Question 1

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 determine the relationship between one or more independent variables and a dependent variable. It only shows the association or correlation between the variables and does not establish causation. Therefore, regression analysis does not assume or imply any causality.

Question 2

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 identify that employee benefits and appointment fees were significant variables impacting sales staff decline for Avon.

Question 3

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

Accepted Answer

The order of a partial correlation indicates how many variables are being controlled for. For example, a partial correlation between variables A and B, controlling for variable C, would have an order of 3 (A, B, and C are all included in the analysis).

Question 4

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

Accepted Answer

Kendall's τ and Spearman's ρ are both rank correlation coefficients and measure the strength and direction of association between two ranked variables. However, neither is specifically closer to Pearson's ρ in all situations, as their approximation to Pearson's ρ depends on the distribution and relationship of the data. Pearson's ρ measures linear relationships between variables on an interval or ratio scale, while Kendall's τ and Spearman's ρ are non-parametric measures that do not assume a linear relationship or normally distributed data.

Question 5

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 6

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 7

The covariance may be either positive or negative.

Accepted Answer

The covariance is a measure of the linear relationship between two variables. It can be positive when both variables tend to increase or decrease together, or negative when one variable tends to increase while the other decreases. Therefore, the statement is true.

Question 8

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

Accepted Answer

The partial correlation coefficient measures the degree of association between two variables while controlling for the effects of one or more additional variables. It is generally considered more important than the partial correlation coefficient, which only measures the association between two variables without considering the effects of other variables.

Question 9

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 10

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

Accepted Answer

This is the correct null hypothesis for bivariate regression.

Question 11

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 12

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 13

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 is true as the null hypothesis (H₀: ρ = 0) assumes that there is no significant relationship between the two variables (i.e. correlation coefficient is zero) and the alternative hypothesis (H₁:ρ ≠ 0) assumes that there is a significant relationship (i.e. correlation coefficient is not equal to zero). The significance level and p-value will determine whether the null hypothesis can be rejected or not.

Question 14

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 as r, the correlation coefficient, measures the strength and direction of the linear relationship between two variables, and it can be expressed as the ratio of the covariance between the variables to the product of their standard deviations. Therefore, it can also be used to describe the proportion of variation in one variable that is explained by the other variable, and it can be expressed in terms of the decomposition of the total variation.

Question 15

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 coefficient, typically denoted as r, indeed measures the strength and direction of a linear relationship between two variables, X and Y. However, the notation "r²" does not accurately represent any standard notation for this coefficient. The correct notation is simply "r".

Question 16

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 17

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

This statement is true. Both r and r² are symmetric measures of association, meaning the correlation between X and Y is the same as the correlation between Y and X.

Question 18

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

Accepted Answer

The correlation coefficient between two variables is a unitless measure, meaning it is not affected by the units of measurement used for each variable.

Question 19

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 is a correct definition of partial correlation coefficient.

Question 20

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

Accepted Answer

A correlation matrix displays the numerical value of the coefficient of correlation between each pair of variables.

Quiz 17: Correlation and Regression