Question

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 2.9644 meters, appears in the table as 644. 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 644 646 658 668 675 689 697 700 715 719 727 743 759

(a) Plot the data. Consider whether or not the trend in lean over time appears to be linear.

(b) What is the equation of the least-squares line? y =___ +___ x

What percent of the variation in lean is explained by this line? %

(c) Give a 99% confidence interval for the average rate of change (tenths of a millimeter per year) of the lean.( , )

Answer 1

we can solve this in excel by entering the data in excel and then going to data > data analysis tab and selecting regression

The regression equation is formed using the coefficients as

Lean = -58.98 +9.313*year

the r2 value is 0.9888 , which means that the model is able to explain 98.8% variation in the data

The 99% CI for year is 8.65 , 9.96