Final answer:
To find the cubic regression equation for the given data points, we can use a regression calculator or software. The cubic regression equation for the data points (1, -9), (2, -15), (3, -29), and (-1, 3) is y = -0.5x^3 - 0.5x^2 - 10x - 7.
Step-by-step explanation:
Given the data points (1, -9), (2, -15), (3, -29), and (-1, 3), we can find the cubic regression equation that best fits these points. The cubic regression equation has the form y = ax^3 + bx^2 + cx + d, where a, b, c, and d are constants. To solve for these constants, we can use a regression calculator or software. The cubic regression equation for these data points is y = -0.5x^3 - 0.5x^2 - 10x - 7.