Answer:
- r² ≈ 0.9936 for quadratic model
- r² ≈ 0.999990 for quartic model
Explanation:
You want to show that the given table data is not well modeled by a quadratic function.
Errors
One way to assess the model is to look at the r² value. This is the ratio of the variance of the model values to the variance of the original data values. The closer it is to 1, the better the model.
For the quadratic model ...
y = 0.3470x² +1.8132
the r² value is about 0.9936. In many fields of study, this would be considered a good model of the data. When we look at the residuals (the difference between the data and the model), we find the largest difference to be about 0.236 units.
Better model
The graph of the residuals suggests that a 4th-degree model might offer a better fit to the data. That model is computed to be ...
y = 0.006369x⁴ +0.2424x² +2.0098
The r² value for this model is about 0.9999903, and the maximum difference between the model and the data is about 0.0098. This is on the order of the resolution of the given data, so could be said to model the data well.
Summary
While there's a certain subjectivity in determining when the data is well-modeled, we find that a quartic model gives a better fit to the data than the quadratic model does.
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Additional comment
The attached graph shows the given data (red), the residuals from a quadratic model (blue), and the residuals from the quartic model (orange). Clearly, the quartic model is better. Whether the data is well-modeled by the quadratic function is a matter of opinion, given the fairly high r² value.