Corey used the regression equation y = 1.505x − 88.21, where x is the temperature and y is the number of swimmers, to determine a possible outside temperature when 80 swimmers are at City Pool.

1. y = 1.505(80) − 88.21

2. y = 120.4 − 88.21

3. y = 32.19

4. If there are 80 swimmers at the pool, the temperature is likely to be 32.2°F.

Analyze Corey’s work to find his error. What is Corey’s mistake?
He substituted 80 for x instead of y.
He should have added 88.21 to both sides.
He should have rounded down to 32.1°F.
He should have predicted about 40 swimmers when the temperature is 80°F.

1 answer

Let's analyze Corey’s work step by step to identify the mistake:

  1. Equation: The regression equation is given as y=1.505x88.21. In this equation, x represents the temperature, and y represents the number of swimmers.

  2. Substituting Values: Corey tried to find the temperature when there are 80 swimmers at the pool by substituting 80 into the equation as y: y=1.505(80)88.21

  3. Calculating: He calculated y: y=120.488.21 y=32.19

  4. 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 y in the equation represents the number of swimmers, if Corey is interested in finding the corresponding temperature for a specific number of swimmers (80), he should have substituted 80 for y instead of x.

Thus, the correct substitution should be: 80=1.505x88.21 From here, Corey should solve for x, which represents the temperature.

Conclusion: The correct identification of Corey’s mistake is:

  • He substituted 80 for x instead of y.