et's practice time-series forecasting of new home sales. Click here (https://www.census.gov/construction/nrs/historical_data/index.html) to see the newest data in the first table: Houses Sold (Excel file is sold_cust.xls). Look at the monthly data on the "Reg Sold" tab. If you have trouble with the link, I have recreated the data in moodle in the Excel file "A3Q3 Census Housing Data."

Only keep the dates beginning in January 2004, so delete the earlier observations, and use the data through September 2021. Keep only the US data, both the seasonally unadjusted monthly (column B) and the seasonally adjusted annual (column G). Make a new column of seasonally adjusted monthly by dividing the annual data by 12. Make a column called "t" where t will go from 1 (Jan. 2004) to 213 (September 2021); make a t² column too (since, if you look at the data, you can see sales are U-shaped; hence the quadratic). Also make a column "D" that is a dummy variable equal to one during the spring and summer months of March through August.

Determine the correlation between the unadjusted and the adjusted monthly data (=CORREL(unadjust., adjust.) in Excel), and produce scatterplots (with straight lines) of both. Do you think making a seasonal adjustment will be useful, given what you observe at this point?

Run four regressions:

1) seasonally unadjusted monthly as the dependent, and t and t² as the independents,

2) seasonally unadjusted monthly as the dependent, and t, t², and D as the independents,

3) seasonally adjusted monthly as the dependent, and t and t² as the independents,

4) seasonally adjusted monthly as the dependent, and t, t², and D as the independents.

Discuss your findings, and determine which of the four models is the best for forecasting new home sales. When interpreting your p-values, remember that, say, 1.0E-08 is 1.0 * 10^-8, which is 0.00000001. State the equation that would be used to forecast sales.

