Question

Engineers concerned about a tower's stability have done extensive studies of its increasing tilt. Measurements of the lean of the tower over time provide much useful information. The following table gives measurements for the years 1975 to 1987. The variable "lean" represents the difference between where a point on the tower would be if the tower were straight and where it actually is. The data are coded as tenths of a millimeter in excess of 2.9 meters, so that the 1975 lean, which was 2.9643 meters, appears in the table as 643. Only the last two digits of the year were entered into the computer.

Year	75	76	77	78	79	80	81	82	83	84	85	86	87
Lean	643	646	657	669	674	690	698	700	715	718	726	744	758

What is the equation of the least-squares line? Round answers to three decimal places

y = ____________ + _____________ x

What percent of the variation in lean is explained by this line? Round your answer to one decimal place

Give a 99% confidence interval for the average rate of change (tenths of a millimeter per year) of the lean. Round your answers to two decimal places

( ________, ____________)

Answer 1

Here we have data:

Year	Lean
75	643
76	646
77	657
78	669
79	674
80	690
81	698
82	700
83	715
84	718
85	726
86	744
87	758

Here we are using Excel for calculation:

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9938
R Square	0.9876
Adjusted R Square	0.9865
Standard Error	4.2475
Observations	13
ANOVA
	df	SS	MS	F	Significance F
Regression	1	15785.8516	15785.8516	874.9765	7.77174E-12
Residual	11	198.4560	18.0415
Total	12	15984.3077
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	-59.137	25.5298	-2.3164	0.0408	-115.3282	-2.9466	-138.43	20.15
X Variable 1	9.313	0.3148	29.5800	0.0000	8.6202	10.0062	8.34	10.29

Equation of the least square line:

Y = -59.137 + 9.313X

99% Confidence interval

(-138.43, 20.15