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 2.9648 meters, appears in the table as 648. 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 | 648 | 650 | 661 | 672 | 678 | 694 | 701 | 703 | 718 | 723 | 731 | 747 | 762 |
(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.)
The statistical software output for this problem is:
Hence,
b) y = -53.511 + 9.291 x
Percent of variation explained = R square = 98.8 %
c) 99% confidence interval:
(8.35, 10.23)
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