date	US NSA month	US SA year	seasonally adjusted monthly rate	t	t^2
Jan-04	89	1165	97.08	1	1
Feb-04	102	1159	96.58	2	4
Mar-04	123	1276	106.33	3	9
Apr-04	109	1186	98.83	4	16
May-04	115	1241	103.42	5	25
Jun-04	105	1180	98.33	6	36
Jul-04	96	1088	90.67	7	49
Aug-04	102	1175	97.92	8	64
Sep-04	94	1214	101.17	9	81
Oct-04	101	1305	108.75	10	100
Nov-04	84	1179	98.25	11	121
Dec-04	83	1242	103.50	12	144
Jan-05	92	1203	100.25	13	169
Feb-05	109	1319	109.92	14	196
Mar-05	127	1328	110.67	15	225
Apr-05	116	1260	105.00	16	256
May-05	120	1286	107.17	17	289
Jun-05	115	1274	106.17	18	324
Jul-05	117	1389	115.75	19	361
Aug-05	110	1255	104.58	20	400
Sep-05	99	1244	103.67	21	441
Oct-05	105	1336	111.33	22	484
Nov-05	86	1214	101.17	23	529
Dec-05	87	1239	103.25	24	576
Jan-06	89	1174	97.83	25	625
Feb-06	88	1061	88.42	26	676
Mar-06	108	1116	93.00	27	729
Apr-06	100	1123	93.58	28	784
May-06	102	1086	90.50	29	841
Jun-06	98	1074	89.50	30	900
Jul-06	83	965	80.42	31	961
Aug-06	88	1035	86.25	32	1024
Sep-06	80	1016	84.67	33	1089
Oct-06	74	941	78.42	34	1156
Nov-06	71	1003	83.58	35	1225
Dec-06	71	998	83.17	36	1296
Jan-07	66	891	74.25	37	1369
Feb-07	68	828	69.00	38	1444
Mar-07	80	833	69.42	39	1521
Apr-07	83	887	73.92	40	1600
May-07	79	842	70.17	41	1681
Jun-07	73	793	66.08	42	1764
Jul-07	68	778	64.83	43	1849
Aug-07	60	699	58.25	44	1936
Sep-07	53	686	57.17	45	2025
Oct-07	57	727	60.58	46	2116
Nov-07	45	641	53.42	47	2209
Dec-07	44	619	51.58	48	2304
Jan-08	44	627	52.25	49	2401
Feb-08	48	593	49.42	50	2500
Mar-08	49	535	44.58	51	2601
Apr-08	49	536	44.67	52	2704
May-08	49	504	42.00	53	2809
Jun-08	45	487	40.58	54	2916
Jul-08	43	477	39.75	55	3025
Aug-08	38	435	36.25	56	3136
Sep-08	35	433	36.08	57	3249
Oct-08	32	393	32.75	58	3364
Nov-08	27	389	32.42	59	3481
Dec-08	26	377	31.42	60	3600
Jan-09	24	336	28.00	61	3721
Feb-09	29	372	31.00	62	3844
Mar-09	31	339	28.25	63	3969
Apr-09	32	337	28.08	64	4096
May-09	34	376	31.33	65	4225
Jun-09	37	393	32.75	66	4356
Jul-09	38	411	34.25	67	4489
Aug-09	36	418	34.83	68	4624
Sep-09	30	386	32.17	69	4761
Oct-09	33	396	33.00	70	4900
Nov-09	26	375	31.25	71	5041
Dec-09	24	352	29.33	72	5184
Jan-10	24	345	28.75	73	5329
Feb-10	27	336	28.00	74	5476
Mar-10	36	381	31.75	75	5625
Apr-10	41	422	35.17	76	5776
May-10	26	280	23.33	77	5929
Jun-10	28	305	25.42	78	6084
Jul-10	26	283	23.58	79	6241
Aug-10	23	282	23.50	80	6400
Sep-10	25	317	26.42	81	6561
Oct-10	23	291	24.25	82	6724
Nov-10	20	287	23.92	83	6889
Dec-10	23	326	27.17	84	7056
Jan-11	21	307	25.58	85	7225
Feb-11	22	270	22.50	86	7396
Mar-11	28	300	25.00	87	7569
Apr-11	30	310	25.83	88	7744
May-11	28	305	25.42	89	7921
Jun-11	28	301	25.08	90	8100
Jul-11	27	296	24.67	91	8281
Aug-11	25	299	24.92	92	8464
Sep-11	24	304	25.33	93	8649
Oct-11	25	316	26.33	94	8836
Nov-11	23	328	27.33	95	9025
Dec-11	24	341	28.42	96	9216
Jan-12	23	335	27.92	97	9409
Feb-12	30	366	30.50	98	9604
Mar-12	34	354	29.50	99	9801
Apr-12	34	354	29.50	100	10000
May-12	35	370	30.83	101	10201
Jun-12	34	360	30.00	102	10404
Jul-12	33	369	30.75	103	10609
Aug-12	31	375	31.25	104	10816
Sep-12	30	385	32.08	105	11025
Oct-12	29	358	29.83	106	11236
Nov-12	28	392	32.67	107	11449
Dec-12	28	399	33.25	108	11664
