Run linear regressions to determine whether the differences observed between the treatment and control groups are statistically significant? Please note that the regression equation for this particular dataset is: yi = a + bxi+ ei, where i denotes the switchback period (the unit of observation), and xi is a variable equal to 0 for the control group and 1 for the treatment group. The outcome variable of interest is denoted yi. The estimate of b is the difference in the average outcome between the treatment and control groups. Please refer to Question 1 to use the customer experience metrics and efficiency metrics as yi and run the regressions. Please note that 7 regressions need to be conducted. Please report a summary (table) of your regression results and discuss your observations.

city_id	period_start	wait_time	treat	commute	trips_pool	trips_express	rider_cancellations	total_driver_payout	total_matches	total_double_matches	total_trips	cost_per_trip	match_rate	double_match_rate
Boston	2/19/2018 7:00	2 mins	FALSE	TRUE	1415	3245	256	34458.41	3372	1476	4660	7.394508934	0.72360515	0.316738197
Boston	2/19/2018 9:40	5 mins	TRUE	FALSE	1461	2363	203	29764.35	2288	1275	3824	7.783564284	0.59832636	0.333420502
Boston	2/19/2018 12:20	2 mins	FALSE	FALSE	1362	2184	118	27437.37	2283	962	3546	7.737554248	0.643824027	0.271291596
Boston	2/19/2018 15:00	5 mins	TRUE	TRUE	1984	3584	355	44995.45	4035	2021	5568	8.08107992	0.724676724	0.362966954
Boston	2/19/2018 17:40	2 mins	FALSE	FALSE	1371	2580	181	27583.96	2200	979	3951	6.98151235	0.556821058	0.247785371
Boston	2/19/2018 20:20	5 mins	TRUE	FALSE	1401	2022	135	23888.11	2066	1062	3423	6.978706061	0.603564125	0.310254163
Boston	2/19/2018 23:00	2 mins	FALSE	FALSE	1216	2543	103	29642.91	2600	1406	3759	7.885848808	0.691673317	0.374035648
Boston	2/20/2018 1:40	5 mins	TRUE	FALSE	1691	2018	150	25794.87	1918	1281	3709	6.954669701	0.517120518	0.345376112
Boston	2/20/2018 4:20	2 mins	FALSE	FALSE	1248	2481	131	23238.95	2623	1059	3729	6.231951271	0.703405739	0.283990346
Boston	2/20/2018 7:00	5 mins	TRUE	TRUE	1815	2539	284	34047.47	2624	1565	4354	7.819814859	0.602664217	0.359439596
Boston	2/20/2018 9:40	2 mins	FALSE	FALSE	1594	2773	166	28053.36	2723	855	4367	6.42394431	0.623540188	0.195786581
Boston	2/20/2018 12:20	5 mins	TRUE	FALSE	1629	2380	185	25964.42	2477	1322	4009	6.476532528	0.617859815	0.329758044
Boston	2/20/2018 15:00	2 mins	FALSE	TRUE	1640	3290	236	39912.4	3777	1969	4930	8.095821808	0.766125761	0.399391481
Boston	2/20/2018 17:40	5 mins	TRUE	FALSE	1173	1891	144	22029.73	1893	998	3064	7.189861068	0.617819843	0.325718016
Boston	2/20/2018 20:20	2 mins	FALSE	FALSE	1853	2305	159	33299.09	2234	1145	4158	8.008439809	0.537277537	0.275372775
Boston	2/20/2018 23:00	5 mins	TRUE	FALSE	1145	2419	182	25062.18	2214	1104	3564	7.032037797	0.621212121	0.30976431
Boston	2/21/2018 1:40	2 mins	FALSE	FALSE	1490	1949	125	25419.06	1904	1120	3439	7.39141056	0.553649317	0.325676069
Boston	2/21/2018 4:20	5 mins	TRUE	FALSE	1560	2309	180	25104.44	2125	990	3869	6.488613307	0.549237529	0.255880072
