Question

Which function best models the dataset in the table?

This table presents the x and y values to identify the function that most accurately models the given dataset.
x
−5
−2
−1
0 1 2 5 8 12
y
6.2 8.3 9.1 10 11 12.1 16.1 21.4 31.4
Option #1: f(x)=1.467x+10.696


Option #2: f(x)=10.004(1.100)x


Option #3: f(x)=0.066x2+0.981x+9.810

Answer 1

Option #2, f(x) = 10.004(1.100)^x, best models the data.

Reason: the exponential's predicted y-values are essentially the given y's (residuals on the order of 0.01). Sum of squared errors (SSE) for each model (approx):
- Option #1 (linear): SSE ≈ 26.95
- Option #2 (exponential): SSE ≈ 0.0027
- Option #3 (quadratic): SSE ≈ 0.665

Because Option #2 has by far the smallest SSE (and tiny residuals at every x), it is the best fit.