Jan-13	32	446	37.17	109	11881
Feb-13	36	447	37.25	110	12100
Mar-13	41	444	37.00	111	12321
Apr-13	43	441	36.75	112	12544
May-13	40	428	35.67	113	12769
Jun-13	43	470	39.17	114	12996
Jul-13	33	375	31.25	115	13225
Aug-13	31	381	31.75	116	13456
Sep-13	31	403	33.58	117	13689
Oct-13	36	444	37.00	118	13924
Nov-13	32	446	37.17	119	14161
Dec-13	31	433	36.08	120	14400
Jan-14	33	443	36.92	121	14641
Feb-14	35	420	35.00	122	14884
Mar-14	39	405	33.75	123	15129
Apr-14	39	403	33.58	124	15376
May-14	43	451	37.58	125	15625
Jun-14	38	418	34.83	126	15876
Jul-14	35	402	33.50	127	16129
Aug-14	36	456	38.00	128	16384
Sep-14	37	470	39.17	129	16641
Oct-14	38	476	39.67	130	16900
Nov-14	31	442	36.83	131	17161
Dec-14	35	497	41.42	132	17424
Jan-15	39	515	42.92	133	17689
Feb-15	45	540	45.00	134	17956
Mar-15	46	480	40.00	135	18225
Apr-15	48	502	41.83	136	18496
May-15	47	502	41.83	137	18769
Jun-15	44	480	40.00	138	19044
Jul-15	43	506	42.17	139	19321
Aug-15	41	518	43.17	140	19600
Sep-15	35	456	38.00	141	19881
Oct-15	39	482	40.17	142	20164
Nov-15	36	504	42.00	143	20449
Dec-15	38	546	45.50	144	20736
Jan-16	39	505	42.08	145	21025
Feb-16	45	517	43.08	146	21316
Mar-16	50	532	44.33	147	21609
Apr-16	55	576	48.00	148	21904
May-16	53	571	47.58	149	22201
Jun-16	50	557	46.42	150	22500
Jul-16	54	628	52.33	151	22801
Aug-16	46	575	47.92	152	23104
Sep-16	44	558	46.50	153	23409
Oct-16	46	575	47.92	154	23716
Nov-16	40	571	47.58	155	24025
Dec-16	39	561	46.75	156	24336
Jan-17	45	578	48.17	157	24649
Feb-17	51	601	50.08	158	24964
Mar-17	61	643	53.58	159	25281
Apr-17	56	604	50.33	160	25600
May-17	57	627	52.25	161	25921
Jun-17	56	612	51.00	162	26244
Jul-17	48	553	46.08	163	26569
Aug-17	45	550	45.83	164	26896
Sep-17	50	622	51.83	165	27225
Oct-17	49	625	52.08	166	27556
Nov-17	50	718	59.83	167	27889
Dec-17	45	658	54.83	168	28224
Jan-18	48	610	50.83	169	28561
Feb-18	54	644	53.67	170	28900
Mar-18	66	680	56.67	171	29241
Apr-18	61	658	54.83	172	29584
May-18	62	680	56.67	173	29929
Jun-18	56	598	49.83	174	30276
Jul-18	52	600	50.00	175	30625
Aug-18	47	582	48.50	176	30976
Sep-18	46	584	48.67	177	31329
Oct-18	43	546	45.50	178	31684
Nov-18	44	618	51.50	179	32041
Dec-18	38	566	47.17	180	32400
Jan-19	49	628	52.33	181	32761
Feb-19	57	675	56.25	182	33124
Mar-19	68	721	60.08	183	33489
Apr-19	64	689	57.42	184	33856
May-19	56	619	51.58	185	34225
Jun-19	66	711	59.25	186	34596
Jul-19	55	636	53.00	187	34969
Aug-19	57	677	56.42	188	35344
Sep-19	56	706	58.83	189	35721
Oct-19	55	703	58.58	190	36100
Nov-19	50	700	58.33	191	36481
Dec-19	49	733	61.08	192	36864
Jan-20	59	756	63.00	193	37249
Feb-20	63	730	60.83	194	37636
Mar-20	59	623	51.92	195	38025
Apr-20	52	582	48.50	196	38416
May-20	64	704	58.67	197	38809
Jun-20	79	839	69.92	198	39204
Jul-20	85	972	81.00	199	39601
Aug-20	81	977	81.42	200	40000
Sep-20	77	971	80.92	201	40401
Oct-20	78	969	80.75	202	40804
Nov-20	61	865	72.08	203	41209
Dec-20	63	943	78.58	204	41616
Jan-21	77	993	82.75	205	42025
Feb-21	70	823	68.58	206	42436
Mar-21	83	873	72.75	207	42849
Apr-21	74	796	66.33	208	43264
May-21	65	733	61.08	209	43681
Jun-21	61	683	56.92	210	44100
Jul-21	63	712	59.33	211	44521
Aug-21	57	702	58.50	212	44944
Sep-21	65	800	66.67	213	45369