Boston	2/21/2018 7:00	2 mins	FALSE	TRUE	1916	3469	245	44871.11	3575	1809	5385	8.332610185	0.663881151	0.335933148
Boston	2/21/2018 9:40	5 mins	TRUE	FALSE	1664	2320	183	27626.14	2344	1309	3984	6.934271082	0.588353414	0.328564257
Boston	2/21/2018 12:20	2 mins	FALSE	FALSE	1039	3188	168	29259.94	3045	1607	4227	6.922151756	0.720369056	0.380175065
Boston	2/21/2018 15:00	5 mins	TRUE	TRUE	1741	3392	290	40452.02	4116	1690	5133	7.880775094	0.801870251	0.329242159
Boston	2/21/2018 17:40	2 mins	FALSE	FALSE	1596	2256	151	30605.28	2280	1480	3852	7.945295039	0.591900312	0.384215992
Boston	2/21/2018 20:20	5 mins	TRUE	FALSE	1408	1638	155	23986.18	1746	754	3046	7.874649373	0.573210768	0.247537754
Boston	2/21/2018 23:00	2 mins	FALSE	FALSE	1248	2561	165	27110.77	2213	1329	3809	7.117556952	0.580992386	0.348910475
Boston	2/22/2018 1:40	5 mins	TRUE	FALSE	1304	2121	157	22830.55	2188	728	3425	6.665854035	0.638832117	0.212554745
Boston	2/22/2018 4:20	2 mins	FALSE	FALSE	1268	2198	118	24991.39	2015	1099	3466	7.210442209	0.5813618	0.317080208
Boston	2/22/2018 7:00	5 mins	TRUE	TRUE	1498	2377	275	28585.28	2656	1442	3875	7.376847249	0.685419355	0.372129032
Boston	2/22/2018 9:40	2 mins	FALSE	FALSE	1519	2060	145	25858.75	2117	836	3579	7.225132336	0.591506007	0.2335848
Boston	2/22/2018 12:20	5 mins	TRUE	FALSE	1744	2276	172	27385.13	2171	1481	4020	6.812222032	0.540049751	0.36840796
Boston	2/22/2018 15:00	2 mins	FALSE	TRUE	1502	4507	350	48600.42	5005	2533	6009	8.08793842	0.832917291	0.421534365
Boston	2/22/2018 17:40	5 mins	TRUE	FALSE	1555	2229	156	24975.7	2085	1488	3784	6.600343456	0.551004228	0.393234672
Boston	2/22/2018 20:20	2 mins	FALSE	FALSE	1620	2243	160	28000.42	2154	959	3863	7.248362162	0.557597722	0.248252653
Boston	2/22/2018 23:00	5 mins	TRUE	FALSE	1021	2540	183	25506.9	2362	1276	3561	7.162846582	0.663296827	0.358326313
Boston	2/23/2018 1:40	2 mins	FALSE	FALSE	987	2015	129	23769.41	1935	742	3002	7.917858349	0.644570286	0.247168554
Boston	2/23/2018 4:20	5 mins	TRUE	FALSE	1324	2054	147	21882.92	2148	1141	3378	6.478069555	0.635879218	0.337773831
Boston	2/23/2018 7:00	2 mins	FALSE	TRUE	1178	3591	228	34077.77	3816	1619	4769	7.145684654	0.80016775	0.339484169
Boston	2/23/2018 9:40	5 mins	TRUE	FALSE	1253	2479	175	26375.1	2592	1555	3732	7.067282794	0.694533762	0.416666667
Boston	2/23/2018 12:20	2 mins	FALSE	FALSE	1640	2664	183	34025.03	2597	1348	4304	7.905444012	0.603392193	0.313197026
Boston	2/23/2018 15:00	5 mins	TRUE	TRUE	1177	3946	333	37418.69	4203	2739	5123	7.304057771	0.820417724	0.534647667
Boston	2/23/2018 17:40	2 mins	FALSE	FALSE	1364	2397	175	24965.47	2433	981	3761	6.637988031	0.64690242	0.260834884
Boston	2/23/2018 20:20	5 mins	TRUE	FALSE	1635	1988	162	28523.28	1745	1389	3623	7.872835542	0.481645046	0.383383936
Boston	2/23/2018 23:00	2 mins	FALSE	FALSE	1371	2467	140	30717.88	2740	1132	3838	8.003617595	0.713913497	0.294945284
Boston	2/24/2018 1:40	5 mins	TRUE	FALSE	1346	2296	174	23742.42	2279	1065	3642	6.519059604	0.62575508	0.292421746
Boston	2/24/2018 4:20	2 mins	FALSE	FALSE	771	2515	95	23565.36	2616	1352	3286	7.171443333	0.796104687	0.411442483
