Over the past few years the percentage of students who leave Dana College at the end of their first year has increased. Last year, Dana started voluntary one-credit hour-long seminars with faculty to help first-year students establish an on-campus connection. If Dana is able to show that the seminars have a positive effect on retention, college administrators will be convinced to continue funding this initiative. Dana’s administration also suspects that first-year students with lower high school GPAs have a higher probability of leaving Dana at the end of the first year. The file Dana contains data on the 500 first-year students from last year. Each observation consists of a first-year student’s high school GPA, whether they enrolled in a seminar, and whether they dropped out and did not return to Dana. Apply logistic regression to classify observations as dropped out or not dropped out by using GPA and Seminar as input variables and Dropped as the output variable.

a) Evaluate the candidate logistic regression models based on their predictive performance on the validation set. Recommend a final model and express the model as a mathematical equation relating the output variable to the input variables. What is the implication on the effectiveness of the first-year seminars on retention?

b) The data analyst team realized that they jumped directly into building a predictive model without exploring the data. Using descriptive statistics and charts, investigate any relationships in the data that may explain the unsatisfactory result in part (a). For next year’s first-year class, what could Dana’s administration do regarding the enrollment of the seminars to better determine whether they have an effect on retention?

Student	GPA	Seminar	Dropped
1	3.78	1	0
2	3.22	0	0
3	2.69	0	1
4	3.12	0	0
5	2.96	0	1
6	2.47	0	0
7	2.37	0	0
8	2.76	0	1
9	3.10	0	0
10	2.86	0	0
11	2.62	0	0
12	3.07	0	0
13	3.30	0	0
14	2.43	0	1
15	2.98	0	1
16	2.63	0	0
17	2.68	0	1
18	2.62	0	1
19	2.82	1	0
20	2.38	0	0
21	3.33	0	0
22	2.33	0	1
23	2.93	0	1
24	3.06	0	0
25	3.98	1	0
26	2.88	0	0
27	3.12	0	0
28	3.12	0	0
29	3.38	0	0
30	3.29	1	0
31	3.49	1	0
32	2.89	0	0
33	2.77	0	0
34	2.61	0	1
35	3.10	0	0
36	3.06	1	0
37	2.61	0	1
38	2.91	1	0
39	2.49	0	1
40	3.45	0	0
41	2.93	0	1
42	2.22	0	1
43	2.51	0	1
44	3.71	1	0
45	2.11	0	1
46	2.87	0	0
47	2.64	1	0
48	3.04	0	0
49	2.54	0	1
50	2.57	0	0
51	3.85	0	0
52	2.53	0	0
53	3.20	1	0
54	3.12	0	0
55	2.90	0	0
56	3.27	0	0
57	2.73	0	1
58	2.70	0	1
59	2.29	0	0
60	2.34	0	0
61	3.40	0	0
62	2.62	0	0
63	2.62	1	0
64	2.64	0	0
65	2.14	0	0
66	3.06	0	0
67	2.83	0	1
68	3.35	1	0
69	3.33	0	0
70	2.16	0	0
71	2.40	0	0
72	2.51	0	0
73	2.86	1	0
74	3.12	0	0
75	3.38	1	0
76	2.82	1	0
77	3.04	0	0
78	2.78	0	0
79	2.74	0	0
80	2.02	0	0
