Refer to Scenario 8-1. You can see from the information in (1) that Charlie got a lot more education than the average person. When compared to the average person, the standardized regression model predicts that

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The prompt asks us to refer to Scenario 8-1 and compare Charlie’s education level to the average person, noting that the standardized regression model makes a prediction about how Charlie’s wealth relates to his education.

Option provided: "He will be less rich than he is well-educated."

Analytical note: In most standardized regression models that examine the relationship between education and wealth, education is positively associated with wealth. That is, higher education levels tend to predict higher income or wealth after accounting for other factors. Therefore, when someone has substantially more education than the average person, the model would typically predict that this person is not less rich than someone with less education, but rather more rich, all else equal.

Reason this option is unlikely: It asserts a negative or counterintuitive relationship (more education leading to being less rich than the well-educated person), which goes against the common positive association between education and wealth in many regressions. It also conflates being well-educated with wealth in a way that contradicts the usual interpretation of the education–wealth slope.

What to consider about model interpretation: If Charlie’s education is unusually high, the regression line for wealth as a function of education would generally slope upward, predicting higher wealth with higher education, unless there are strong confounders or nonlinearity not captured by the model. However, the statement in the option focuses on being "less rich" relative to being well-educated, which is an awkward phrasing and inconsistent with a straightforward positive relationship.

Because the option reflects a negative expectation about wealth given high education, and given the typical positive association between education and wealth in regression analyses, this choice is not supported by standard interpretations of such a model. If there were other options, we would compare them similarly by evaluating whether each statement aligns with the direction and magnitude of the education–wealth relationship implied by the standardized regression.

Statistics 8.1 Quick Quiz - The Standardized Regression Line

Refer to Scenario 8-1. You can see from the information in (1) that Charlie got a lot more education than the average person. When compared to the average person, the standardized regression model predicts that

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