Question
A fitness trainer decided to track the combined weight loss of several new customers. She recorded the combined weight loss each month and kept track for 6 months. Identify the best mathematical model with its corresponding π
Β² value and tell whether it is a good model.
Month: 1 2 3 4 5 6
Weight Loss: 175 120 95 63 44 33
A) exponential model, 0.996. No, 0.996 is too high an π Β² value.
B) quadratic model, 0.994. No, 0.994 is too high an π Β² value.
C) exponential model, 0.996. Yes, 0.996 is very close to 1.
D) quadratic model, 0.994. Yes, 0.994 is very close to 1.
Month: 1 2 3 4 5 6
Weight Loss: 175 120 95 63 44 33
A) exponential model, 0.996. No, 0.996 is too high an π Β² value.
B) quadratic model, 0.994. No, 0.994 is too high an π Β² value.
C) exponential model, 0.996. Yes, 0.996 is very close to 1.
D) quadratic model, 0.994. Yes, 0.994 is very close to 1.
Answers
GPT-4o mini
To determine the best mathematical model for the given data on weight loss over 6 months based on the provided options:
1. **Exponential Model with π Β² = 0.996 (Option A and C)**: An π Β² value close to 1 indicates a strong fit, meaning the model explains a large proportion of the variance in the data. An π Β² value of 0.996 suggests an excellent fit.
2. **Quadratic Model with π Β² = 0.994 (Option B and D)**: Similarly, this π Β² value is also very high and indicates a good fit for the quadratic model.
Now regarding the options:
- Option A states that **0.996 is too high an π Β² value**, which is incorrect. A high π Β² value is typically desirable in determining a good fit.
- Option B states that **0.994 is too high an π Β² value**, which is also incorrect as a high π Β² is favorable.
- Option C states that **0.996 is very close to 1**, which is correct.
- Option D states that **0.994 is very close to 1**, which is also correct.
Based on this, the best choice would be:
**C) exponential model, 0.996. Yes, 0.996 is very close to 1.**
This is because both the model is appropriate (exponential models are often used for decay processes such as weight loss), and a high π Β² value indicates it's a good model.
1. **Exponential Model with π Β² = 0.996 (Option A and C)**: An π Β² value close to 1 indicates a strong fit, meaning the model explains a large proportion of the variance in the data. An π Β² value of 0.996 suggests an excellent fit.
2. **Quadratic Model with π Β² = 0.994 (Option B and D)**: Similarly, this π Β² value is also very high and indicates a good fit for the quadratic model.
Now regarding the options:
- Option A states that **0.996 is too high an π Β² value**, which is incorrect. A high π Β² value is typically desirable in determining a good fit.
- Option B states that **0.994 is too high an π Β² value**, which is also incorrect as a high π Β² is favorable.
- Option C states that **0.996 is very close to 1**, which is correct.
- Option D states that **0.994 is very close to 1**, which is also correct.
Based on this, the best choice would be:
**C) exponential model, 0.996. Yes, 0.996 is very close to 1.**
This is because both the model is appropriate (exponential models are often used for decay processes such as weight loss), and a high π Β² value indicates it's a good model.