Question

The table shows the reduction in costs (in hundreds) after a manager found ways each month to cut back in his store. Identify the best fit mathematical model with its corresponding R^2 value and tell whether it is a good model.

Month: 1. 2. 3. 4. 5
Profit Loss: 86. 82. 72. 45. 15

A: Quadratic model, 0.997
No 0.997 is too high an R^2 value.
B: quadratic model, 0.997
Yes, 0.997 is very close to 1.
C. linear model, 0.902
No, 0.902 is too high an R^2 value.
D. linear model, 0.902
Yes, 0.902 is very close to 1.

Answer 1

B: quadratic model, 0.997

Yes, 0.997 is very close to 1.

Explanation:

In general, the better the model, the closer the R²-value is to 1. A graph shows the quadratic model to be a good fit.

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Comment on "better models"

A 4th-degree polynomial can be written that will fit each of the 5 points exactly and give an R²-value of 1. However, the model does not appear to interpolate or extrapolate well. The quadratic offers a reasonable fit that is better than that of the linear model and seems to have reasonable behavior between and beyond the given data points.