81	2.56	0	0
82	3.48	0	0
83	2.64	0	1
84	2.63	0	0
85	2.11	0	0
86	3.03	0	0
87	2.33	0	0
88	2.01	0	0
89	2.94	0	1
90	3.81	1	0
91	2.68	0	0
92	2.58	0	0
93	2.70	1	0
94	2.75	0	1
95	2.53	0	0
96	3.08	0	1
97	2.78	0	0
98	3.23	0	0
99	3.17	0	0
100	2.40	0	0
101	3.27	1	0
102	2.57	0	1
103	3.64	1	0
104	3.03	0	0
105	2.77	0	1
106	2.85	0	1
107	2.91	0	1
108	2.93	0	0
109	3.17	0	0
110	3.45	0	0
111	2.64	1	0
112	3.02	0	0
113	2.90	1	1
114	2.31	0	0
115	2.70	0	1
116	2.24	0	0
117	3.08	0	0
118	3.12	0	0
119	2.59	1	0
120	2.86	0	0
121	2.70	0	0
122	3.78	1	0
123	3.40	0	0
124	3.46	0	0
125	2.77	0	0
126	2.11	0	0
127	2.86	0	0
128	2.33	0	0
129	3.64	1	0
130	3.07	1	0
131	3.23	0	0
132	2.63	0	0
133	2.41	0	0
134	3.50	0	0
135	3.42	0	0
136	2.69	0	1
137	2.99	0	0
138	3.23	0	0
139	2.63	0	0
140	2.79	0	0
141	2.17	0	0
142	2.68	0	1
143	3.37	0	0
144	3.31	0	0
145	2.93	0	1
146	2.93	1	0
147	2.17	0	0
148	2.26	0	0
149	2.79	0	0
150	2.25	0	0
151	2.47	0	0
152	2.88	0	0
153	2.79	0	1
154	3.19	0	0
155	2.66	0	0
156	2.19	0	0
157	2.13	0	0
158	3.15	1	1
159	2.41	0	0
160	2.84	0	0
161	2.85	0	0
162	3.03	0	1
163	3.10	0	0
164	2.57	0	0
165	3.01	0	0
166	3.01	1	0
167	2.81	0	1
168	2.82	0	1
169	3.02	1	0
170	2.46	0	0
171	2.63	1	0
172	2.96	1	1
173	2.57	0	0
174	2.24	0	0
175	2.62	0	0
176	3.59	1	0
177	3.53	1	0
178	2.14	0	0
179	2.90	0	0
180	3.78	1	0
181	2.92	0	1
182	2.17	0	0
183	2.41	0	0
184	2.68	1	0
185	2.19	0	0
186	2.46	0	0
187	3.10	0	0
188	2.82	1	1
189	2.29	0	0
190	2.72	1	0
191	2.10	0	0
192	2.54	1	0
193	2.70	0	0
194	3.48	1	0
195	2.77	0	1
196	2.67	1	0
197	2.21	0	0
198	2.61	0	0
199	3.42	0	0
200	3.47	0	0
201	2.49	0	0
202	2.62	0	1
203	2.27	0	0
204	2.64	0	0
205	2.60	1	1
206	2.31	0	0
207	3.00	0	0
208	2.48	0	0
209	3.65	1	0
210	2.01	0	0
211	3.67	1	0
212	2.32	0	0
213	2.94	1	1
214	3.42	0	0
215	3.87	1	0
216	2.71	0	0
217	3.90	1	0
218	2.79	0	0
219	2.19	0	0
220	3.01	1	0
221	3.29	0	0
222	2.41	0	0
223	3.46	0	0
224	2.58	1	0
225	2.48	0	0
226	2.64	1	0
227	2.59	0	0
228	2.16	0	0
229	3.48	0	0
230	2.94	0	0
231	2.92	0	1
232	3.41	0	0
233	3.64	1	0
234	2.73	0	0
235	3.06	1	0
236	3.03	0	0
237	2.28	0	0
238	2.72	1	0
239	2.85	0	0
240	3.42	0	0
241	2.16	0	0
242	2.88	0	0
243	2.10	0	0
244	2.94	0	0
245	2.66	1	1
246	2.44	0	0
247	2.18	0	0
248	2.69	1	1
249	2.93	0	1
250	2.82	0	0
251	2.97	1	0
252	2.43	0	0
253	3.69	1	0
254	3.21	0	0
255	3.05	0	1
256	2.66	0	1
257	3.25	0	0
258	2.82	0	0
259	3.34	1	0
260	3.75	1	0
261	3.14	1	0
262	2.46	0	0
263	3.39	0	0
264	3.14	0	0
265	2.52	0	0
266	3.37	0	0
267	3.67	1	0
268	3.55	1	0
269	3.36	0	0
270	2.10	0	0
271	2.47	0	0
272	2.86	0	1
273	3.25	0	0
274	2.89	1	0
275	2.78	1	1
276	3.21	1	0
277	2.83	1	0
278	3.24	0	0
279	2.26	0	0
280	2.89	0	1
281	2.88	1	1
282	2.60	0	0
283	2.24	0	0
284	2.74	0	0
285	3.14	1	0
286	2.71	1	1
287	2.62	1	0
288	3.41	0	0
289	2.66	0	1
290	2.75	0	0
291	2.74	0	0
