Final answer:
The R-squared value of 0.617 indicates that approximately 61.7% of the variation in grizzly bear weight can be explained by their age. It is related to the linear correlation coefficient (r), as R² is the square of r. For example values, if r is -0.56, R² is 0.3136, and if r is 0.6631, R² is approximately 0.44.
Step-by-step explanation:
The R-squared value (R²) represents the proportion of the variance in the dependent variable that is predictable from the independent variable. In the context given, the R² value is 0.617, which means approximately 61.7 percent of the variation in bear weight can be explained by its age. This value is related to the linear correlation coefficient (r value) found in question 6, as the R² value is the square of the correlation coefficient. For instance, if the correlation coefficient (r) between bear age and weight was found to be 0.786, then R² would be r-squared, which would be (0.786)².
In the example of body weight and fuel efficiency, a correlation coefficient of -0.56 was given, which when squared gives a coefficient of determination (R²) of 0.3136, indicating that 31.36% of the variation in fuel efficiency can be explained by the variation in body weight. Similarly, if a correlation coefficient of 0.6631 was given for another example, then the R² value would be (0.6631)², or approximately 44 percent, meaning that around 44 percent of the variation in the final exam grades can be explained by variation in the grades on the third exam.