Question 1
Data from an experiment shows a relationship where the output variable increases to a single maximum value and then decreases, appearing to be symmetric. Both a quadratic and a quartic ( degree) polynomial model fit the data well. In the absence of a theoretical reason to prefer one over the other, why might a researcher choose the quadratic model?
- The quartic model is always a better choice because its higher degree allows it to capture more complex variations that might exist in the data.
- The quadratic model is often preferred because it is a simpler model that still captures the essential features of the data (one maximum, symmetry).
- The choice is arbitrary because both models fit the data well, and their predictions will be effectively identical for all possible input values.
- The quadratic model is chosen only if its leading coefficient is positive, ensuring the function opens upwards to match the symmetric data.
Explanation: The principle of parsimony suggests that when multiple models fit data well, the simplest model is generally preferred. A quadratic function is simpler (degree 2) than a quartic function (degree 4) and adequately describes the key features of the data: a single maximum and symmetric behavior.