How to solve this problem in R? Thank you for telling me how to write this code.

Question

How to solve this problem in R? Thank you for telling me how to write this code.

Polyester fiber ropes are increasingly being used as components of mooring lines for offshore structures in
deep water.The authors of the paper "Quantifying the Residual CreepLife of Polyester Mooring Ropes"
(IntL J. of Offshore andPolar Exploration 2005: 223—228) used the accompanying data as a basis for studying
how time to failure (hr) depended on load (% of breaking load)
L : 77.7 77.8 77.9 77.8 85.5 85.5 89.2 89.3 73.1 85.5 89.2 85.5 89.2 85.5 89.2 82.3 82.0 82.3
T : 5.067 552.056 127.809 7.611 .124 .077 .008 .013 49.439 .503 362 9.930 .677 5.322 .289 53.079 7.625 155.299
A linear regression of log(time) versus load was fit. The investigators were particularly interested in estimating
the slope of the true regression line relating these variables. Investigate the quality of the fit,
estimate the slope, and predict time to failure when load is 80, in a way that conveys information about
reliability and precision.
in other words: log(T) ~ L

Explanation / Answer

A)

The Regression Model is

y=a+bx

from Excel the fitted model is

The fitted model is

y=607.3 - 6.38X

b) When X=80

Then The fitted model is

y=607.3 -6.38X

y=607.3 -6.38*80 = 96.9

SUMMARY OUTPUT Regression Statistics Multiple R 0.213003 R Square 0.04537 Adjusted R Square -0.01429 Standard Error 151.0673 Observations 18 ANOVA df SS MS F Significance F Regression 1 17353.98 17353.98 0.760429 0.396092 Residual 16 365141.1 22821.32 Total 17 382495.1 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 607.2834 612.2679 0.991859 0.33603 -690.667 1905.233 -690.667 1905.233 L -6.37698 7.312841 -0.87203 0.396092 -21.8795 9.125546 -21.8795 9.125546

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