Y	X1	X2	X3	X4	X5	X6	X7	X8
29	301	181	234	76	260	232	472	296
19	293	138	204	73	312	237	377	325
25	310	217	211	70	278	232	461	190
32	318	190	239	81	248	239	633	240
21	290	157	200	85	280	239	583	322
33	297	243	230	72	245	241	467	205
36	339	214	264	89	245	238	365	282
35	332	218	247	51	248	238	353	268
35	319	212	262	76	245	241	553	305
36	340	228	262	64	253	240	505	275
34	292	245	268	60	249	240	399	207
23	276	196	211	63	277	241	587	264
26	279	151	251	81	272	231	355	294
33	290	229	273	72	255	239	542	240
22	271	160	230	91	285	237	433	301
33	328	221	241	50	256	240	535	289
33	334	146	270	60	252	237	514	255
35	324	223	250	62	247	238	490	315
30	298	199	244	86	265	238	599	312
33	331	171	244	69	249	239	438	267
32	313	195	253	101	251	239	665	229
31	311	184	266	52	273	240	650	292
27	296	153	249	79	268	233	485	272
30	302	148	264	107	253	240	513	219
30	326	231	252	76	289	235	551	299
25	312	200	219	91	292	239	575	247
28	287	209	233	69	262	240	567	245
23	279	129	229	82	264	237	444	306
28	321	141	240	58	279	241	326	279
28	290	199	232	82	267	238	272	269
31	305	165	223	84	247	240	471	284
35	316	179	269	67	246	240	691	254
23	266	166	224	99	274	239	510	277
32	319	237	222	73	251	240	607	266
33	300	232	258	65	250	239	550	198
25	288	163	216	53	270	241	389	252
36	320	263	286	55	252	239	430	221
36	296	209	271	88	244	240	337	328
30	273	201	257	57	253	233	543	260
37	342	247	267	95	246	236	522	293
34	323	205	275	73	255	240	498	296
25	280	179	225	74	256	222	426	238
31	317	211	256	74	267	240	536	169
27	284	170	243	80	262	226	545	309
30	308	174	255	84	254	232	479	237
26	278	192	238	87	276	241	528	273
23	275	135	214	77	256	237	379	258
32	314	187	265	66	259	235	445	271
28	303	182	228	83	268	236	556	319
28	295	177	235	84	259	236	580	270
20	252	156	217	71	288	241	560	217
24	265	184	248	70	287	237	501	309
27	295	182	219	85	258	236	417	242
19	262	131	242	68	300	235	493	222
38	347	226	279	63	247	236	409	314
27	270	167	237	97	252	235	519	224
24	294	144	208	70	263	235	313	281
22	312	122	205	66	271	230	561	244
29	308	219	243	46	282	236	507	282
28	283	172	231	75	254	240	421	248
31	304	180	274	59	265	234	476	250
31	315	225	235	71	257	234	592	210
26	299	201	206	79	261	237	462	232
34	309	206	251	74	244	238	610	289
30	324	196	236	66	259	229	528	227
27	273	191	245	61	262	238	480	227
34	305	215	246	65	247	241	415	274
18	259	161	210	79	309	239	394	290
31	307	239	261	93	266	227	603	256
28	282	204	246	74	264	233	630	304
29	263	250	253	60	275	237	367	263
22	246	162	217	68	270	237	488	261
29	316	208	238	75	270	229	403	231
29	291	193	241	62	261	231	517	257
35	336	185	285	63	249	238	496	214
33	329	222	240	58	258	238	598	286
32	301	177	282	57	265	239	384	331
31	275	189	260	78	249	239	484	287
20	257	148	213	77	273	239	540	249
26	288	187	259	80	291	236	407	241
25	282	213	227	89	282	236	458	247
24	268	169	222	95	263	240	637	235
32	309	233	237	92	251	228	581	259
27	304	193	234	55	283	241	613	225
27	306	206	215	90	273	240	428	261
29	294	176	248	67	254	231	565	216
29	287	255	226	92	260	234	569	233
22	277	159	227	78	284	235	450	251
25	283	158	254	69	295	240	503	298
17	267	142	198	71	304	234	526	340
24	286	189	223	86	281	233	619	194
32	325	151	256	88	250	239	642	319
34	300	236	277	80	259	237	572	302
30	328	154	258	87	269	235	531	265
21	258	203	221	63	297	238	455	212
31	322	216	233	68	255	232	451	278
26	298	168	229	82	276	240	466	279
24	285	168	220	77	267	235	622	202
37	334	197	293	56	243	234	441	285
30	315	174	249	64	257	238	590	234

(Requires StatTools) Run a series of multiple regressions of Y versus the X's as follows. Start with an equation that has all of the X's. Then if any X has a p-value greater than 0.10, run another regression without the variable that has the largest p-value. Keep running regressions, always deleting the variable with the largest p-value, until all of the remaining p-values are less than 0.10. Which of the following is true?

Click here to reference the data needed to answer the question.

a. The final equation has a standard error of estimate greater than the standard error of estimate for the equation with all of the X's, but the difference is less than 0.10.

b. The final equation contains 6 of the 8 X's, and the two variables missing both have a correlation less than 0.20 (in magnitude) with Y.

c. The final equation has an R-square value less than the R-square value for the equation with all of the X's, but the difference is less than 0.001.

d. All of these choices are true.

Please explain why option A is correct