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	658	669	676	690	699	700	716	719	727	744	760

(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)

b)

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9933
R Square	0.9865
Adjusted R Square	0.9853
Standard Error	4.4134
Observations	13
ANOVA
	df	SS	MS	F	Significance F
Regression	1	15711.4341	15711.4341	806.6237	0.0000
Residual	11	214.2582	19.4780
Total	12	15925.6923
	Coefficients	Standard Error	t Stat	P-value	Lower 99.0%	Upper 99.0%
Intercept	-56.4341	26.5268	-2.1274	0.0568	-138.8211	25.9530
Year	9.2912	0.3271	28.4011	0.0000	8.2752	10.3072

y^ = -56.434 + 9.291 year

R^2 = 0.987

hence 98.7% of variation is explained

c)

99% confidence interval for slope = (8.28,10.31)