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. (data128.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.) ( , )

obs     year    lean
1       75      645
2       76      655
3       77      655
4       78      673
5       79      683
6       80      694
7       81      699
8       82      715
9       83      721
10      84      733
11      85      739
12      86      751
13      87      756

Answer 1

122 1 YEAR LEAN 75 76 Regression Statistics Multiple R R Square Adjusted R Square Standard Error Observations 1.00 0.99 0.99 3.23 13.00 655 655 4 683 694 699 81 82 83 ANOVA MS Significance F 10 721 733 739 751 756 Regression Residual Total 1.00 11.00 12.00 17000.45 114.79 17115.23 17000.45 1629.17 0.00 10.44 12 13 14 15 16 17 86 87 Coefficients |Standard Error 19.42 0.24 t Stat P-value Lower 95% U er 95% Intercept -4.19 81.39 9.66 0.00 124.12 38.66 X Variable 1 40.36 0.00 9.14 10.19 b) Regression Equation: Y:-81.39+9.66*X 99% of Variation in Lean explained by this line c) The 99% Confidance interval for slope is (8.93,10.39) Where , Y=lean,X-year 19 21

Scatter Plot 780 760 740 720 700 680 660 640 620 ◆ LEAN 76 80 82 84 86 Year