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 2.9647 meters, appears in the table as 647. 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	647	650	661	673	678	694	701	704	718	722	730	748	763

(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.)

Answer 1

Let independent variable, X : Year

Dependent variable, Y : Lean

(a)

Following is the scatter plot:

(b)

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	75	647	5625	418609	48525
	76	650	5776	422500	49400
	77	661	5929	436921	50897
	78	673	6084	452929	52494
	79	678	6241	459684	53562
	80	694	6400	481636	55520
	81	701	6561	491401	56781
	82	704	6724	495616	57728
	83	718	6889	515524	59594
	84	722	7056	521284	60648
	85	730	7225	532900	62050
	86	748	7396	559504	64328
	87	763	7569	582169	66381
Total	1053	9089	85475	6370677	737908

(b)

That is 98.8% of the variation in lean is explained by this line.

(c)