Question 1

Which of the following represents the proportion of the total variance of a variable accounted for by another value of another variable?
A)product-moment correlation
B)correlation coefficient
C)F-test
D)coefficient of determination

Accepted Answer

The coefficient of determination (also known as R-squared) represents the proportion of the total variance of a variable that can be explained by another variable. It is calculated as the square of the product-moment correlation coefficient (choice A). The F-test (choice C) is used to test whether the variances of two populations are equal.

Question 2

The extent to which a change in one variable corresponds systematically to a change in another is called:
A)spurious association
B)significance
C)covariance
D)standardized coefficient

Accepted Answer

The extent to which two variables have a systematic relationship is called covariance.

Question 3

If the correlation between X and Y is -.72,approximately what percentage of the variance in Y can be explained by X?
A)52 percent
B)72 percent
C)85 percent
D)28 percent

Accepted Answer

The square of the correlation coefficient (r^2) represents the proportion of variance in one variable that is explained by the other variable. In this case, r^2 = (-.72)^2 = .52, which means that approximately 52% of the variance in Y can be explained by X.

Question 4

When there is a strong positive correlation between two variables,but,in fact,both variables are caused by a third variable,the relationship between the first two variables is said to be:
A)strong and negative
B)weak and negative
C)inverse
D)spurious

Accepted Answer

When a correlation exists between two variables that is actually due to a third variable, it is called a spurious relationship. Therefore, the best choice is D.

Question 5

When the on-time performance of airlines is used to predict the number of customer complaints in a regression equation,on-time performance is the ____ variable and the number of customer complaints is the ____ variable.
A)independent;dependent
B)dependent;dependent
C)dependent;independent
D)independent;predictor

Accepted Answer

On-time performance is the predictor or independent variable, as it is the variable causing or influencing the number of customer complaints, which is the dependent variable. The number of customer complaints is dependent on the on-time performance of airlines.

Question 6

If there is no relationship between two variables,the correlation coefficient between them would be:
A)+1.0
B)-1.0
C)+0.50
D)0

Accepted Answer

A correlation coefficient of 0 indicates no linear relationship between two variables.

Question 7

The statistical significance of a regression model is determined by a c² test.

Accepted Answer

An F-test provides the statistical significance of a regression model.

Question 8

A bivariate statistical technique that is used to measure the strength of the relationship between two variables is called the:
A)one-group t-test
B)two-group t-test
C)measure of association
D)correlation matrix

Accepted Answer

A measure of association, such as a correlation coefficient, is specifically designed to determine the strength of the relationship between two variables. The other options (one-group t-test, two-group t-test, correlation matrix) are not designed for this purpose.

Question 9

The Pearson product-moment correlation requires what type of scale for the data?
A)nominal
B)interval
C)ordinal
D)all of the above

Accepted Answer

The Pearson product-moment correlation requires interval scale data, which has equal intervals between values and a meaningful zero point. Nominal and ordinal data do not meet this requirement.

Question 10

The explanatory power of regression lies in hypothesis testing.

Accepted Answer

Hypothesis testing is an integral part of regression analysis, as it allows us to determine the significance of the relationship between the independent and dependent variables. By testing hypotheses, we can determine whether the observed effects are statistically significant or simply due to chance, which helps us determine the explanatory power of the regression model. Therefore, the statement is true.

Question 11

In a correlation matrix,the correlations in the main diagonal are all equal to:
A)-1.00
B)0
C)+0.50
D)+1.00

Accepted Answer

The correlations in the main diagonal of a correlation matrix always show the correlation of a variable with itself, which is always perfect and positive, therefore equal to +1.00.

Question 12

Which of the following is the standard form for reporting observed correlations among multiple variables?
A)correlation matrix
B)contingency table
C)Pearson grid
D)inverse table

Accepted Answer

The standard form for reporting observed correlations among multiple variables is a correlation matrix, which presents the pairwise correlations between all variables in a matrix format. Contingency tables are used to display the frequency distribution of categorical variables, Pearson grid and inverse tables are not common terms used in statistics.

Question 13

The first step in interpreting simple regression output is to interpret the overall significance of the model.

Accepted Answer

It is important to interpret the overall significance of the model, usually indicated by the p-value of the F-statistic, before interpreting the coefficients of the individual variables. A significant overall model suggests that there is a relationship between the independent variable(s) and dependent variable.

