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. (data56.dat)

(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

#You can use R language to solve above problem. https://cran.r-project.org/bin/windows/base/ link to download r

#Here is complete explanation. just run these all command in r

year=c(75,76,77,78,79,80,81,82,83,84,85,86,87) #this will store your year observation in variable year

lean=c(635,649,662,672,683,689,697,712,720,729,736,747,760) #this will store lean observations in variable len

plot(year,lean) #this will plot variable lean over different years and you can clearly see there is a linear trend

model=lm(lean~year) #this will fit a least square model on lean over the years as (lean= a + b* year )

abline(model) # this will show you linear pattern

model$coefficients #this will return you the intercept a = -103.57 and b = 9.91 so least square estimate is lean =  -103.57 +  9.91*year

summary(model) #this will give you the summary of least square model and "Multiple R-squared: 0.9958" tells you that 99.58 % variation in lean is covered by year

#now average rate of chage in lean is simply "b" and you can get 99% confidence interval for b by following

confint(model, 'year', level=0.99) # this will return the 99% confidence intervel for average rate of change lean as (9.31, 10.51) in 10th of milimeter

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