Question

Variables in Wooldridge's data set (description):
Cross-sectional data set from Wooldridge
1. return % change stock price, 90-94
2. dkr debt/capital, 1990
3. eps earnings per share, 1990
4. netinc net income, 1990 (millions $)
5. salary CEO salary, 1990 (thousands $)
Dataset:
return	dkr	eps	netinc	salary
-20.84211	4	48.1	1144	1090
-9.138381	27.3	-85.3	35	1923
86.21795	36.8	-44.1	127	1012
131.8367	46.4	192.4	367	579
-8.189655	36.2	-60.4	214	600
-26.00733	18.7	-79.8	118	735
52.27273	34.4	39	175	994
-36.10315	57.8	-62.8	1692	1227
3.508772	33.4	-16.2	157	913
28.61953	33.4	-19.1	315	733
-21.62162	16.7	12.8	407	1247
6.574394	18.3	-34.8	165	925
100.6061	27.6	-8.6	288	602
-5.21327	27.3	9.5	147	1006
-27.6	35	19.3	177	593
-33.33333	12.3	59.5	1845	3142
-43.35938	53.9	12.8	1013	1893
32.14286	33.2	9	829	1740
-6.603774	19.9	5	475	1558
-7.03125	31.4	2.7	230	1095
2.564103	14.5	2.6	335	1235
3.361345	0	16	63	569
-5.779335	32.9	-42.6	1537	930
-65	36.1	9.1	228	940
-9.666667	6.6	20.6	174	926
64.38849	20.4	-3.4	191	756
-20.93023	41.8	13.4	4237	2969
50.53078	40.2	43.5	1131	3836
5.109489	10.9	13.9	66	477
104.5685	69.9	4.3	282	2600
-27.22513	68.1	-54.4	151	1182
-35.07194	25.7	8.6	229	930
-52.02206	4.2	15.7	939	1165
-58.97436	26.7	28.8	24	357
-41.62791	34.1	13.8	1207	1704
-47.88462	18.2	15.7	127	1336
-20.12987	10.7	-42.1	217	1345
63.48315	3.8	-1.8	290	578
-0.6423983	15.2	5.8	522	932
-12.10191	1.5	14.2	64	518
59.9359	12.7	4.6	613	1769
-10.81081	15.5	4.2	474	1942
-24.9467	28.9	5	27	1416
-7.925408	0	7.9	113	729
-46.75325	22.9	-30.5	147	1081
-18.7056	40.1	20.8	138	1123
-17.57576	33.3	-5.7	112	1048
43.54166	2.8	11.9	156	773
-8.333333	26.5	0.8	114	763
-37.31343	13.8	6.6	204	1191
6.918239	51.3	-2.5	208	727
16.10942	46.6	-65.1	317	947
9.405941	17.9	266.6	1383	3667
-58.92857	24.5	17.6	824	11338
4.651163	19	-61.6	211	1017
-8.709826	28.7	-26.3	415	1434
-30.52326	21.7	17.9	290	918
-36.57143	18	6.7	76	780
-2.506964	29.3	11.9	178	842
-33.0091	3.6	6.9	1305	1275
-5.084746	15.4	29.8	103	1064
-21.76871	5.5	17.2	130	725
-8.641975	35.5	-17.5	1525	2262
-34.05904	23.8	-49.9	1349	1359
21.5	13.5	3	3940	1550
34.42361	16.3	-7.7	1724	1872
-29.66361	22.3	-89.3	8	488
1.698514	25.6	-49.9	1349	1938
-8.403361	51.3	-21.1	337	1186
-15.13158	44.9	27.4	249	1300
-9.6	44.3	18.1	540	1338
14.95327	26.3	-31.2	115	4206
3.125	1	19.9	122	832
-18.76641	17.8	16.7	474	1147
6.932773	12	-16.4	395	1278
-30.08048	23.7	-8.9	879	1249
-8.704062	35.1	-10.9	361	2146
34.62783	14.6	-11.2	265	574
-37.44395	33.7	19.3	233	1814
10.6383	0	6.8	475	2193
19.38775	6.5	13.9	216	778
-50.31446	4	11.1	399	2332
111.3757	2.1	-13.1	739	1366
-21.91235	20.1	-22.9	4150	2011
-29.74138	0	60.9	317	1162
-44.75806	14.9	81.3	76	267
72.92577	45.9	-62.4	220	1190
-22.51462	8.1	90.2	186	1101
2.544529	9.1	23.9	517	1494
47.42268	61.9	-22.4	460	1500
33.40708	27.4	-11.7	743	1444
32.31292	36.1	-29.3	157	549
35.7466	50.6	-68.7	206	647
-13.63636	32.7	-5.8	169	552
40.17857	18.3	17.4	147	806
52.4173	50.9	10.6	341	783
-11.74377	20.2	12.6	1593	1439
-44.82143	0	-68	21	740
-84.8881	30.6	15.6	502	1033
-70.2957	21.1	16.2	327	1356
-6.766917	29.8	-61.3	123	537
22.41379	27.4	-0.4	387	1300
17.84141	35.4	-88.2	23	1030
22.04969	1.8	20.2	185	1188
6.476399	11.9	4.5	184	424
52.77778	46.3	88.5	265	1283
5.483029	32.2	-50.1	90	799
-47.74775	13.9	17.4	220	694
-20.96154	8.9	10.3	152	598
25.59727	44.8	45.4	152	1587
-48.02868	32.2	20.1	379	1836
-30.81232	2.1	6.7	388	1212
12.75168	34.9	-22.5	101	300
-38.65979	28.8	-11.7	738	997
-6.684492	12.2	13.2	175	917
-42.43903	25	3.2	226	767
31.69399	46.2	-15.1	128	581
14.28571	4.1	5.2	205	565
-10.46512	0.2	10.9	125	722
-4.635762	2.4	10.4	76	439
7.97546	79.5	24.3	130	780
-67.5	31.8	20.9	667	1571
-8.091287	6	-30.4	70	526
-22.50804	38.3	11.6	185	752
-40.625	27.9	7.5	1299	1296
-55.2809	34.1	-13.8	1134	1289
2.51938	47.7	19.4	280	1264
-43.42432	30	2.1	1156	960
-36.79061	27.5	2.5	1131	1380
-52.10356	2.2	27.5	191	1222
19.4	2.8	42.3	267	545
107.8947	10.5	16.3	172	14336
52.54902	37.2	-87	4	889
-27.02703	18.8	19.7	65	653
-47.1831	32.4	26.1	757	1630
-55.68513	39.8	16.6	365	334
-23.03665	47.3	-15.9	187	447
-9.40171	40.4	-3.5	524	732
-62.85714	42.5	-5.7	214	506
-31.33047	47.4	-30.1	621	884
-19.14063	37.9	12.6	187	334
38.13814	53.9	45.1	3523	1316