Question 14

If the correlation between two variables is - 0.75,this means that:
A)there is a weak positive relationship between the variables
B)there is a strong inverse relationship between the variables
C)there is a weak negative relationship between the variables
D)there is a strong positive relationship between the variables

Accepted Answer

A negative correlation coefficient means that as one variable increases, the other variable decreases. The negative sign indicates the direction of the relationship, while the absolute value (0.75 in this case) indicates the strength. Since the correlation coefficient is relatively close to -1, there is a strong inverse relationship between the variables.

Question 15

When the correlation between two variables is +.92,this means that as one variable ____,the other variable ____.
A)decreases;increases
B)increases;decreases
C)increases;increases
D)decreases;stays the same

Accepted Answer

A correlation of +.92 indicates a strong positive relationship, meaning as one variable increases, the other variable also increases.

Question 16

If the correlation coefficient is - 0.62,the coefficient of determination is approximately:
A)+ 0.38
B)+ 0.62
C)- 0.38
D)- 0.23

Accepted Answer

The coefficient of determination is the square of the correlation coefficient, also known as r-squared. If the correlation coefficient is -0.62, the calculation for the coefficient of determination is:
(-0.62)^2 = 0.3844, which is approximately 0.38. Therefore, choice A is the best answer.

Question 17

The coefficient of determination reflects the proportion of variance that can be explained by the regression line.

Accepted Answer

The coefficient of determination (R-squared) measures how well the regression line fits the data by indicating the proportion of variance in the dependent variable that can be explained by the independent variable(s). Therefore, the statement is true.

Question 18

A rule of thumb for R² is that it must be greater than 0.80 for a regression model to be significant.

Accepted Answer

Guidelines for R² values are neither simple nor straightforward.Additionally,R² does not provide a test of significance,but rather reflects the proportion of variance explained by the regression line.

Question 19

The Pearson product-moment correlation coefficient ranges between:
A)zero and +1.0
B)-1.0 and zero
C)-1.0 and +1.0
D)-2.0 and +2.0

Accepted Answer

The Pearson product-moment correlation coefficient ranges from -1.0 to +1.0, with values closer to -1.0 indicating a strong negative correlation and values closer to +1.0 indicating a strong positive correlation. A value of zero indicates no correlation between the two variables. Therefore, option C is the correct choice as it encompasses the correct range of the Pearson correlation coefficient.

Question 20

The ____ is a measure obtained by squaring the correlation coefficient.
A)t-statistic
B)coefficient of determination (R²)
C)F-ratio
D)Pearson coefficient

Accepted Answer

The coefficient of determination (R²) is the measure obtained by squaring the correlation coefficient, indicating the proportion of the variance explained by the linear relationship between two variables. The t-statistic is used to test the significance of the coefficients in a regression analysis, the F-ratio is used to test the overall significance of the regression model, and the Pearson coefficient is used to measure the strength and direction of a linear relationship between two variables.

Quiz 23: Bivariate Statistical Analysis: Measures of Association

Which of the following represents the proportion of the total variance of a variable accounted for by another value of another variable?

The extent to which a change in one variable corresponds systematically to a change in another is called:

If the correlation between X and Y is -.72,approximately what percentage of the variance in Y can be explained by X?

When there is a strong positive correlation between two variables,but,in fact,both variables are caused by a third variable,the relationship between the first two variables is said to be:

When the on-time performance of airlines is used to predict the number of customer complaints in a regression equation,on-time performance is the variable and the number of customer complaints is the variable.

If there is no relationship between two variables,the correlation coefficient between them would be:

The statistical significance of a regression model is determined by a c² test.

A bivariate statistical technique that is used to measure the strength of the relationship between two variables is called the:

The Pearson product-moment correlation requires what type of scale for the data?

The explanatory power of regression lies in hypothesis testing.

In a correlation matrix,the correlations in the main diagonal are all equal to:

Which of the following is the standard form for reporting observed correlations among multiple variables?

The first step in interpreting simple regression output is to interpret the overall significance of the model.

If the correlation between two variables is - 0.75,this means that:

When the correlation between two variables is +.92,this means that as one variable ,the other variable .

If the correlation coefficient is - 0.62,the coefficient of determination is approximately:

The coefficient of determination reflects the proportion of variance that can be explained by the regression line.

A rule of thumb for R² is that it must be greater than 0.80 for a regression model to be significant.

The Pearson product-moment correlation coefficient ranges between:

The ____ is a measure obtained by squaring the correlation coefficient.