Question

year	lean
1975	642
1976	644
1977	656
1978	667
1979	673
1980	688
1981	696
1982	698
1983	713
1984	717
1985	725
1986	742
1987	757

The engineers working on the tower were very interested in how
much the tower would lean if no corrective action was taken. Use
the OLS estimation to predict the tower's lean in the year 2000 if
no corrective action had been taken.

Answer 1

year	t	lean	(t-tbar)^2	(y-ybar)^2	(t-tbar)(y-ybar)
1975	1	642	36	2671.8561	310.14
1976	2	644	25	2469.0961	248.45
1977	3	656	16	1420.5361	150.76
1978	4	667	9	712.3561	80.07
1979	5	673	4	428.0761	41.38
1980	6	688	1	32.3761	5.69
1981	7	696	0	5.3361	0
1982	8	698	1	18.5761	4.31
1983	9	713	4	372.8761	38.62
1984	10	717	9	543.3561	69.93
1985	11	725	16	980.3161	125.24
1986	12	742	25	2333.8561	241.55
1987	13	757	36	4008.1561	379.86
Total	91	9018	182	15996.769	1696

The linear trend equation is given by,

y = a + b t

where,

= 1696 / 182 = 9.319

  

= 693.69 - 9.319*7 = 628.457

The linear trend equation is given by,

y = 628.457 +9.319 t

The OLS estimation to predict the tower's lean in the year 2000

For the year 2000, t = 26

Hence, predicted y = 628.457 + 9.319*26 = 870.751

**** If you have any queries or doubts please comment below, if you're satisfied please give a like. Thank you!