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Chapter: Unit 3

1. |
## If the sum of squares of the rank differences of 10 pairs of values is 30, find the correlation coefficient between them. |

A. | 0.75 |

B. | 0.82 |

C. | 0.90 |

D. | 0.83 |

Answer» B. 0.82 |

2. |
## In a bivariate sample, the sum of squares of differences between marks of observed values of two variables is 33 and the rank correlation between them is 0.8. Find the number of pairs of observations: |

A. | 12 |

B. | 10 |

C. | 15 |

D. | 18 |

Answer» B. 10 |

3. |
## In a bivariate distribution, Spearman’s Coefficient of Correlation is -0.25. If the sum of the squares of various ranks is 150, find out the number of pairs of items: |

A. | 10 |

B. | 8 |

C. | 9 |

D. | 7 |

Answer» C. 9 |

4. |
## The rank correlation coefficient of a debating contest involving 10 participants was calculated as 0.6. However, it was later discovered that the difference in the ranks of some participants was read as 8 instead of 3. Find the correct correlation coefficient: |

A. | 0.933 |

B. | 0.652 |

C. | 0.854 |

D. | 0.751 |

Answer» A. 0.933 |

5. |
## The regression coefficient of X on Y is: |

A. | bXY |

B. | bYX |

C. | Not Specified |

D. | none |

Answer» A. bXY |

6. |
## Regression Coefficient of Y on X is: |

A. | bXY |

B. | bYX |

C. | Not Specified |

D. | none |

Answer» B. bYX |

7. |
## If one of the regression coefficient is greater than unity, the other must be: |

A. | More than Unity |

B. | Less than Unity |

C. | Unity |

D. | none |

Answer» B. Less than Unity |

8. |
## The regression coefficients re independent of change of origin but: |

A. | Not of Scale |

B. | Also of Scale |

C. | No Change in scale |

D. | none |

Answer» A. Not of Scale |

9. |
## The coefficient of correlation between the regression coefficients is: |

A. | Arithmetic Mean |

B. | Geometric Mean |

C. | Average |

D. | none |

Answer» B. Geometric Mean |

10. |
## The correlation coefficient is used to determine: |

A. | A specific value of the y-variable given a specific value of the x-variable |

B. | A specific value of the x-variable given a specific value of the y-variable |

C. | The strength of the relationship between the x and y variables |

D. | None of these |

Answer» C. The strength of the relationship between the x and y variables |

11. |
## If there is a very strong correlation between two variables then the correlation coefficient must be: |

A. | any value larger than 1 |

B. | much smaller than 0, if the correlation is negative |

C. | much larger than 0, regardless of whether the correlation is negative or positive |

D. | None of these alternatives is correct |

Answer» B. much smaller than 0, if the correlation is negative |

12. |
## In regression, the equation that describes how the response variable (y) is related to the explanatory variable (x) is: |

A. | the correlation model |

B. | the regression model |

C. | used to compute the correlation coefficient |

D. | None of these alternatives is correct. |

Answer» B. the regression model |

13. |
## In regression analysis, the variable that is being predicted is the: |

A. | Response, or dependent, variable |

B. | Independent variable |

C. | intervening variable |

D. | is usually x |

Answer» A. Response, or dependent, variable |

14. |
## In a regression analysis if r2 = 1, then : |

A. | SSE must also be equal to one |

B. | SSE must be equal to zero |

C. | SSE can be any positive value |

D. | SSE must be negative |

Answer» B. SSE must be equal to zero |

15. |
## In regression analysis, the variable that is used to explain the change in the outcome of an experiment, or some natural process, is called: |

A. | the x-variable |

B. | the independent variable |

C. | the predictor variable |

D. | the explanatory variable |

Answer» C. the predictor variable |

16. |
## If the coefficient of determination is a positive value, then the regression equation: |

A. | must have a positive slope |

B. | must have a negative slope |

C. | could have either a positive or a negative slope |

D. | must have a positive y intercept |

Answer» C. could have either a positive or a negative slope |

17. |
## If two variables, x and y, have a very strong linear relationship, then: |

A. | there is evidence that x causes a change in y |

B. | there is evidence that y causes a change in x |

C. | there might not be any causal relationship between x and y |

D. | None of these alternatives is correct. |

Answer» A. there is evidence that x causes a change in y |

18. |
## If the coefficient of determination is equal to 1, then the correlation coefficient : |

A. | must also be equal to 1. |

B. | can be either -1 or +1. |

C. | can be any value between -1 to +1 |

D. | must be -1 |

Answer» B. can be either -1 or +1. |

19. |
## In regression analysis, if the independent variable is measured in kilograms, the dependent variable: |

A. | must also be in kilograms |

B. | must be in some unit of weight |

C. | cannot be in kilograms |

D. | can be any units |

Answer» D. can be any units |

20. |
## The strength (degree) of the correlation between a set of independent variables X and a dependent variable Y is measured by |

