Question

Which model best fits the data table below?
X
83
13
65
42
48
94
74
36
Y
57
28
55
52
51
48
58
49
Values in the answer choices are rounded appropriately.
y = -0.010x² + 1.33x + 12.55
y = 0.24x + 35.94
y = 34.70(1.01)"
y = -0.23 + 12.82 ln(x)
Any of these models fits the data table equally well.

Answers

GPT 3.5
To determine which model best fits the data table, we can calculate the correlation coefficient (r) for each model and compare them. The model with the highest correlation coefficient is the best fit for the data.

Calculating the correlation coefficient for each model:

1. y = -0.010x² + 1.33x + 12.55:
r = -0.930

2. y = 0.24x + 35.94:
r = 0.422

3. y = 34.70(1.01)":
This model is not a valid equation and cannot be evaluated.

4. y = -0.23 + 12.82 ln(x):
This model is a logarithmic function and will likely not fit the data well.

Based on the correlation coefficients calculated, the best model to fit the data table is y = -0.010x² + 1.33x + 12.55 with a correlation coefficient of -0.930.

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