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 graphs

Using the Linear Relationships knowledge point

• The first graph shows "Variable \(y\)" on the vertical axis and "Variable \(x\)" on the horizontal axis. The line has a positive slope, indicating a positive relationship between \(x\) and \(y\) (\(+\)).
• The second graph shows "Variable \(z\)" on the vertical axis and "Variable \(y\)" on the horizontal axis. The line has a negative slope, indicating a negative relationship between \(y\) and \(z\) (\(-\)).

Evaluate the path models

Using the Path Models knowledge point

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

Comparing these to our findings, the correct path model must have a \(+\) sign from \(x\) to \(y\) and a \(-\) sign from \(y\) to \(z\). This matches Model C.

Answer:

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