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Unit 6: Correlation, Regression and Analysis of Variance - Practice Quiz

ECAP790 60 Questions
0 Correct 0 Wrong 60 Left
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1 What does Pearson's correlation coefficient primarily measure?

Pearson’s Correlation coefficient Easy
A. The difference between two population means
B. The variation within a single variable
C. The ranks assigned to several treatments
D. The linear relationship between two variables

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

Pearson’s Correlation coefficient Easy
A. to
B. to
C. to
D. to

3 What does a Pearson correlation coefficient of indicate?

Pearson’s Correlation coefficient Easy
A. A weak positive linear relationship
B. A perfect positive linear relationship
C. No relationship between the variables
D. A perfect negative linear relationship

4 Spearman's rank correlation coefficient is most suitable for data expressed as what?

Spearman’s Rank correlation coefficient Easy
A. Residuals
B. Frequencies
C. Variances
D. Ranks

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

Spearman’s Rank correlation coefficient Easy
A.
B.
C.
D.

6 Which formula gives Spearman's rank correlation coefficient when there are no tied ranks?

Spearman’s Rank correlation coefficient Easy
A.
B.
C.
D.

7 What is the main purpose of regression analysis?

Regression Concepts Easy
A. To calculate only the sample size
B. To arrange observations into ranks
C. To compare only population variances
D. To predict one variable from another

8 In regression analysis, what is the variable being predicted called?

Regression Concepts Easy
A. Dependent variable
B. Independent variable
C. Ranking variable
D. Control variable

9 In the simple regression equation , what does represent?

Regression Concepts Easy
A. The regression slope
B. The sample mean
C. The error variance
D. The vertical intercept

10 How many regression lines are generally associated with two variables and ?

Regression lines Easy
A. Four
B. Three
C. One
D. Two

11 Through which point do both regression lines pass?

Regression lines Easy
A.
B.
C.
D.

12 Which regression line is used to predict when is known?

Regression lines Easy
A. Regression line of on
B. Regression line of on
C. Regression line of on
D. Regression line of on

13 How many independent variables are used in multiple regression?

Multiple correlation and regression Easy
A. Two or more
B. Only one pair
C. Exactly one
D. Exactly zero

14 What does a multiple correlation coefficient measure?

Multiple correlation and regression Easy
A. Association between one outcome and several predictors
B. Frequency of values in grouped data
C. Variation among ranks within one sample
D. Difference between two independent sample means

15 Which equation represents a multiple linear regression model with two predictors?

Multiple correlation and regression Easy
A.
B.
C.
D.

16 How many factors are studied in a one-way ANOVA?

Analysis of Variance: One-way classification Easy
A. Four factors
B. One factor
C. Two factors
D. Three factors

17 What is the usual null hypothesis in a one-way ANOVA?

Analysis of Variance: One-way classification Easy
A. All group means are equal
B. All group variances are zero
C. All observations are identical
D. All sample sizes are equal

18 Which statistic is used to test significance in ANOVA?

Analysis of Variance: One-way classification Easy
A. -statistic
B. Median
C. -score
D. Range

19 How many factors are studied in a two-way ANOVA?

Analysis of Variance: Two-way classification Easy
A. Two factors
B. Three factors
C. One factor
D. Four factors

20 What can a two-way ANOVA examine in addition to the main effects of two factors?

Analysis of Variance: Two-way classification Easy
A. The median of each observation
B. The correlation of each factor
C. The ranks of all responses
D. The interaction between the factors

21 The covariance between and is , while their standard deviations are and , respectively. What is Pearson's correlation coefficient?

Pearson’s Correlation coefficient Medium
A.
B.
C.
D.

22 The correlation between and is . If and , what is the correlation between and ?

Pearson’s Correlation coefficient Medium
A.
B.
C.
D.

23 For five observations, and . What is Pearson's correlation coefficient?

Pearson’s Correlation coefficient Medium
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B.
C.
D.

24 Two judges rank six participants. If the sum of squared rank differences is , what is Spearman's rank correlation coefficient?

Spearman’s Rank correlation coefficient Medium
A.
B.
C.
D.

25 Two rankings of five items are identical except that one pair of adjacent items is interchanged. What is Spearman's rank correlation coefficient?

Spearman’s Rank correlation coefficient Medium
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B.
C.
D.

26 Five students are ranked in exactly reverse order by two examiners. What is Spearman's rank correlation coefficient?

Spearman’s Rank correlation coefficient Medium
A.
B.
C.
D.

27 In a simple linear regression, the correlation between the response and predictor is . What percentage of variation in the response is explained by the regression?

Regression Concepts Medium
A.
B.
C.
D.

28 A regression model predicts a student's score as , but the observed score is . What is the residual for this observation?

Regression Concepts Medium
A.
B.
C.
D.

29 The regression line of on is . What value of is predicted when ?

Regression lines Medium
A.
B.
C.
D.

30 The regression coefficients are and . If the correlation is positive, what is its value?

Regression lines Medium
A.
B.
C.
D.

31 The two regression lines are and . What are the means ?

Regression lines Medium
A.
B.
C.
D.

32 Given , , and , approximately what is the multiple correlation coefficient ?

Multiple correlation and regression Medium
A.
B.
C.
D.