Boston	2/24/2018 7:00	5 mins	TRUE	FALSE	1283	2141	161	20430.22	2238	996	3424	5.966770047	0.653621495	0.29088785
Boston	2/24/2018 9:40	2 mins	FALSE	FALSE	1273	2620	165	29641.44	2612	1104	3893	7.614034174	0.670947855	0.283585923
Boston	2/24/2018 12:20	5 mins	TRUE	FALSE	1598	2565	183	32106.15	2472	1338	4163	7.712263663	0.593802546	0.321402834
Boston	2/24/2018 15:00	2 mins	FALSE	FALSE	1409	2434	132	25026.82	2571	1257	3843	6.51231277	0.669008587	0.327088212
Boston	2/24/2018 17:40	5 mins	TRUE	FALSE	1593	2582	180	27320.55	2365	1291	4175	6.543843971	0.566467066	0.309221557
Boston	2/24/2018 20:20	2 mins	FALSE	FALSE	1201	2666	185	26725.52	2971	1541	3867	6.911176057	0.768295837	0.398500129
Boston	2/24/2018 23:00	5 mins	TRUE	FALSE	930	2437	139	21754.25	2352	1185	3367	6.461017337	0.698544699	0.351945352
Boston	2/25/2018 1:40	2 mins	FALSE	FALSE	1064	2500	101	22153.19	2735	1288	3564	6.215821768	0.767396184	0.361391695
Boston	2/25/2018 4:20	5 mins	TRUE	FALSE	1005	2140	154	22076.64	2299	1250	3145	7.019597852	0.73100159	0.39745628
Boston	2/25/2018 7:00	2 mins	FALSE	FALSE	1745	2496	159	28170.2	2510	1022	4241	6.642348472	0.591841547	0.240980901
Boston	2/25/2018 9:40	5 mins	TRUE	FALSE	1514	3062	194	31142.51	3120	1662	4576	6.805617565	0.681818182	0.363199301
Boston	2/25/2018 12:20	2 mins	FALSE	FALSE	1259	2457	126	28525.79	2304	1106	3716	7.67647806	0.620021529	0.297631862
Boston	2/25/2018 15:00	5 mins	TRUE	FALSE	1587	1914	157	23986.56	1924	1300	3501	6.851344531	0.549557269	0.371322479
Boston	2/25/2018 17:40	2 mins	FALSE	FALSE	1311	2736	176	31276.06	2905	1683	4047	7.728208561	0.717815666	0.415863603
Boston	2/25/2018 20:20	5 mins	TRUE	FALSE	1422	2244	154	25226.18	2222	1114	3666	6.881117055	0.606110202	0.303873432
Boston	2/25/2018 23:00	2 mins	FALSE	FALSE	1259	3292	168	31725.5	3209	1857	4551	6.971105885	0.705119754	0.408042189
Boston	2/26/2018 1:40	5 mins	TRUE	FALSE	1435	1996	173	24969.84	1871	1157	3431	7.277715082	0.545322064	0.33721947
Boston	2/26/2018 4:20	2 mins	FALSE	FALSE	1401	2371	146	26992.55	2365	814	3772	7.156031115	0.626988335	0.215800636
Boston	2/26/2018 7:00	5 mins	TRUE	TRUE	1739	2762	289	38010.25	3112	1391	4501	8.444844609	0.691401911	0.309042435
Boston	2/26/2018 9:40	2 mins	FALSE	FALSE	1251	2234	128	25681.26	2167	1198	3485	7.36908434	0.621807747	0.343758967
Boston	2/26/2018 12:20	5 mins	TRUE	FALSE	1414	2515	194	28686.21	2457	1482	3929	7.301147312	0.625349962	0.377195215
Boston	2/26/2018 15:00	2 mins	FALSE	TRUE	1474	2905	197	33547.23	2810	1049	4379	7.66093446	0.641699018	0.239552409
Boston	2/26/2018 17:40	5 mins	TRUE	FALSE	1499	2928	218	23572.38	2972	1814	4427	5.324684529	0.67133499	0.409758301
Boston	2/26/2018 20:20	2 mins	FALSE	FALSE	1548	2225	166	25184.9	2422	1236	3773	6.675032113	0.641929499	0.327590777
Boston	2/26/2018 23:00	5 mins	TRUE	FALSE	1923	2525	190	29670.23	2747	1417	4448	6.67046645	0.617580935	0.318570144
Boston	2/27/2018 1:40	2 mins	FALSE	FALSE	1005	2608	160	26605.25	2727	1177	3613	7.363755837	0.754774426	0.32576806
Boston	2/27/2018 4:20	5 mins	TRUE	FALSE	1412	1867	164	19163.21	1588	1420	3279	5.844222365	0.484293992	0.433058859
