Researchers are interested in identifying if completion of a summer individualized remedial program for 160 eighth graders (coded 1 for completion, 0 if not), which is the outcome, is related to several predictor variables. The predictor variables include student aptitude, an award for good behavior given by teachers during the school year (coded 1 if received, 0 if not), and age. Use these results to address the questions that appear at the end of the output.

For the model with the Intercept only: −2 LL = 219.300

For the model with predictors: −2 LL = 160.278

Logistic Regression Estimates
				Odds ratio
Variable (coefficient)	β(SE)	Wald chi-square test	p value	Estimate	95% CI
Aptitude (β 1 )	.138(.028)	23.376	.000	1.148	[1.085, 1.213]
Award (β 2 )	3.062(.573)	28.583	.000	21.364	[6.954, 65.639]
Age (β 3 )	1.307(.793)	2.717	.099	3.694	[.781, 17.471]
Constant	-22.457(8.931)	6.323	.012	.000

Cases Having Standardized Residuals > |2|
Case	Observed Outcome	Predicted Probability	Residual	Pearson
22	0	.951	-.951	-4.386
33	1	.873	-.873	-2.623
90	1	.128	.872	2.605
105	0	.966	-.966	-5.306

Classification Results (With Cut Value of .05)
	Predicted
Observed	Dropped out	Completed	Total	Percent correct
Dropped out	50	20	70	71.4
Completed	11	79	90	87.8
Total				80.6

Complete the following:

a. Report and interpret the test result for the overall null hypothesis.

b. Compute and interpret the odds ratio for a 10-point increase in aptitude.

c. Interpret the odds ratio for the award variable.

d. Determine the number of outliers that appear to be present.

e. Describe how you would implement the Box–Tidwell procedure with these data.

f. Assuming that classification is a study goal, list the percent of cases correctly classified by the model, compute and interpret the proportional reduction in classification errors due to the model, and compute the binomial d test to determine if a reduction in classification errors is present in the population.

g. What statistical assumptions must be met to use logistic regression?