In an important study of college graduation rates of all high school matriculants and Black-only matriculants, Bowen and Bok obtained the results in the following table, based on the logit model.*

a. What general conclusion do you draw about graduation rates of all matriculants and black only matriculants?

b. The odds ratio is the ratio of two odds. Compare two groups of all matriculants, one with a SAT score of greater than 1,299 and the other with a SAT score of less than 1,000 (the base category). The odds ratio of 1.393 means the odds of matriculants in the first category graduating from college are 39 percent higher than those in the latter category. Do the various odds ratios shown in the table accord with a priori expectations?

c. What can you say about the statistical significance of the estimated parameters? What about the overall significance of the estimated model?

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All Matriculants Black Only Odds Ratio Parameter Estimate Parameter Standard Standard Odds Variable Estimate Error Error Ratio 0.112 Intercept Female 0.957 0.052 0.455 1.303 0.280 0.031 1.323 0.265 0.101 Black -0.513 0.056 0.599 0.080 0.055 0.104 0.705 Hispanic -0.350 Asian 0.122 1.130 Other race -0.330 0.719 SAT > 1,299 SAT 1,200–1,299 SAT 1,100–1,199 SAT 1,000–1,099 SAT not available 0.331 0.059 1.393 0.128 0.248 1.137 0.253 0.055 1.288 0.232 0.179 1.261 0.350 0.053 1.420 0.308 0.149 1.361 1.211 0.719 0.192 0.054 0.141 0.136 1.151 -0.330 0.127 0.048 0.349 1.050 Top 10% of high school class High school class rank not available 0.036 0.342 1.407 0.315 0.117 1.370 -0.065 0.046 0.937 -0.065 0.148 0.937 High socioeconomic status (SES) Low SES SES not available 0.283 0.036 1.327 0.557 0.175 1.746 -0.385 0.079 0.680 0.143 0.737 -0.305 0.110 0.050 1.116 0.031 0.172 1.031 2.979 1.212 SEL-1 1.092 0.058 0.712 0.161 2.038 SEL-2 0.280 0.193 0.036 0.119 1.323 Women's college 0.069 0.742 -0.299 0.158 0.269 1.171 Number of observations 32,524 2,354 -2 log likelihood Restricted 31,553 30,160 1,393 with 18 d.f. 2,667 2,569 98 with 14 d.f. Unrestricted Chi square