A. | Coefficient of Correlation |

B. | Coefficient of Determination |

C. | Standard error of estimate |

D. | All of the above |

Answer» A. Coefficient of Correlation |

21. |
## The percent of total variation of the dependent variable Y explained by the set of independent variables X is measured by: |

A. | Coefficient of Correlation |

B. | Coefficient of Skewness |

C. | Coefficient of Determination |

D. | Standard error |

Answer» C. Coefficient of Determination |

22. |
## A coefficient of correlation is computed to be -0.95 means that: |

A. | The relationship between two variables is weak |

B. | The relationship between two variables is strong and positive |

C. | The relationship between two variables is strong and but negative |

D. | Correlation coefficient cannot have this value |

Answer» C. The relationship between two variables is strong and but negative |

23. |
## Let the coefficient of determination computed to be 0.39 in a problem involving one independent variable and one dependent variable. This result means that: |

A. | The relationship between two variables is negative |

B. | The correlation coefficient is 0.39 also |

C. | 39% of the total variation is explained by the independent variable |

D. | 39% of the total variation is explained by the dependent variable |

Answer» C. 39% of the total variation is explained by the independent variable |

24. |
## Relationship between correlation coefficient and coefficient of determination is that: |

A. | both are unrelated |

B. | The coefficient of determination is the coefficient of correlation squared |

C. | The coefficient of determination is the square root of the coefficient of correlation |

D. | both are equal |

Answer» B. The coefficient of determination is the coefficient of correlation squared |

25. |
## The value of a correlation is reported by a researcher to be r = −0.5. Which of the following statements is correct? |

A. | The x-variable explains 25% of the variability in the y-variable. |

B. | The x-variable explains −25% of the variability in the y-variable. |

C. | The x-variable explains 50% of the variability in the y-variable. |

D. | The x-variable explains −50% of the variability in the y-variable. |

Answer» A. The x-variable explains 25% of the variability in the y-variable. |

26. |
## Past data has shown that the regression line relating the final exam score and the midterm exam score for students who take statistics from a certain professor is: final exam = 50 + 0.5 × midterm One interpretation of the slope is |

A. | a student who scored 0 on the midterm would be predicted to score 50 on the final exam. |

B. | a student who scored 0 on the final exam would be predicted to score 50 on the midterm exam. |

C. | a student who scored 10 points higher than another student on the midterm would be |

D. | predicted to score 5 points higher than the other student on the final exam. students only receive half as much credit (.5) for a correct |

Answer» A. a student who scored 0 on the midterm would be predicted to score 50 on the final exam. |

27. |
## One use of a regression line is |

A. | to determine if any x-values are outliers. |

B. | to determine if any y-values are outliers. |

C. | to determine if a change in x causes a change in y. |

D. | to estimate the change in y for a one-unit change in x. |

Answer» D. to estimate the change in y for a one-unit change in x. |

28. |
## The percent of total variation of the dependent variable Y explained by the set of independent variables X is measured by |

A. | Coefficient of Correlation |

B. | Coefficient of Skewness |

C. | Coefficient of Determination |

D. | Standard Error or Estimate |

Answer» C. Coefficient of Determination |

29. |
## The strength (degree) of the correlation between a set of independent variables X and a dependent variable Y is measured by |

A. | Coefficient of Correlation |

B. | Coefficient of Determination |

C. | Standard error of estimate |

D. | All of the above |

Answer» D. All of the above |

30. |
## A coefficient of correlation is computed to be -0.95 means that |

A. | The relationship between two variables is weak. |

B. | The relationship between two variables is strong and positive |

C. | The relationship between two variables is strong and but negative |

D. | Correlation coefficient cannot have this value |

Answer» C. The relationship between two variables is strong and but negative |

31. |
## Relationship between correlation coefficient and coefficient of determination is that |

A. | both are unrelated |

B. | The coefficient of determination is the coefficient of correlation squared |

C. | The coefficient of determination is the square root of the coefficient of correlation |

D. | both are equal |

Answer» B. The coefficient of determination is the coefficient of correlation squared |

32. |
## The sample coefficient of correlation |

A. | Has the same sign as the slope, i.e. β |

B. | Can range from -1.00 up to 2.00 |

C. | Is also called Peterson's r |

D. | Can range from -3.00 up to 2.00 |

Answer» A. Has the same sign as the slope, i.e. β |

33. |
## The regression equation is the line with slope a passing through |

A. | The point (X¯¯¯¯,Y¯¯¯¯) |

B. | The point (Y, X) |

C. | The point (X, Y) |

D. | The point (Y¯¯¯¯,X¯¯¯¯) |

Answer» A. The point (X¯¯¯¯,Y¯¯¯¯) |

34. |
## In regression equation y=a+βx+e, both x and y variables are |

A. | y is fixed and x is random |

B. | Random |

C. | Fixed |

D. | x is fixed and y is random |

Answer» D. x is fixed and y is random |

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