In the 11 years before the passage of the Federal Coal Mine Health and Safety Act of 1969, the fatality rates decreased steadily until 1979. The fatality rates for the years of 1970 through 1981 are provided below; for computational purposes, calendar year have been converted to a scale beginning at 1. This information is contained in the dataset miner.

Calendar Year	Year	Fatality Rate per 1000 Employees
1970	1	2.419
1971	2	1.732
1972	3	1.361
1973	4	1.108
1974	5	0.996
1975	6	0.952
1976	7	0.904
1977	8	0.792
1978	9	0.701
1979	10	0.890
1980	11	0.799
1981	12	1.084

1. Construct a two-way scatter plot of fatality rate versus year. What does this plot suggest about the relationship between these two variables?
2. To model the trend in fatality rates, fit the least squares regression line

Where x represents years. Using both the coefficient of determination R² and a plot of the residual versus the fitted values of fatality rate, comment on the fit of the model on the observed data.

1. Now transform the explanatory variable x to ln(x). Create a scatter plot of fatality rate versus the natural logarithm of year.

Fit the least squares model

Use the coefficient determination and plot of the residuals versus the fitted values of fatality rate to compare the fit of this model to the model constructed in part (b)

1. Transform x to 1/x. Construct a two-way scatter plot of fatality rate versus the reciprocal of year.
2. Fit the least squares model

Using the coefficient of determination and a plot of the residuals, comment on the fit of this model and compare it to the previous ones.

1. Which of the three models appears to fit the data best? Defend your selection