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 2.9644 meters, appears in the table as 644. 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	644	645	658	668	674	689	697	700	715	718	727	743	759

(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)scatterplot:

b)

SST=Syy=		16,057.6923
SSE =Syy-(Sxy)2/Sxx=		197.2473
SSR =(Sxy)2/Sxx =		15,860.4451

percent of the variation in lean is explained by this line R² =(SSR/SST)*100 =98.8 %

c)

	s2 =SSE/(n-2)=	17.9316
std error σ              =	=se =√s2=	4.2346

estimated std error of slope =se(β1) =s/√Sxx=

0.3139

for 99 % CI value of t=			3.1060
margin of error E=t*std error                            =			0.975
lower bound=estimated slope-margin of error =			8.36
Upper bound=estimated slope+margin of error=			10.31

99% confidence interval for the average rate of change =(8.36 , 10.31)