Data given for question The Leaning Tower of Pisa is an architectural wonder. En
ID: 3053520 • Letter: D
Question
Data given for 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. (data196.dat)
(a) 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.)
________%
(b) 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 = -84.846154 + 9.6923077 year
Sample size: 13
R (correlation coefficient) = 0.99699913
R-sq = 0.99400726
Estimate of error standard deviation: 3.0611484
Parameter estimates:
Analysis of variance table for regression model:
Hence,
a) y = -84.85 + 9.69x
b) Percentage of variation explained = 99.4%
c) 99% confidence interval for rate of change:
(8.99, 10.40)
Parameter Estimate Std. Err. DF 99% L. Limit 99% U. Limit Intercept -84.846154 18.399099 11 -141.9902 -27.702112 Slope 9.6923077 0.22690741 11 8.9875772 10.397038Related Questions
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