Confidence Interval for the Slope

The following extract from the Minitab output gives information needed to find a confidence interval for the slope of the regression line.

...

Predictor       Coef       Stdev    t-ratio        p
...
logLen       2.64043     0.05017      52.63    0.000

The 95% confidence interval is therefore

2.540 to 2.740

(Strictly, the constant '2' above should have been replaced by a value from t-tables with n - 2 = 97 degrees of freedom, 1.984, but there is little difference in the resulting interval.)

We are therefore 95% confident that slug weight is proportional to a power of length between

len**2.540 to len**2.740

Another interpretation of the confidence interval is that the effect of doubling slug length is to increase weight by a factor of between 22.54 = 5.8 and 22.74 = 6.7.