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. (data62.dat)

Data

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.)
____%

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

Independent variable, X: Year

Dependent variable, Y: Lean

Following is the output of regression analysis:

The  equation of the least-squares line is

y' = 10.05x - 115.24

The percent of the variation in lean is explained by this line, the r-square, is

0.9963 or 99.63%

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

(9.48, 10.62)

SUMMARY OUTPUT Regression Statistics Multiple R 0.998159041 R Square 0.996321471 Adjusted R Square 0.995987059 Standard Error 2.483813735 Observations 13 ANOVA df SS MS F Significance F Regression 1 18380.44505 18380.44505 2979.325642 9.62215E-15 Residual 11 67.86263736 6.169330669 Total 12 18448.30769 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 99.0% Upper 99.0% Intercept -115.2362637 14.92901687 -7.718945241 9.16268E-06 -148.0948083 -82.37771917 -161.6029016 -68.86962589 year, X 10.04945055 0.184112523 54.58319926 9.62215E-15 9.644221618 10.45467948 9.477632675 10.62126842

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