As part of the study underlying Example 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 = b0 + b1D(Plausible) + b2 D(Stretch) + b2 D(Outrageous) + b3 Gullible + e
Why would this regression be better than the ANOVA regression used in Example 1?