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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 𝑅² 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 𝑅² value.
B) quadratic model, 0.994. No, 0.994 is too high an 𝑅² 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.

1 answer

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 𝑅² = 0.996 (Option A and C): An 𝑅² value close to 1 indicates a strong fit, meaning the model explains a large proportion of the variance in the data. An 𝑅² value of 0.996 suggests an excellent fit.

  2. Quadratic Model with 𝑅² = 0.994 (Option B and D): Similarly, this 𝑅² 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 𝑅² value, which is incorrect. A high 𝑅² value is typically desirable in determining a good fit.
  • Option B states that 0.994 is too high an 𝑅² value, which is also incorrect as a high 𝑅² 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 𝑅² value indicates it's a good model.