33 A fitted multiple regression equation is . What is the predicted value when and ?

Multiple correlation and regression Medium
A.
B.
C.
D.

34 If , , and , what is the partial correlation , approximately?

Multiple correlation and regression Medium
A.
B.
C.
D.

35 A one-way ANOVA compares four treatments using observations in total. What are the between-treatment and within-treatment degrees of freedom?

Analysis of Variance: One-way classification Medium
A. and
B. and
C. and
D. and

36 In a one-way ANOVA, the between-group sum of squares is with degrees of freedom, and the error sum of squares is with degrees of freedom. What is the statistic?

Analysis of Variance: One-way classification Medium
A.
B.
C.
D.

37 Three groups each contain four observations and have means , , and . If the grand mean is , what is the between-group sum of squares?

Analysis of Variance: One-way classification Medium
A.
B.
C.
D.

38 A two-way ANOVA without replication has row levels and column levels. What are the degrees of freedom for rows, columns, and error?

Analysis of Variance: Two-way classification Medium
A.
B.
C.
D.

39 In a two-way ANOVA without replication, the row sum of squares is with degrees of freedom, and the error sum of squares is with degrees of freedom. What is the row statistic?

Analysis of Variance: Two-way classification Medium
A.
B.
C.
D.

40 In a two-way ANOVA with replication, the interaction between factors and is statistically significant. What does this indicate?

Analysis of Variance: Two-way classification Medium
A. Only factor has a statistically significant main effect
B. The effect of is identical at every level of
C. The effect of depends on the level of
D. Only factor has a statistically significant main effect

41 Two groups have the following summary statistics. Group 1: , , and within-group corrected sums . Group 2: , , and within-group corrected sums . What is the Pearson correlation after pooling all observations?

Pearson’s Correlation coefficient Hard
A.
B.
C.
D.

42 A correlation matrix for variables has and . Which proposed value of can produce a valid positive semidefinite correlation matrix?

Pearson’s Correlation coefficient Hard
A.
B.
C.
D.

43 Centered variables and satisfy , , and . If and , what is ?

Pearson’s Correlation coefficient Hard
A.
B.
C.
D.

44 For six paired observations, the values are and the corresponding values are . Using average ranks for ties, what is Spearman's rank correlation?

Spearman’s Rank correlation coefficient Hard
A.
B.
C.
D.

45 For , the sum of squared differences between midranks is . Variable has tie groups of sizes and , while variable has one tie group of size . What is Spearman's rank correlation, rounded to three decimals?

Spearman’s Rank correlation coefficient Hard
A.
B.
C.
D.

46 The Spearman correlation between and is , with ties handled by average ranks. Variable is replaced by a strictly decreasing function of , while is replaced by a strictly increasing function of . What is the new Spearman correlation?

Spearman’s Rank correlation coefficient Hard
A.
B.
C.
D.

47 The population model is . Instead of , a researcher observes , where is independent of and . If the reliability ratio is , what is the population slope from regressing on ?

Regression Concepts Hard
A.
B.
C.
D.

48 The true model is , with . If is omitted and , what is the population slope in the simple regression of on ?

Regression Concepts Hard
A.
B.
C.
D.

49 Variables and are standardized and have correlation . Let be the residual from regressing on , and let be the residual from regressing on . What is ?

Regression Concepts Hard
A.
B.
C.
D.

50 The unordered pair of equations and represents the two regression lines of and . Which pair gives and the correlation coefficient ?

Regression lines Hard
A. and
B. and
C. and
D. and

51 The regression lines are and . What is the ratio ?

Regression lines Hard
A.
B.
C.
D.

52 A dataset has , , , , and . Which pair gives the prediction of at and the prediction of at , respectively?

Regression lines Hard
A.
B.
C.
D.

53 Suppose , , and . What is the multiple correlation coefficient ?

Multiple correlation and regression Hard
A.
B.
C.
D.

54 In a sample of observations, the partial correlation between and after controlling for and is . What is the statistic and its residual degrees of freedom for testing zero partial correlation?

Multiple correlation and regression Hard
A. with df
B. with df
C. with df
D. with df

55 All variables are standardized, with , , and . Which values of result from regressing on and ?

Multiple correlation and regression Hard
A.
B.
C.
D.

56 Three groups have sizes , sample means , and within-group sums of squares . What is the one-way ANOVA statistic?

Analysis of Variance: One-way classification Hard
A.
B.
C.
D.

57 A one-way ANOVA has groups, , total sum of squares , and . What is its statistic?

Analysis of Variance: One-way classification Hard
A.
B.
C.
D.

58 Four groups each contain observations and have means . The pooled error mean square is . For the contrast , what is the equivalent one-degree-of-freedom statistic?

Analysis of Variance: One-way classification Hard
A.
B.
C.
D.

59 In a two-way ANOVA without replication, the data matrix is . What are the row and column statistics, respectively?

Analysis of Variance: Two-way classification Hard
A.
B.
C.
D.

60 A balanced factorial experiment has replicates per cell. The cell means are , and the within-cell error sum of squares is . Which pair gives the interaction sum of squares and interaction statistic ?

Analysis of Variance: Two-way classification Hard
A.
B.
C.
D.
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