Question

Which model best fits the data table below?
X
83
57
13
28
65
42
48
94
74
36
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.

Answer 1

To determine which model best fits the data table, we can calculate the coefficient of determination (R-squared) for each model and compare them to see which one has the highest value.

However, we first need to determine the actual values of y for each corresponding x value in the data table based on the given models.

1) For the model y = -0.010x² + 1.33x + 12.55:

Using the x values from the data table:
y = -0.010(83)² + 1.33(83) + 12.55 = 47.62
Similarly, calculate y values for all x values in the data table.

2) For the model y = 0.24x + 35.94:

Using the x values from the data table:
y = 0.24(83) + 35.94 = 55.82
Similarly, calculate y values for all x values in the data table.

3) For the model y = 34.70(1.01)^x:

Using the x values from the data table:
y = 34.70(1.01)^83 = 54.48
Similarly, calculate y values for all x values in the data table.

4) For the model y = -0.23 + 12.82 ln(x):

This model is not suitable for this data set as it involves natural logarithm values of x.

Next, calculate the coefficient of determination (R-squared) for each model by comparing the actual y values from the data table to the predicted y values from each model. The model with the highest R-squared value is the best fit for the data.

Based on these calculations, we can determine which model best fits the data table.