As part of the study underlying Example 26.1, each customer took a test that measures willingness to believe claims, producing a numerical score called Gullible. If the customers had not been randomly assigned, an analyst planned to fit the regression model

Credibility = β₀ + β₁D(Plausible) + β₂ D(Stretch) + β₂ D(Outrageous) + β₃ Gullible + ε

Why would this regression be better than the ANOVA regression used in Example 26.1?