The Leaning Tower of Pisa is an architectural wonder. Engineers concerned about

Question

The Leaning Tower of Pisa is an architectural wonder. Engineers concerned about the 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 2.9642 meters, appears in the table as 642. Only the last two digits of the year were entered into the computer.

(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 two 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.)
(  ,  )

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: lean
Independent Variable: year
lean = -90.186813 + 9.7582418 year
Sample size: 13
R (correlation coefficient) = 0.99759476
R-sq = 0.99519531
Estimate of error standard deviation: 2.7579691

Parameter estimates:

Analysis of variance table for regression model:

Hence,

b) Regression equation:

y = -90.19 + 9.76*x

Percentage of variation in lean explained by the line = 99.5%

c) 99% confidence interval for slope:

(9.12, 10.39)

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept -90.186813 16.576834 ? 0 11 -5.4405331 0.0002 Slope 9.7582418 0.20443427 ? 0 11 47.732905 <0.0001

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