Boston	2/27/2018 7:00	2 mins	FALSE	TRUE	1473	3800	279	41714.54	4060	2034	5273	7.910968401	0.769960174	0.385738669
Boston	2/27/2018 9:40	5 mins	TRUE	FALSE	1364	2055	188	22526.41	2083	1196	3419	6.588595511	0.609242469	0.349809886
Boston	2/27/2018 12:20	2 mins	FALSE	FALSE	1121	2280	103	23695.54	2232	949	3401	6.96722728	0.656277565	0.279035578
Boston	2/27/2018 15:00	5 mins	TRUE	TRUE	1249	3638	289	32674.14	3842	1686	4887	6.685930961	0.786167383	0.344996931
Boston	2/27/2018 17:40	2 mins	FALSE	FALSE	990	2668	121	24063.37	2541	1055	3658	6.578285147	0.694641881	0.288408967
Boston	2/27/2018 20:20	5 mins	TRUE	FALSE	1473	2243	170	25668.43	2306	1229	3716	6.907542077	0.620559742	0.33073197
Boston	2/27/2018 23:00	2 mins	FALSE	FALSE	1674	1932	173	27881.7	1885	1211	3606	7.732030521	0.522739878	0.335829174
Boston	2/28/2018 1:40	5 mins	TRUE	FALSE	829	2419	173	18769.99	2183	1657	3248	5.778938728	0.672105911	0.510160099
Boston	2/28/2018 4:20	2 mins	FALSE	FALSE	1053	2273	141	22713.8	2224	1397	3326	6.829163732	0.668671076	0.420024053
Boston	2/28/2018 7:00	5 mins	TRUE	TRUE	1385	3043	307	34278.22	3439	1985	4428	7.741242097	0.7766486	0.44828365
Boston	2/28/2018 9:40	2 mins	FALSE	FALSE	1481	2742	166	30141.76	2686	1321	4223	7.137522688	0.636040729	0.312810798
Boston	2/28/2018 12:20	5 mins	TRUE	FALSE	1174	2137	157	26216.06	2201	1032	3311	7.917868828	0.664753851	0.311688312
Boston	2/28/2018 15:00	2 mins	FALSE	TRUE	1716	3851	289	44887.99	4229	2001	5567	8.063228702	0.75965511	0.359439555
Boston	2/28/2018 17:40	5 mins	TRUE	FALSE	1419	2534	163	28329.33	2495	988	3953	7.166538337	0.631166203	0.249936757
Boston	2/28/2018 20:20	2 mins	FALSE	FALSE	1529	2604	159	30528.6	2545	1237	4133	7.386547454	0.615775466	0.299298331
Boston	2/28/2018 23:00	5 mins	TRUE	FALSE	1557	1915	154	24718.48	1806	1419	3472	7.119378605	0.52016129	0.408698157
Boston	3/1/2018 1:40	2 mins	FALSE	FALSE	1075	2500	168	24732.11	2606	1274	3575	6.918071455	0.728951049	0.356363636
Boston	3/1/2018 4:20	5 mins	TRUE	FALSE	1099	2517	144	25928.74	2327	1637	3616	7.170559622	0.643528761	0.452710177
Boston	3/1/2018 7:00	2 mins	FALSE	TRUE	1482	3217	185	38605.55	3404	1864	4699	8.215695575	0.724409449	0.396680145
Boston	3/1/2018 9:40	5 mins	TRUE	FALSE	1875	2361	207	31795.24	2269	1227	4236	7.505959417	0.535646837	0.289660057
Boston	3/1/2018 12:20	2 mins	FALSE	FALSE	1377	2953	156	30318.06	2561	1854	4330	7.001861381	0.591454965	0.42817552
Boston	3/1/2018 15:00	5 mins	TRUE	TRUE	1742	3349	320	34639.93	3240	1858	5091	6.80415105	0.636417207	0.364957769
Boston	3/1/2018 17:40	2 mins	FALSE	FALSE	1957	2524	200	32913.81	2689	1044	4481	7.345192297	0.600089266	0.232983709
Boston	3/1/2018 20:20	5 mins	TRUE	FALSE	1492	2437	162	27966.58	2367	1429	3929	7.11798925	0.60244337	0.363705778
Boston	3/1/2018 23:00	2 mins	FALSE	FALSE	1202	1949	121	25286.4	2050	735	3151	8.024880678	0.650587115	0.233259283
Boston	3/2/2018 1:40	5 mins	TRUE	FALSE	1292	1961	171	20078.31	2174	1284	3253	6.172244708	0.668306179	0.394712573
Boston	3/2/2018 4:20	2 mins	FALSE	FALSE	1270	1845	133	23459.27	2028	1000	3115	7.531065667	0.651043339	0.321027287
