Question

the top figure shows a set of linear relationships among three variables.

the bottom figure shows four path models (a through d). each variable is represented by a solid black box. an arrow connecting one box to another indicates a relationship between two variables. the sign above an arrow (+ or -) indicates whether the variables are positively or negatively related.

which path model accurately describes the relationships among the three variables?

a. model a
b. model b
c. model c
d. model d
e. i do not know the answer.

Explanation:

Analyze the linear relationships

Using the Linear Relationships knowledge point

• The first graph plots Variable \(y\) (vertical axis) against Variable \(x\) (horizontal axis). The line has a negative slope, meaning \(x\) and \(y\) are negatively related: \(x \xrightarrow{-} y\).
• The second graph plots Variable \(z\) (vertical axis) against Variable \(y\) (horizontal axis). The line has a negative slope, meaning \(y\) and \(z\) are negatively related: \(y \xrightarrow{-} z\).

Evaluate the path models

Using the Path Models and Causal Diagrams knowledge points

• Model A shows \(x \xrightarrow{+} y\) and \(y \xrightarrow{+} z\).
• Model B shows \(x \xrightarrow{-} y\) and \(y \xrightarrow{+} z\).
• Model C shows \(x \xrightarrow{+} y\) and \(y \xrightarrow{-} z\).
• Model D shows \(x \xrightarrow{-} y\) and \(y \xrightarrow{-} z\).

Since both relationships are negative, Model D is the correct representation.

Answer:

• a. Model A
• b. Model B
• c. Model C
• d. Model D (Correct answer)
• e. I do not know the answer.