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 206 (February 2022); 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 - Seasonally Unadjusted	US SA year- Seasonally Adjusted Annual
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	62	704
Aug-21	55	668
Sep-21	58	725
Oct-21	51	667
Nov-21	54	753
Dec-21	61	860
Jan-22	64	788
Feb-22	65	772