Let'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 2005, so delete the earlier observations, and use the data through December 2023. 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. 2005) to 228 (December 2023); make a t² column too (since, if you look at the data, you can see sales are somewhat 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, and 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.

Month	US NSA month	US SA month	T	T2	D
Jan-05	92	100.25	1	1	0
Feb-05	109	109.92	2	4	0
Mar-05	127	110.67	3	9	1
Apr-05	116	105.00	4	16	1
May-05	120	107.17	5	25	1
Jun-05	115	106.17	6	36	1
Jul-05	117	115.75	7	49	1
Aug-05	110	104.58	8	64	1
Sep-05	99	103.67	9	81	1
Oct-05	105	111.33	10	100	0
Nov-05	86	101.17	11	121	0
Dec-05	87	103.25	12	144	0
Jan-06	89	97.83	13	169	0
Feb-06	88	88.42	14	196	0
Mar-06	108	93.00	15	225	1
Apr-06	100	93.58	16	256	1
May-06	102	90.50	17	289	1
Jun-06	98	89.50	18	324	1
Jul-06	83	80.42	19	361	1
Aug-06	88	86.25	20	400	1
Sep-06	80	84.67	21	441	1
Oct-06	74	78.42	22	484	0
Nov-06	71	83.58	23	529	0
Dec-06	71	83.17	24	576	0
Jan-07	66	74.25	25	625	0
Feb-07	68	69.00	26	676	0
Mar-07	80	69.42	27	729	1
Apr-07	83	73.92	28	784	1
May-07	79	70.17	29	841	1
Jun-07	73	66.08	30	900	1
Jul-07	68	64.83	31	961	1
Aug-07	60	58.25	32	1024	1
Sep-07	53	57.17	33	1089	1
Oct-07	57	60.58	34	1156	0
Nov-07	45	53.42	35	1225	0
Dec-07	44	51.58	36	1296	0
Jan-08	44	52.25	37	1369	0
Feb-08	48	49.42	38	1444	0
Mar-08	49	44.58	39	1521	1
Apr-08	49	44.67	40	1600	1
May-08	49	42.00	41	1681	1
Jun-08	45	40.58	42	1764	1
Jul-08	43	39.75	43	1849	1
Aug-08	38	36.25	44	1936	1
Sep-08	35	36.08	45	2025	1
Oct-08	32	32.75	46	2116	0
Nov-08	27	32.42	47	2209	0
Dec-08	26	31.42	48	2304	0
Jan-09	24	28.00	49	2401	0
Feb-09	29	31.00	50	2500	0
Mar-09	31	28.25	51	2601	1
Apr-09	32	28.08	52	2704	1
May-09	34	31.33	53	2809	1
Jun-09	37	32.75	54	2916	1
Jul-09	38	34.25	55	3025	1
Aug-09	36	34.83	56	3136	1
Sep-09	30	32.17	57	3249	1
Oct-09	33	33.00	58	3364	0
Nov-09	26	31.25	59	3481	0
Dec-09	24	29.33	60	3600	0
Jan-10	24	28.75	61	3721	0
Feb-10	27	28.00	62	3844	0
Mar-10	36	31.75	63	3969	1
Apr-10	41	35.17	64	4096	1
May-10	26	23.33	65	4225	1
Jun-10	28	25.42	66	4356	1
Jul-10	26	23.58	67	4489	1
Aug-10	23	23.50	68	4624	1
Sep-10	25	26.42	69	4761	1
Oct-10	23	24.25	70	4900	0
Nov-10	20	23.92	71	5041	0
Dec-10	23	27.17	72	5184	0
Jan-11	21	25.58	73	5329	0
Feb-11	22	22.50	74	5476	0
Mar-11	28	25.00	75	5625	1
Apr-11	30	25.83	76	5776	1
May-11	28	25.42	77	5929	1
Jun-11	28	25.08	78	6084	1
Jul-11	27	24.67	79	6241	1
Aug-11	25	24.92	80	6400	1
Sep-11	24	25.33	81	6561	1
Oct-11	25	26.33	82	6724	0
Nov-11	23	27.33	83	6889	0
Dec-11	24	28.42	84	7056	0
Jan-12	23	27.92	85	7225	0
Feb-12	30	30.50	86	7396	0
Mar-12	34	29.50	87	7569	1
Apr-12	34	29.50	88	7744	1
May-12	35	30.83	89	7921	1
Jun-12	34	30.00	90	8100	1
Jul-12	33	30.75	91	8281	1
Aug-12	31	31.25	92	8464	1
Sep-12	30	32.08	93	8649	1
Oct-12	29	29.83	94	8836	0
Nov-12	28	32.67	95	9025	0
Dec-12	28	33.25	96	9216	0
Jan-13	32	37.17	97	9409	0
Feb-13	36	37.25	98	9604	0
Mar-13	41	37.00	99	9801	1
Apr-13	43	36.75	100	10000	1
May-13	40	35.67	101	10201	1
Jun-13	43	39.17	102	10404	1
Jul-13	33	31.25	103	10609	1
Aug-13	31	31.75	104	10816	1
Sep-13	31	33.58	105	11025	1
Oct-13	36	37.00	106	11236	0
Nov-13	32	37.17	107	11449	0
Dec-13	31	36.08	108	11664	0
Jan-14	33	36.92	109	11881	0
Feb-14	35	35.00	110	12100	0
