1. **Problem Statement:** Given the data points $(x, y)$: $$ \begin{array}{c|c} x & y \\\hline -4 & -33 \\ -3 & 21 \\ -2 & 15 \\ -1 & -20 \\ 0 & 7 \\ 1 & -5 \\ 2 & 20 \\ 3 & -20 \\ 4 & 15 \\ 5 & 21 \\ 6 & -33 \\ \end{array} $$ We need to determine which type of regression best fits this data: linear, quadratic, cubic, or none. 2. **Understanding Regression Types:** - Linear regression fits data to a line: $y = ax + b$. - Quadratic regression fits data to a parabola: $y = ax^2 + bx + c$. - Cubic regression fits data to a cubic curve: $y = ax^3 + bx^2 + cx + d$. 3. **Analyzing the Data:** - The data shows symmetry and multiple peaks and troughs. - Linear regression is unlikely because the data is not a straight line. - Quadratic regression typically has one peak or trough; here, there are multiple. - Cubic regression can model multiple turning points, matching the data's behavior. 4. **Conclusion:** The data's pattern with multiple peaks and troughs suggests a cubic regression is the best fit. **Final answer:** C) Cubic Regression