Boston	3/2/2018 7:00	5 mins	TRUE	TRUE	1069	3212	290	32340.82	3477	1701	4281	7.554502082	0.812193413	0.397337071
Boston	3/2/2018 9:40	2 mins	FALSE	FALSE	1293	2235	139	28041.73	2288	1031	3528	7.948335725	0.648526077	0.29223356
Boston	3/2/2018 12:20	5 mins	TRUE	FALSE	1782	2090	152	26964.73	2021	1420	3872	6.964032622	0.521952479	0.366735537
Boston	3/2/2018 15:00	2 mins	FALSE	TRUE	1389	3400	204	34568.8	3845	1589	4789	7.218375229	0.802881604	0.331802046
Boston	3/2/2018 17:40	5 mins	TRUE	FALSE	1425	2459	170	24389.91	2513	1233	3884	6.279584785	0.647013388	0.317456231
Boston	3/2/2018 20:20	2 mins	FALSE	FALSE	1390	2091	174	25019.77	1928	1119	3481	7.187524171	0.553863832	0.321459351
Boston	3/2/2018 23:00	5 mins	TRUE	FALSE	2241	2031	197	29304.25	1962	1133	4272	6.859609849	0.459269663	0.265215356
Boston	3/3/2018 1:40	2 mins	FALSE	FALSE	1414	2287	151	31954.65	2003	1315	3701	8.634057641	0.54120508	0.355309376
Boston	3/3/2018 4:20	5 mins	TRUE	FALSE	1355	2501	180	31204.88	2432	1405	3856	8.09255066	0.630705394	0.36436722
Boston	3/3/2018 7:00	2 mins	FALSE	FALSE	1348	2471	145	28158.74	2075	1464	3819	7.373327631	0.543335952	0.383346426
Boston	3/3/2018 9:40	5 mins	TRUE	FALSE	1710	2732	169	28075.73	2921	1698	4442	6.320515131	0.657586673	0.382260243
Boston	3/3/2018 12:20	2 mins	FALSE	FALSE	1165	2453	193	23013.78	2361	820	3618	6.360913217	0.652570481	0.226644555
Boston	3/3/2018 15:00	5 mins	TRUE	FALSE	1630	2081	159	26807.74	1980	978	3711	7.223857902	0.533548909	0.263540825
Boston	3/3/2018 17:40	2 mins	FALSE	FALSE	1302	3110	170	29810.33	3080	1838	4412	6.756647089	0.698096102	0.416591115
Boston	3/3/2018 20:20	5 mins	TRUE	FALSE	1324	2158	125	27884.23	2208	1373	3482	8.008108137	0.634118323	0.394313613
Boston	3/3/2018 23:00	2 mins	FALSE	FALSE	1103	2403	136	23997.49	2498	1032	3506	6.844692073	0.712492869	0.294352539
Boston	3/4/2018 1:40	5 mins	TRUE	FALSE	1087	2225	145	22757.18	2267	1055	3312	6.871129749	0.684480676	0.318538647
Boston	3/4/2018 4:20	2 mins	FALSE	FALSE	1156	2254	132	31600.01	2177	1304	3410	9.266866024	0.638416422	0.382404692
Boston	3/4/2018 7:00	5 mins	TRUE	FALSE	1515	2059	129	22995.16	1828	1063	3574	6.434012032	0.51147174	0.297425853
Boston	3/4/2018 9:40	2 mins	FALSE	FALSE	1151	2793	193	29426.91	2732	1752	3944	7.461183974	0.692697769	0.444219067
Boston	3/4/2018 12:20	5 mins	TRUE	FALSE	1818	1970	204	24339.58	1974	1510	3788	6.425444446	0.521119324	0.398627244
Boston	3/4/2018 15:00	2 mins	FALSE	FALSE	1393	2301	161	28015.26	2179	882	3694	7.583989606	0.589875474	0.238765566
Boston	3/4/2018 17:40	5 mins	TRUE	FALSE	1718	2655	173	28288.52	2600	1361	4373	6.468904905	0.594557512	0.31122799
Boston	3/4/2018 20:20	2 mins	FALSE	FALSE	1303	2334	158	27072.61	2164	940	3637	7.443664106	0.594995876	0.25845477
Boston	3/4/2018 23:00	5 mins	TRUE	FALSE	1157	2359	154	23525.12	2323	1473	3516	6.690874844	0.66069397	0.41894198
Boston	3/5/2018 1:40	2 mins	FALSE	FALSE	1170	2240	131	23005.27	2257	900	3410	6.746413569	0.661876833	0.263929619
Boston	3/5/2018 4:20	5 mins	TRUE	FALSE	1360	2421	196	26017.53	2361	1015	3781	6.881122989	0.624437979	0.268447501