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.

Question

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.

Answer 1

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

1. Equation: The regression equation is given as \( y = 1.505x - 88.21 \). 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 \( y \): \[ y = 120.4 - 88.21 \] \[ y = 32.19 \]

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: \[ 80 = 1.505x - 88.21 \] 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.