Unit 5: Correlation and Regression - Practice Quiz

1 Which assumption states that the relationship between two variables should follow approximately a straight line?

2 Which type of variables is generally appropriate for Pearson correlation?

3 Which feature of a dataset can strongly distort the value of Pearson correlation?

4 What does the independence assumption require in correlation analysis?

5 What does Pearson's correlation coefficient measure?

6 What is the possible range of Pearson's correlation coefficient ?

7 What does a Pearson correlation of indicate?

8 What does a Pearson correlation close to generally indicate?

9 Spearman correlation is calculated primarily using what type of information?

10 Which symbol is commonly used for Spearman's rank correlation coefficient?

11 Spearman correlation is most suitable for measuring which type of relationship?

12 When is Spearman correlation often preferred over Pearson correlation?

13 What is the main purpose of regression analysis?

14 In regression, what is the variable being predicted called?

15 In regression, what is an independent variable also commonly called?

16 What is a residual in a regression model?

17 Which equation represents a simple linear regression model?

18 In the equation , what does represent?

19 In the equation , what does represent?

20 What does a positive slope in a linear regression model indicate?

21 A researcher wants to examine the correlation between study hours and examination scores using Pearson correlation. Which assumption should be checked first to ensure that the relationship is suitable for this analysis?

22 A scatterplot shows that most observations follow a linear pattern, but one extreme observation lies far from the remaining points. What is the main concern before calculating Pearson correlation?

23 Which situation most clearly violates the assumption of independence of observations in a correlation study?

24 A researcher records income in highly unequal groups and finds a strongly skewed distribution. Which action is most appropriate before using Pearson correlation?

25 A study reports between stress level and sleep quality. What is the best interpretation?

26 If the Pearson correlation between two variables is , approximately what proportion of variance is shared by the variables?

27 A correlation of is found between two variables in a large sample, with a statistically significant -value. What conclusion is most appropriate?

28 When every observed value of variable is multiplied by 10, while the values of remain unchanged, what happens to Pearson's correlation?

29 A scatterplot forms a clear U-shaped pattern, but the Pearson correlation is close to zero. What does this result suggest?

30 A researcher collects customer satisfaction ratings on an ordered scale from 1 to 5 and wants to assess whether satisfaction increases with service quality. Which correlation is most suitable?

31 Two participants receive the same rank for a variable because they have equal scores. How should this tied rank generally be assigned?

32 A Spearman correlation of is obtained between two rankings. What does this indicate?

33 Which data pattern is especially appropriate for Spearman correlation rather than Pearson correlation?

34 In a regression model predicting exam score from study hours, which variable is the predictor?

35 What does a residual represent in a regression model?

36 A regression model has an value of . What does this value indicate?

37 Why is extrapolating far beyond the observed range of a predictor potentially risky?

38 A fitted regression equation is . What is the predicted value of when ?

39 In the equation , what does the slope indicate?

40 A regression analysis produces residuals that become larger as the predicted values increase. Which assumption may be violated?

41 A researcher obtains a Pearson correlation of between continuous variables and . Under which additional condition does this result imply that and are statistically independent?

42 A scatterplot shows a strong U-shaped relationship between and , but Pearson's correlation is approximately zero. Which interpretation is most appropriate?

43 In a study of blood pressure and age, each participant contributes four repeated measurements, but all measurements are analyzed as independent pairs. What is the most likely consequence for conventional correlation inference?

44 A population has a linear positive relationship between aptitude and performance. A study includes only applicants whose aptitude scores fall in the top 5%. Assuming no other selection mechanism, what is the most likely effect on the observed Pearson correlation?

45 Suppose , , and . What is the partial correlation ?

46 For independent pairs, a sample Pearson correlation is . Under the null hypothesis , what is the corresponding statistic?

47 If and , and , what is ?

48 Two equally sized groups each have internally. Group 1 has means and Group 2 has means . What can occur when the groups are pooled?

49 For five untied pairs, the differences between corresponding ranks are . What is Spearman's rank correlation?

50 In a dataset with tied observations, which procedure correctly computes Spearman's correlation?

51 Suppose for observations having distinct values, with no measurement error. Which pair of correlations is most plausible?

52 The observed Spearman correlation between and is . Every value is transformed using , where all , and every value using . What is the new Spearman correlation?

53 The correlation between and is , with and . What is the least-squares slope when regressing on ?

54 Let be the slope from regressing on , and the slope from regressing on . If both variables have positive variance, which identity is correct?

55 A regression of examination score on study time gives a slope of . Which statement is justified by this coefficient alone?

56 A simple regression of on has a positive slope, but after controlling for , the coefficient of becomes negative. Which explanation is most defensible?

57 In a simple linear regression with an intercept, , , and the estimated slope is . What is the estimated intercept?

58 A simple linear regression with an intercept has total sum of squares and residual sum of squares . If the estimated slope is negative, what are and the sample correlation ?

59 A fitted model is . A researcher replaces with and refits the same observations. What fitted equation results?

60 An observation in a simple linear regression has an extreme value, a small residual under the fitted model, and the fitted slope changes substantially when it is removed. How should the observation be characterized?