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 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, 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.

date	US NSA month	US SA year
Jan-04	89	1165
Feb-04	102	1159
Mar-04	123	1276
Apr-04	109	1186
May-04	115	1241
Jun-04	105	1180
Jul-04	96	1088
Aug-04	102	1175
Sep-04	94	1214
Oct-04	101	1305
Nov-04	84	1179
Dec-04	83	1242
Jan-05	92	1203
Feb-05	109	1319
Mar-05	127	1328
Apr-05	116	1260
May-05	120	1286
Jun-05	115	1274
Jul-05	117	1389
Aug-05	110	1255
Sep-05	99	1244
Oct-05	105	1336
Nov-05	86	1214
Dec-05	87	1239
Jan-06	89	1174
Feb-06	88	1061
Mar-06	108	1116
Apr-06	100	1123
May-06	102	1086
Jun-06	98	1074
Jul-06	83	965
Aug-06	88	1035
Sep-06	80	1016
Oct-06	74	941
Nov-06	71	1003
Dec-06	71	998
Jan-07	66	891
Feb-07	68	828
Mar-07	80	833
Apr-07	83	887
May-07	79	842
Jun-07	73	793
Jul-07	68	778
Aug-07	60	699
Sep-07	53	686
Oct-07	57	727
Nov-07	45	641
Dec-07	44	619
Jan-08	44	627
Feb-08	48	593
Mar-08	49	535
Apr-08	49	536
May-08	49	504
Jun-08	45	487
Jul-08	43	477
Aug-08	38	435
Sep-08	35	433
Oct-08	32	393
Nov-08	27	389
Dec-08	26	377
Jan-09	24	336
Feb-09	29	372
Mar-09	31	339
Apr-09	32	337
May-09	34	376
Jun-09	37	393
Jul-09	38	411
Aug-09	36	418
Sep-09	30	386
Oct-09	33	396
Nov-09	26	375
Dec-09	24	352
Jan-10	24	345
Feb-10	27	336
Mar-10	36	381
Apr-10	41	422
May-10	26	280
Jun-10	28	305
Jul-10	26	283
Aug-10	23	282
Sep-10	25	317
Oct-10	23	291
Nov-10	20	287
Dec-10	23	326
Jan-11	21	307
Feb-11	22	270
Mar-11	28	300
Apr-11	30	310
May-11	28	305
Jun-11	28	301
Jul-11	27	296
Aug-11	25	299
Sep-11	24	304
Oct-11	25	316
Nov-11	23	328
Dec-11	24	341
Jan-12	23	335
Feb-12	30	366
Mar-12	34	354
Apr-12	34	354
May-12	35	370
Jun-12	34	360
Jul-12	33	369
Aug-12	31	375
Sep-12	30	385
Oct-12	29	358
Nov-12	28	392
Dec-12	28	399
Jan-13	32	446
Feb-13	36	447
Mar-13	41	444
Apr-13	43	441
May-13	40	428
Jun-13	43	470
Jul-13	33	375
Aug-13	31	381
Sep-13	31	403
Oct-13	36	444
Nov-13	32	446
Dec-13	31	433
Jan-14	33	443
Feb-14	35	420
Mar-14	39	405
Apr-14	39	403
May-14	43	451
Jun-14	38	418
Jul-14	35	402
Aug-14	36	456
Sep-14	37	470
Oct-14	38	476
Nov-14	31	442
Dec-14	35	497
Jan-15	39	515
Feb-15	45	540
Mar-15	46	480
Apr-15	48	502
May-15	47	502
Jun-15	44	480
Jul-15	43	506
Aug-15	41	518
Sep-15	35	456
Oct-15	39	482
Nov-15	36	504
Dec-15	38	546
Jan-16	39	505
Feb-16	45	517
Mar-16	50	532
Apr-16	55	576
May-16	53	571
Jun-16	50	557
Jul-16	54	628
Aug-16	46	575
Sep-16	44	558
Oct-16	46	575
Nov-16	40	571
Dec-16	39	561
Jan-17	45	578
Feb-17	51	601
Mar-17	61	643
Apr-17	56	604
May-17	57	627
Jun-17	56	612
Jul-17	48	553
Aug-17	45	550
Sep-17	50	622
Oct-17	49	625
Nov-17	50	718
Dec-17	45	658
Jan-18	48	610
Feb-18	54	644
Mar-18	66	680
Apr-18	61	658
May-18	62	680
Jun-18	56	598
Jul-18	52	600
Aug-18	47	582
Sep-18	46	584
Oct-18	43	546
Nov-18	44	618
Dec-18	38	566
Jan-19	49	628
Feb-19	57	675
Mar-19	68	721
Apr-19	64	689
May-19	56	619
Jun-19	66	711
Jul-19	55	636
Aug-19	57	677
Sep-19	56	706
Oct-19	55	703
Nov-19	50	700
Dec-19	49	733
Jan-20	59	756
Feb-20	63	730
Mar-20	59	623
Apr-20	52	582
May-20	64	704
Jun-20	79	839
Jul-20	85	972
Aug-20	81	977
Sep-20	77	971
Oct-20	78	969
Nov-20	61	865
Dec-20	63	943
Jan-21	77	993
Feb-21	70	823
Mar-21	83	873
Apr-21	74	796
May-21	65	733
Jun-21	61	683
Jul-21	63	712
Aug-21	57	702
Sep-21	65	800