Question 1

A correlation matrix indicates the coefficient of correlation between each pair of variables.

Accepted Answer

A correlation matrix does indeed indicate the coefficient of correlation between each pair of variables.

Question 2

A partial correlation coefficient measures the association between two variables after controlling for or adjusting for the effects of one or more additional variables.

Accepted Answer

This statement is true. A partial correlation coefficient calculates the relationship between two variables while controlling for the influence of other variables.

Question 3

The partial correlation coefficient is generally viewed as more important than the part correlation coefficient.

Accepted Answer

Partial correlation coefficient measures the strength of the relationship between two variables while controlling for the effect of one or more additional variables, thus giving a more accurate picture of the true relationship between the variables. Hence, it is considered more important than the simple correlation coefficient.

Question 4

Because r indicates the degrees to which variation in one variable is related to variation in another,it can also be expressed in terms of the decomposition of the total variation.

Accepted Answer

This statement is true. The coefficient of correlation (r) measures the strength and direction of the linear relationship between two variables. It can also be expressed in terms of the proportion of variation in one variable that is related to variation in the other variable, which is the decomposition of the total variation.

Question 5

Regression analysis is concerned with the nature and degree of association between variables and does not imply or assume any causality.

Accepted Answer

Regression analysis is a statistical method used to explore the relationship between variables, however, it cannot establish causality between them. It only measures the degree and direction of association.

Question 6

The covariance may be either positive or negative.

Accepted Answer

This statement is true. The covariance measures the degree of association between two variables, and it can be positive if the variables tend to move together or negative if they tend to move in opposite directions.

Question 7

In the absence of ties,Kendall's τ yields a closer approximation to the Pearson product moment correlation coefficient,ǫ,than Spearman's ǫs.

Accepted Answer

Kendall's τ and Spearman's ρ are both rank-based correlation measures, but neither is inherently closer to Pearson's correlation coefficient, which measures linear relationships. The choice between Kendall's τ and Spearman's ρ depends on the data and context.

Question 8

The product moment correlation,r,is the most widely used statistic summarizing the strength of association between two metric (interval or ordinal scaled)variable,say X and Y.

Accepted Answer

The product moment correlation, r, is used for summarizing the strength of association between two metric (interval or ratio scaled) variables, not ordinal scaled variables. For ordinal data, Spearman's rank correlation is more appropriate.

Question 9

If the nonmetric variables are nominal and numeric,Spearman's rho and Kendall's tau are two measures of nonmetric correlation that can be used to examine the correlation between them.

Accepted Answer

Spearman's rho and Kendall's tau are measures of rank correlation and are used for ordinal data, not for nominal data which does not have a meaningful order.

Question 10

The product moment correlation helps us determine the strength of the association between two metric variables.Regression analysis helps us determine which variables cause a change in other variables.

Accepted Answer

The answer of The product moment correlation helps us determine...

Question 11

The product moment correlation,r²,is an index used to determine whether a linear,or straight-line,relationship exists between X and Y.It indicates the degree to which the variation in one variable,X,is related to the variation in another variable,Y.

Accepted Answer

The product moment correlation is denoted by "r", not "r²". "r²" is the coefficient of determination, which indicates the proportion of variance in one variable that is predictable from the other variable.

Question 12

Both r and r² are symmetric measures of association.In other words,the correlation of X and Y is the same as the correlation of Y and X.

Accepted Answer

Both r and r² are Pearson correlation coefficients, which are symmetric measures of association. Symmetric measures of association mean that the correlation between two variables X and Y is the same whether we compute the correlation of X and Y or the correlation of Y and X. Therefore, the statement is true.

Question 13

In bivariate regression,the null hypothesis is that no linear relationship exists between X and Y,or H₀: β₁ = 0.

Accepted Answer

The null hypothesis in bivariate regression states that the slope coefficient (β1) is zero, indicating no linear relationship between the independent variable X and the dependent variable Y.

Question 14

The correlation coefficient between two variables varies depending on their underlying units of measurement.

Accepted Answer

The correlation coefficient is a unitless measure that is unaffected by the units of measurement of the variables.

Question 15

The partial correlation coefficient is a measure of the correlation between Y and X when the linear effects of the other independent variables have been removed from X but not from Y.

Accepted Answer

The partial correlation coefficient is a measure of the correlation between two variables (e.g., Y and X) after removing the effects of other variables from both Y and X, not just from one of them.

Question 16

The estimated parameter b is usually referred to as the non-standardized regression coefficient.

Accepted Answer

The estimated parameter b in regression analysis is referred to as the non-standardized or unstandardized regression coefficient because it reflects the change in the dependent variable for a one-unit change in the independent variable without being adjusted for the scale of the variables.

Question 17

The order associated with a partial correlation indicates how many variables are being adjusted or controlled.

Accepted Answer

The order associated with a partial correlation represents the number of variables being adjusted for or controlled in the analysis.

Question 18

When determining the correlation coefficient,r,it does matter which variable is considered to be the dependent variable and which is the independent.

Accepted Answer

The correlation coefficient, r, is not affected by which variable is considered to be the dependent or independent variable. The coefficient only measures the strength and direction of the linear relationship between two variables.

Question 19

When determining the statistical significance of the relationship between two variables measured by using r,the hypotheses to be tested are H₀: ρ = 0 and H₁:ρ ≠ 0

Accepted Answer

This statement is true as the null hypothesis (H₀) is that the correlation coefficient (ρ) is equal to 0 and the alternative hypothesis (H₁) is that ρ is not equal to 0.

Question 20

Regression analysis models helped Avon realize that employee benefits and the appointment fee that representatives pay for materials were significant variables affecting the decline in their sales staff.

Accepted Answer

Regression analysis models helped Avon identify the significance of employee benefits and appointment fees on the decline in sales staff.

Quiz 17: Correlation and Regression