In some cases, the best-fitting multiple regression equation is of the form $\hat{y} = b_0 + b_1 x + b_2 x^2 + b_3 x^3.$ The graph of such an equation is called a cubic. Using the data set given below, and letting $x_1 = x,$ $x_2 = x^2,$ and $x_3 = x^3,$ find the multiple regression equation for the cubic that best fits the given data. $$\begin{array}{c|ccccccc} x & -10 & -6 & -4 & 1 & 4 & 6 & 8 \cr \hline y & -5 & 7.6 & 8.7 & 3.9 & 4.5 & 9.7 & 20.1 \end{array}$$ The equation is $\hat{y} =$ $+$ $x+$ $x^2 +$ $x^3.$