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 top figure relationships

The top figure shows two plots representing linear relationships:

1. The first plot has \(x\) on the horizontal axis and \(y\) on the vertical axis, showing a line with a positive slope. This indicates a positive relationship between \(x\) and \(y\) (\(x \xrightarrow{+} y\)).
2. The second plot has \(y\) on the horizontal axis and \(z\) on the vertical axis, showing a line with a positive slope. This indicates a positive relationship between \(y\) and \(z\) (\(y \xrightarrow{+} z\)).

Evaluate the path models

Let's examine the four path models (A through D) shown in the bottom figure:

• 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 \(y \xrightarrow{-} z\).

Match the correct model

Since both relationships (\(x\) to \(y\) and \(y\) to \(z\)) are positive, the correct path model must have positive signs (\(+\)) above both arrows. This corresponds exactly to Model A.

Answer:

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