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 Creep Life of Polyester Mooring Ropes" (Intl. J. of Offshore and Polar Exploration, 2005: 223-228) used the accompanying data as a basis for studying how time to failure (hr) depended on load (% of breaking load):

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.

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x | 77.7 77.8 77.9 77.8 85.5 85.5 y 5.067 552.056 127.809 7.611 124 077 x | 89.289.3 73.85.589.285.5 y.008 .013 49.439.503 .362 9.930 x | 89.2 85.5 89.2 82.3 82.0 82.3 y.6775.322 .289 53.079 7.625 155.299