Engineers concerned about a tower's stability have doneextensive studies of its increasing tilt. Measurements of the leanof the tower over time provide much useful information. Thefollowing table gives measurements for the years 1975 to 1987. Thevariable \"lean\" represents the difference between where a point onthe tower would be if the tower were straight and where it actuallyis. The data are coded as tenths of a millimeter in excess of 2.9meters, so that the 1975 lean, which was 2.9643 meters, appears inthe table as 643. Only the last two digits of the year were enteredinto the computer.
| Year | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 |
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| Lean | 643 | 646 | 658 | 669 | 674 | 689 | 698 | 699 | 715 | 718 | 727 | 744 | 758 |
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(a) Plot the data. Consider whether or not the trend in leanover time appears to be linear. (Do this on paper. Your instructormay ask you to turn in this graph.)
(b) What is the equation of the least-squares line? (Round youranswers to three decimal places.)
y =Â Â +Â Â 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 answersto two decimal places.)
(  ,  )
