(Requires StatTools) Run a series of multiple regressions of Y versus all potential 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 contains 7 of the 8 X's, and the only variable missing has a correlation less than 0.04 (in magnitude) with Y.

b. 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.

c. 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 0.002.

d. All of these choices are true.

Y	X1	X2	X3	X4	X5	X6	X7	X8
76	240	379	226	332	324	233	99	579
92	243	387	223	210	324	208	105	454
89	229	336	221	233	319	210	103	542
77	252	456	221	261	310	234	94	410
72	265	483	227	257	373	231	95	461
61	279	514	218	291	442	248	93	607
78	235	432	224	300	344	211	85	400
61	271	446	220	351	422	246	84	520
63	276	417	225	337	425	252	84	448
87	241	460	221	229	323	212	95	396
79	223	474	219	310	328	240	102	507
80	257	301	219	305	345	204	96	363
75	258	421	213	324	334	249	102	458
86	234	384	224	249	339	232	103	530
83	225	404	226	255	341	231	94	516
83	238	264	221	343	316	190	90	504
81	251	310	222	236	343	228	98	489
90	222	351	221	272	351	194	100	537
86	236	360	227	303	313	225	98	474
68	256	370	218	239	378	244	79	614
73	247	534	223	331	359	199	92	526
79	257	344	224	258	365	218	96	497
74	237	308	223	252	365	246	92	629
109	194	316	224	201	311	201	110	389
82	248	437	224	281	306	235	101	408
83	225	409	222	269	377	209	99	384
85	246	313	217	240	328	219	100	514
95	231	381	226	231	314	185	105	451
95	215	305	227	207	356	226	104	377
67	231	365	220	254	417	257	92	606
72	243	444	224	325	340	217	92	598
63	272	576	226	279	392	239	91	572
99	235	295	226	259	303	233	106	483
104	221	375	219	202	291	183	106	476
86	242	321	222	294	318	199	104	470
65	253	441	224	288	402	250	81	562
62	274	355	216	334	366	259	88	538
96	211	339	226	263	321	201	103	339
88	246	343	225	221	349	215	98	560
80	232	430	224	227	348	238	100	420
91	229	377	224	265	302	213	97	469
98	220	480	222	185	334	181	108	455
69	261	428	222	370	387	239	100	519
94	227	292	225	283	304	214	103	368
100	226	347	218	192	307	232	106	295
71	247	399	226	298	383	243	91	444
65	270	463	225	296	363	252	85	437
81	246	415	220	218	353	222	101	513
87	218	433	221	170	354	215	98	557
69	269	328	223	316	346	235	82	553
88	237	395	222	231	336	236	109	536
66	254	405	226	290	389	243	78	555
75	234	382	223	306	409	207	96	490
88	224	456	215	189	332	228	101	441
93	260	273	223	195	315	186	97	427
77	255	423	225	242	329	241	100	511
97	232	286	222	215	321	230	107	413
74	257	359	221	321	382	227	102	546
70	261	492	216	277	379	250	91	392
102	208	411	225	244	326	177	107	528
73	245	419	219	226	374	244	90	434
67	264	465	227	314	391	208	87	550
90	244	389	226	246	337	205	102	371
125	211	284	223	196	308	168	110	432
85	262	332	217	206	318	203	97	491
91	248	257	221	249	335	202	104	533
70	259	497	220	234	399	220	87	494
66	259	401	214	299	414	255	94	577
79	245	372	221	275	331	211	94	424
93	217	324	220	217	350	232	106	352
60	266	486	227	347	438	258	77	466
59	268	558	221	289	451	245	75	592
81	227	451	218	278	326	242	99	417
71	243	527	225	308	384	216	86	497
70	236	498	224	293	430	241	97	544
64	253	471	222	329	411	221	83	569
69	254	546	223	273	371	224	83	586
67	249	357	225	354	397	238	87	585
72	250	368	228	302	361	236	93	567
84	239	390	227	223	347	226	101	478
76	250	476	225	245	357	247	101	438
111	204	299	225	180	297	206	105	333
106	213	317	223	266	296	196	107	301
64	275	523	216	287	375	229	88	596
78	239	407	220	268	360	213	88	405
100	216	325	216	159	352	192	111	549
63	266	508	222	319	404	254	90	509
75	242	503	225	285	387	197	93	481
82	241	392	219	270	357	223	95	423
70	267	347	219	317	369	224	93	448
74	251	439	223	275	368	222	95	486
66	263	449	220	261	405	253	89	503
93	228	366	222	263	330	195	108	575
84	238	330	225	250	361	223	104	380
77	263	363	223	283	342	227	97	473
76	252	396	218	241	394	216	96	463
80	233	337	227	313	338	237	99	500
73	255	424	224	307	370	220	89	523
102	221	281	220	222	300	221	105	353
106	230	352	217	211	312	189	108	321