Final answer:
The standard deviation of the residuals (S=3.2) shows the average deviation of the actual hurricane days from the predicted values by the LSRL, while the coefficient of determination (r^2=0.15) indicates that 15% of the variation in hurricane days is explained by the years since 1950.
Step-by-step explanation:
The standard deviation of the residuals, denoted as S, in the context of a Least Squares Regression Line (LSRL) is a measure of how scattered the actual data points are around the predicted regression line.
An S of 3.2 indicates that, on average, the actual number of hurricane days deviates from the number predicted by the LSRL by about 3.2 days.
The coefficient of determination, r2, which is 0.15 (or 15%), tells us that 15% of the variability in hurricane days can be explained by the variability in the years since 1950, using the LSRL.
The remaining 85% of the variation is due to other factors or randomness not captured by this linear model. When interpreting the r2 for the third exam/final exam example, understanding that approximately 44 percent of the variation in final exam grades is explained by variation in third exam grades using the regression line is similar.
It means that the remaining 56 percent of variation in final exam scores is due to factors not accounted for by the third exam scores.