292	3.91	1	0
293	3.23	0	1
294	2.53	1	1
295	3.05	0	0
296	2.72	0	0
297	2.38	0	0
298	2.46	0	0
299	2.59	0	0
300	2.66	0	0
301	2.85	0	0
302	3.05	0	0
303	3.84	0	0
304	3.53	1	0
305	3.08	1	0
306	2.95	0	0
307	2.61	1	1
308	2.95	1	0
309	3.10	0	0
310	2.83	0	0
311	3.26	0	0
312	3.34	0	0
313	3.50	0	0
314	2.35	0	0
315	2.34	0	0
316	2.16	0	0
317	2.67	1	1
318	2.49	0	0
319	2.86	1	1
320	3.01	0	0
321	2.99	0	1
322	3.03	0	0
323	3.85	0	0
324	2.55	0	0
325	2.62	0	1
326	2.87	1	0
327	3.74	1	0
328	2.86	0	0
329	2.81	0	0
330	3.11	1	0
331	2.65	0	0
332	2.05	0	0
333	3.09	0	0
334	2.56	0	1
335	2.12	0	0
336	3.11	0	0
337	2.42	0	0
338	2.21	0	1
339	2.93	0	0
340	2.67	0	0
341	2.38	0	1
342	3.35	0	0
343	3.48	0	0
344	2.94	0	0
345	2.70	0	1
346	2.82	1	0
347	2.65	1	0
348	2.28	0	1
349	2.66	0	0
350	2.19	0	1
351	3.16	0	0
352	3.62	1	0
353	2.40	0	0
354	3.01	0	0
355	2.77	0	1
356	3.64	1	0
357	3.77	0	0
358	2.67	0	0
359	2.40	0	0
360	3.41	1	0
361	2.79	0	0
362	3.20	0	0
363	3.53	1	0
364	2.68	0	0
365	2.57	0	0
366	3.17	0	0
367	2.85	0	0
368	3.71	1	0
369	3.19	0	0
370	2.94	0	1
371	2.91	0	1
372	2.80	0	0
373	2.89	1	1
374	2.32	0	0
375	2.75	0	0
376	3.30	0	0
377	3.22	0	1
378	2.08	0	0
379	3.87	1	0
380	2.16	0	0
381	2.95	0	0
382	2.39	0	0
383	2.75	0	0
384	2.17	0	0
385	3.13	0	0
386	2.82	0	1
387	2.68	1	0
388	2.83	0	0
389	3.14	0	1
390	4.00	1	0
391	3.80	1	0
392	2.54	0	0
393	2.40	0	0
394	2.01	0	0
395	3.05	0	1
396	3.16	0	0
397	3.15	0	0
398	2.24	0	1
399	3.41	1	0
400	2.75	1	0
401	2.99	0	0
402	3.04	0	0
403	2.10	0	0
404	2.90	0	0
405	2.72	0	0
406	2.69	0	0
407	3.20	0	0
408	2.85	0	0
409	2.46	0	0
410	2.40	0	0
411	3.14	1	0
412	2.49	0	1
413	3.67	1	0
414	2.54	0	0
415	2.65	0	0
416	3.38	0	0
417	3.16	0	0
418	2.77	0	1
419	3.01	0	0
420	3.04	0	0
421	2.72	0	1
422	3.48	0	0
423	2.60	0	0
424	3.32	0	0
425	4.00	1	0
426	2.80	0	1
427	2.44	0	1
428	3.25	0	1
429	2.99	0	0
430	2.79	1	0
431	3.33	0	0
432	3.68	1	0
433	3.65	1	0
434	2.50	0	1
435	3.05	0	0
436	2.16	0	1
437	2.35	0	0
438	2.77	0	0
439	3.25	0	0
440	2.56	0	1
441	2.68	0	0
442	3.06	0	0
443	2.47	0	0
444	2.35	0	0
445	2.95	0	0
446	2.83	0	1
447	2.57	0	0
448	2.40	0	0
449	3.31	0	0
450	2.46	0	0
451	2.14	0	0
452	3.41	0	1
453	3.03	0	0
454	2.81	0	1
455	2.42	0	0
456	2.08	0	0
457	3.61	1	0
458	2.86	0	0
459	2.15	0	0
460	2.63	0	0
461	2.80	1	1
462	2.16	0	0
463	2.61	0	0
464	2.71	0	1
465	3.65	1	0
466	2.65	1	1
467	3.10	0	0
468	2.63	0	1
469	2.36	0	0
470	2.52	0	0
471	2.74	0	1
472	2.03	0	0
473	2.63	0	0
474	2.84	1	1
475	2.58	0	1
476	2.17	0	0
477	2.42	0	0
478	2.85	0	0
479	3.91	1	0
480	2.55	1	0
481	2.72	1	0
482	2.65	0	0
483	3.41	0	0
484	2.53	0	0
485	3.29	0	0
486	2.65	0	0
487	2.75	0	0
488	2.25	0	0
489	2.69	0	0
490	3.25	1	0
491	3.62	1	0
492	2.63	0	0
493	2.59	1	0
494	3.17	0	0
495	3.26	0	0
496	3.06	0	0
497	2.13	0	0
498	2.33	0	0
499	2.85	0	0
500	3.17	0	0