Mar-14	39	33.75	111	12321	1
Apr-14	39	33.58	112	12544	1
May-14	43	37.58	113	12769	1
Jun-14	38	34.83	114	12996	1
Jul-14	35	33.50	115	13225	1
Aug-14	36	38.00	116	13456	1
Sep-14	37	39.17	117	13689	1
Oct-14	38	39.67	118	13924	0
Nov-14	31	36.83	119	14161	0
Dec-14	35	41.42	120	14400	0
Jan-15	39	42.92	121	14641	0
Feb-15	45	45.00	122	14884	0
Mar-15	46	40.00	123	15129	1
Apr-15	48	41.83	124	15376	1
May-15	47	41.83	125	15625	1
Jun-15	44	40.00	126	15876	1
Jul-15	43	42.17	127	16129	1
Aug-15	41	43.17	128	16384	1
Sep-15	35	38.00	129	16641	1
Oct-15	39	40.17	130	16900	0
Nov-15	36	42.00	131	17161	0
Dec-15	38	45.50	132	17424	0
Jan-16	39	42.08	133	17689	0
Feb-16	45	43.08	134	17956	0
Mar-16	50	44.33	135	18225	1
Apr-16	55	48.00	136	18496	1
May-16	53	47.58	137	18769	1
Jun-16	50	46.42	138	19044	1
Jul-16	54	52.33	139	19321	1
Aug-16	46	47.92	140	19600	1
Sep-16	44	46.50	141	19881	1
Oct-16	46	47.92	142	20164	0
Nov-16	40	47.58	143	20449	0
Dec-16	39	46.75	144	20736	0
Jan-17	45	47.75	145	21025	0
Feb-17	51	48.92	146	21316	0
Mar-17	61	52.67	147	21609	1
Apr-17	56	49.83	148	21904	1
May-17	57	52.92	149	22201	1
Jun-17	56	51.58	150	22500	1
Jul-17	48	47.67	151	22801	1
Aug-17	45	46.33	152	23104	1
Sep-17	50	53.08	153	23409	1
Oct-17	49	52.17	154	23716	0
Nov-17	50	59.25	155	24025	0
Dec-17	45	52.50	156	24336	0
Jan-18	48	49.17	157	24649	0
Feb-18	54	51.50	158	24964	0
Mar-18	66	56.58	159	25281	1
Apr-18	61	53.50	160	25600	1
May-18	62	55.17	161	25921	1
Jun-18	56	53.00	162	26244	1
Jul-18	52	52.33	163	26569	1
Aug-18	47	49.42	164	26896	1
Sep-18	46	49.58	165	27225	1
Oct-18	43	46.17	166	27556	0
Nov-18	44	52.08	167	27889	0
Dec-18	38	45.50	168	28224	0
Jan-19	49	49.25	169	28561	0
Feb-19	57	53.17	170	28900	0
Mar-19	68	58.75	171	29241	1
Apr-19	64	57.92	172	29584	1
May-19	56	50.17	173	29929	1
Jun-19	66	63.58	174	30276	1
Jul-19	55	55.75	175	30625	1
Aug-19	57	60.00	176	30976	1
Sep-19	56	59.58	177	31329	1
Oct-19	55	60.08	178	31684	0
Nov-19	50	59.17	179	32041	0
Dec-19	49	57.75	180	32400	0
Jan-20	59	57.08	181	32761	0
Feb-20	63	58.25	182	33124	0
Mar-20	59	50.75	183	33489	1
Apr-20	52	47.42	184	33856	1
May-20	64	58.00	185	34225	1
Jun-20	79	78.00	186	34596	1
Jul-20	85	84.92	187	34969	1
Aug-20	81	85.75	188	35344	1
Sep-20	77	82.33	189	35721	1
Oct-20	78	85.58	190	36100	0
Nov-20	61	71.92	191	36481	0
Dec-20	63	72.75	192	36864	0
Jan-21	77	75.08	193	37249	0
Feb-21	70	63.75	194	37636	0
Mar-21	83	70.83	195	38025	1
Apr-21	74	67.50	196	38416	1
May-21	65	59.58	197	38809	1
Jun-21	61	59.67	198	39204	1
Jul-21	62	63.33	199	39601	1
Aug-21	55	57.50	200	40000	1
Sep-21	58	61.83	201	40401	1
Oct-21	51	56.67	202	40804	0
Nov-21	54	64.33	203	41209	0
Dec-21	61	69.17	204	41616	0
Jan-22	70	67.50	205	42025	0
Feb-22	71	64.42	206	42436	0
Mar-22	68	58.92	207	42849	1
Apr-22	56	50.92	208	43264	1
May-22	58	53.00	209	43681	1
Jun-22	48	46.92	210	44100	1
Jul-22	44	45.25	211	44521	1
Aug-22	51	53.17	212	44944	1
Sep-22	44	47.25	213	45369	1
Oct-22	43	48.08	214	45796	0
Nov-22	41	48.50	215	46225	0
Dec-22	47	53.00	216	46656	0
Jan-23	55	54.08	217	47089	0
Feb-23	56	52.08	218	47524	0
Mar-23	62	53.33	219	47961	1
Apr-23	60	56.58	220	48400	1
May-23	67	59.17	221	48841	1
Jun-23	58	56.92	222	49284	1
Jul-23	60	60.67	223	49729	1
Aug-23	52	54.50	224	50176	1
Sep-23	55	58.17	225	50625	1
Oct-23	51	56.33	226	51076	0
Nov-23	42	51.25	227	51529	0
Dec-23	50	55.33	228	51984	0