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 2.9645 meters, appears in the table as 645. 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	645	647	660	671	676	692	699	702	716	720	729	746	761

(a) Plot the data. Consider whether or not the trend in lean over time appears to be linear. (Do this on paper. Your instructor may ask you to turn in this graph.)

(b) What is the equation of the least-squares line? (Round your 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.)
%

(c) 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

a)

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.993778785
R Square	0.987596273
Adjusted R Square	0.986468661
Standard Error	4.267995339
Observations	13
ANOVA
	df	SS	MS	F	Significance F
Regression	1	15953.93407	15953.93407	875.8302073	7.73064E-12
Residual	11	200.3736264	18.21578422
Total	12	16154.30769
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 99.0%	Upper 99.0%
Intercept	-61.14285714	25.6528795	-2.38346955	0.036277907	-117.6044642	-4.681250092	-140.8157374	18.53002309
Year	9.362637363	0.316364863	29.59442865	7.73064E-12	8.666322995	10.05895173	8.380069311	10.34520541

b)

Lean = -61.14 + 9.36 * year

Y = -61.14 + 9.36 * X

c)

99% confidence interval for the average rate of change (tenths of a millimeter per year) of the lean

(8.38, 10.35)

Use regression in excel to get above solution (SUMMARY OUTPUT)