3. Compute the 90%, 95%, and 99% confidence intervals for the intercept. What do you conclude
with respect to the following hypothesis: “If everything else were equal to zero, the predicted
(base) return would be 35%”?

Answer 1

Regression Statistics
Multiple R	0.199
R Square	0.039
Adjusted R Square	0.011
Standard Error	39.193
Observations	142

	Coefficients	Standard Error	t Stat	P-value	Lower 90.0%	Upper 90.0%	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	-14.370	6.894	-2.085	0.039	-25.786	-2.954	-28.002	-0.739	-32.378	3.637
dkr	0.321	0.201	1.595	0.113	-0.012	0.653	-0.077	0.718	-0.204	0.845
eps	0.043	0.078	0.546	0.586	-0.087	0.172	-0.112	0.197	-0.161	0.247
netinc	-0.005	0.005	-1.093	0.276	-0.013	0.003	-0.014	0.004	-0.017	0.007
salary	0.003	0.002	1.595	0.113	0.000	0.007	-0.001	0.008	-0.002	0.009

Confidence intervals for Intercept

90%CI = (-25.786 , -2.954)

95% CI = (-28.002, -0.739)

99%CI = ( - 32.378 , 3.637)

What do you conclude
with respect to the following hypothesis: “If everything else were equal to zero, the predicted
(base) return would be 35%”?

COnclusions:-

with 90% confidence level

We can reject the given hypothesis, because zero is not included in the 90% CI hence we conclude return is not equal to 35% when everything else were equal to zero.

with 95% confidence level

We can reject the given hypothesis, because zero is not included in the 95% CI hence we conclude return is not equal to 35% when everything else were equal to zero.

with 99% Confidence level

We cannot reject the given hypothesis, because zero is included in the 99% CI hence we conclude return is equal to 35% when everything else were equal to zero.

But as the 99% CI does not contain 35%.