3. 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.

Use data below:

date	US NSA month	US SA year
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	573
Feb-17	51	587
Mar-17	61	632
Apr-17	56	598
May-17	57	635
Jun-17	56	619
Jul-17	48	572
Aug-17	45	556
Sep-17	50	637
Oct-17	49	626
Nov-17	50	711
Dec-17	45	630
Jan-18	48	590
Feb-18	54	618
Mar-18	66	679
Apr-18	61	642
May-18	62	662
Jun-18	56	636
Jul-18	52	628
Aug-18	47	593
Sep-18	46	595
Oct-18	43	554
Nov-18	44	625
Dec-18	38	546
Jan-19	49	591
Feb-19	57	638
Mar-19	68	705
Apr-19	64	695
May-19	56	602
Jun-19	66	763
Jul-19	55	669
Aug-19	57	720
Sep-19	56	715
Oct-19	55	721
Nov-19	50	710
Dec-19	49	693
Jan-20	59	685
Feb-20	63	699
Mar-20	59	609
Apr-20	52	569
May-20	64	696
Jun-20	79	936
Jul-20	85	1019
Aug-20	81	1029
Sep-20	77	988
Oct-20	78	1027
Nov-20	61	863
Dec-20	63	873
Jan-21	77	901
Feb-21	70	765
Mar-21	83	850
Apr-21	74	810
May-21	65	715
Jun-21	61	716
Jul-21	62	760
Aug-21	55	690
Sep-21	58	742
Oct-21	51	680
Nov-21	54	772
Dec-21	61	830
Jan-22	70	810
Feb-22	71	773
Mar-22	68	707
Apr-22	56	611
May-22	58	636
Jun-22	48	563
Jul-22	44	543
Aug-22	51	638
Sep-22	44	567
Oct-22	43	577
Nov-22	41	582
Dec-22	47	636
Jan-23	55	649
Feb-23	56	625
Mar-23	62	640
Apr-23	60	679
May-23	67	710
Jun-23	58	683
Jul-23	60	728
Aug-23	52	654
Sep-23	55	698
Oct-23	51	676
Nov-23	42	615
Dec-23	50	664