Question
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. 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.
Answers
GPT-4o mini
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**.
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**.