Question

the top figure shows a path model relating three variables. 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.

the bottom figure shows four sets of linear relationships among variables (a through d).

which set of linear relationships corresponds to the path model?

a. set a
b. set b
c. set c
d. set d

Explanation:

Analyze the path model relationships

The top figure shows a path model with three variables: \(x\), \(y\), and \(z\).

• The arrow from \(x\) to \(y\) has a plus sign (\(+\)) above it, indicating a positive Linear Relationship between \(x\) and \(y\). As \(x\) increases, \(y\) increases (positive slope).
• The arrow from \(y\) to \(z\) has a plus sign (\(+\)) above it, indicating a positive Linear Relationship between \(y\) and \(z\). As \(y\) increases, \(z\) increases (positive slope).

Evaluate the graph sets

We need to find the set of graphs (A through D) where:

1. The first graph (relating \(x\) on the horizontal axis to \(y\) on the vertical axis) has a positive slope.
2. The second graph (relating \(y\) on the horizontal axis to \(z\) on the vertical axis) has a positive slope.

Let's inspect the options:

• Set A:
• Graph 1 (\(y\) vs \(x\)): Positive slope (starts low, goes up to the right).
• Graph 2 (\(z\) vs \(y\)): Positive slope (starts low, goes up to the right).
• Set B:
• Graph 1 (\(y\) vs \(x\)): Negative slope (starts high, goes down to the right).
• Graph 2 (\(z\) vs \(y\)): Positive slope.
• Set C:
• Graph 1 (\(y\) vs \(x\)): Positive slope.
• Graph 2 (\(z\) vs \(y\)): Negative slope.
• Set D:
• Graph 1 (\(y\) vs \(x\)): Negative slope.
• Graph 2 (\(z\) vs \(y\)): Negative slope.

Determine the correct choice

Using our understanding of Path Models, both relationships are positive (\(+\)). Therefore, both linear graphs must show a positive slope. This corresponds to Set A.

Answer:

• a. Set A (Correct answer)
• b. Set B
• c. Set C
• d. Set D