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 2.9646 meters, appears in the table as 646. 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	646	648	659	671	677	691	700	701	717	721	728	746	761

(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

In Excel

data -> data analysis -> regression

M F F G H K. N y 75 646 X Regression 76 648 Input 77 659 OK Input Y Range: SFS1:SFS14 78 671 Cancel Input X Range: SES1:SES14 79 677 Help 80 691 Labels Constant is Zero 81 700 99 Confidence Level: % 82 701 Output options 83 717 Output Range: 84 721 New Worksheet Ply: 85 728 New Workbook 86 746 Residuals 87 761 Residual Plots Line Fit Plots Residuals Standardized Residuals Normal Probability Normal Probability Plots

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.9934
R Square	0.9869
Adjusted R Square	0.9857
Standard Error	4.3755
Observations	13
ANOVA
	df	SS	MS	F	Significance F
Regression	1	15804.4835	15804.4835	825.5212	0.0000
Residual	11	210.5934	19.1449
Total	12	16015.0769
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	-57.4286	26.2989	-2.1837	0.0515	-115.3121
x	9.3187	0.3243	28.7319	0.0000	8.6048

a)

780 760 740 720 700 680 660 640 74 76 78 80 82 84 86 88

b)

y^= -57.429 + 9.319 x

% of variation explained = R^2 = 0.987 = 98.7 %

c)

99% confidence interval for slope = (8.311,10.326)

Please rate

Please look below in comments for future help