Let's analyze Corey’s work step by step to identify the mistake:
-
Equation: The regression equation is given as
. In this equation, represents the temperature, and represents the number of swimmers. -
Substituting Values: Corey tried to find the temperature when there are 80 swimmers at the pool by substituting 80 into the equation as
: -
Calculating: He calculated
: -
Final Interpretation: Corey concluded that the temperature is likely 32.2°F when there are 80 swimmers at the pool.
Identifying the error: The error in Corey's reasoning lies in how he interpreted the values. Since
Thus, the correct substitution should be:
Conclusion: The correct identification of Corey’s mistake is:
- He substituted 80 for x instead of y.