zero C) The correlation coefficient D) The error term

10. What does the coefficient of determination (R-squared) measure in regression analysis?

A) The strength of the correlation B) The proportion of variance in the dependent variable that is predictable from the independent variable(s) C) The slope of the regression line D) The significance of the independent variable

11. A higher R-squared value indicates:

A) A weaker fit of the regression model B) A stronger fit of the regression model C) No relationship between variables D) A negative correlation

12. In multiple regression, the dependent variable is predicted by:

A) One independent variable B) Two or more independent variables C) A constant D) The correlation coefficient

13. The primary goal of regression analysis is to:

A) Measure the association between two variables B) Predict the value of a dependent variable based on independent variable(s) C) Summarize data using central tendency D) Test hypotheses about population means

14. What is an index number used for?

A) To measure the average of a set of numbers B) To compare the level of a variable at different points in time or locations C) To calculate the standard deviation D) To determine the correlation between variables

15. A price index that measures the change in prices of a basket of goods and services over time is known as a:

A) Volume Index B) Value Index C) Price Index D) Quantity Index

16. The base period in an index number is:

A) The most recent period B) A period chosen as a reference point C) The period with the highest values D) The period with the lowest values

17. If the Consumer Price Index (CPI) for a given year is 150, it means that prices, on average, have:

A) Decreased by 50% B) Increased by 150% C) Increased by 50% compared to the base year D) Stayed the same

18. Which type of index number gives more weight to items with larger quantities consumed or produced?

A) Simple Aggregate Index B) Weighted Aggregate Index C) Unweighted Aggregate Index D) Average of Relatives Index

19. The Laspeyres price index uses weights from which period?

A) The current period B) The base period C) An average of periods D) The most recent period

20. The Paasche price index uses weights from which period?

A) The base period B) The current period C) The previous period D) An average of periods

21. Which index number formula is generally considered to be a better measure of price changes because it uses current period weights?

A) Laspeyres Index B) Paasche Index C) Fisher's Ideal Index D) Simple Aggregate Index

22. Fisher's Ideal Index is the geometric mean of:

A) Laspeyres and Paasche quantity indices B) Laspeyres and Paasche price indices C) Simple Aggregate Price Index and Weighted Aggregate Price Index D) Correlation and Regression coefficients

23. What is a potential disadvantage of the Laspeyres index?

A) It overstates price increases due to substitution effects B) It understates price increases due to substitution effects C) It is difficult to calculate D) It does not account for changes in quantities

24. What is a potential disadvantage of the Paasche index?

A) It does not account for changes in quantities B) It is difficult to calculate as current period quantities are needed C) It overstates price increases D) It requires base period quantities

25. Which of the following is a common application of index numbers?

A) Calculating the mean of a dataset B) Measuring inflation C) Determining the standard deviation D) Estimating the slope of a line

26. If the regression line is Y = 5 + 2X, and X = 3, what is the predicted value of Y?

A) 8 B) 11 C) 13 D) 16

27. In a scatter plot, points that are tightly clustered around a straight line indicate:

A) A weak correlation B) A strong correlation C) No correlation D) A non-linear relationship

28. Which method is used to find the 'best-fitting' line in linear regression?

A) Graphical Method B) Method of Moments C) Least Squares Method D) Maximum Likelihood Estimation

29. What does a p-value in regression analysis typically test?

A) The overall significance of the model B) The significance of individual predictor variables C) The correlation between predictors D) The R-squared value

30. When conducting regression analysis, it is assumed that the residuals (errors) are:

A) Correlated and non-normally distributed B) Independent and normally distributed C) Constant variance and skewed D) Zero and heteroscedastic

31. A correlation matrix displays:

A) The regression coefficients for multiple variables B) The pairwise correlation coefficients between multiple variables C) The R-squared values for different models D) The predicted values of the dependent variable

32. If the correlation between variable A and variable B is high, and the correlation between variable B and variable C is high, what can be inferred about the correlation between A and C?

A) It must be high B) It must be low C) It cannot be determined without more information D) It must be zero

33. Which regression technique is used when the dependent variable is categorical?

A) Linear Regression B) Multiple Regression C) Logistic Regression D) Polynomial Regression

34. What is the primary difference between correlation and regression?

A) Correlation measures association, while regression predicts one variable from another. B) Regression measures association, while correlation predicts. C) Correlation requires a linear relationship, while regression does not. D) Regression is always positive, while correlation can be negative.

35. An index number of 120 for a specific commodity means its current value is:

A) 20% of its base period value B) 120% of its base period value C) 20% higher than its base period value D) 120 times its base period value

36. Which of the following is NOT a type of index number?

A) Wholesale Price Index (WPI) B) Consumer Price Index (CPI) C) Gross Domestic Product (GDP) D) Index of Industrial Production (IIP)

37. In a regression context, multicollinearity refers to:

A) A strong correlation between the dependent variable and independent variables B) A strong correlation among independent variables C) A weak correlation between independent variables D) A lack of correlation between variables

38. What is the main purpose of calculating a moving average index?

A) To smooth out short-term fluctuations and highlight longer-term trends B) To capture seasonal variations C) To measure the instantaneous rate of change D) To determine the correlation coefficient

39. If the regression coefficient (slope) is negative, it implies that as the independent variable increases, the dependent variable tends to:

A) Increase B) Decrease C) Stay the same D) Fluctuate randomly

40. When interpreting a correlation coefficient, it's important to remember that:

A) Correlation implies causation B) Causation implies correlation C) Correlation does not imply causation D) Correlation is always positive

41. Which index number is designed to be an 'ideal' measure by being a geometric mean of Laspeyres and Paasche indices?

A) Simple Aggregate Index B) Weighted Average of Relatives Index C) Fisher's Ideal Index D) Marshall-Edgeworth Index

42. In a multiple regression model, the adjusted R-squared is used because:

A) It always increases as more variables are added B) It penalizes the addition of non-significant predictors C) It is simpler to calculate than R-squared D) It measures the correlation between predictors

43. What does a standard error of the regression coefficient indicate?

A) The variability of the predictor variable B) The variability of the dependent variable C) The precision of the estimated regression coefficient D) The R-squared value of the model

44. If the correlation coefficient between two variables is 0.1, this indicates:

A) A strong positive linear relationship B) A weak negative linear relationship C) A very weak positive linear relationship D) No linear relationship

45. Which method is used to construct a weighted index where both base and current period quantities are used as weights?

A) Laspeyres Method B) Paasche Method C) Fisher's Ideal Method D) Marshall-Edgeworth Method

46. In regression analysis, extrapolation refers to:

A) Predicting values within the range of the observed data B) Predicting values outside the range of the observed data C) The process of fitting the regression line D) Calculating the correlation coefficient

47. What is the primary limitation of using only correlation to describe the relationship between two variables?

A) It cannot indicate the direction of the relationship B) It does not provide a predictive model C) It only works for non-linear relationships D) It is sensitive to outliers

48. An index number represents a value relative to a:

A) Median value B) Average value of all periods C) Base period value D) Mode value

49. Which of the following is a key assumption of linear regression?

A) The independent variable is normally distributed B) The dependent variable is categorical C) The relationship between variables is linear D) There is no correlation between variables

Correlation, Regression and Index Numbers - Online Test

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