To determine the best-fitting multiple regression cubic equation for the given data, we need to follow these steps:

1. Define the Cubic Equation: The general form of a cubic equation in multiple regression is:

   $y = a + b_1x + b_2x^2 + b_3x^3$

   Here, $y$ is the dependent variable, and $x$ is the independent variable. The coefficients $a$, $b_1$, $b_2$, and $b_3$ are determined based on the dataset provided.

2. Fit the Model: Using statistical techniques (e.g., least squares regression), estimate the coefficients $a$, $b_1$, $b_2$, and $b_3$ to minimize the sum of squared residuals between observed $y$ values and predicted $y$ values.

3. Interpret the Output: The result is the cubic equation that best fits the data.

If you upload the dataset or provide the values for $x$ and $y$, I can calculate the coefficients and provide the regression equation explicitly. Alternatively, I can guide you through performing this regression using software like Excel, Python, or statistical tools.

Would you like to upload the dataset or proceed with a step-by-step explanation?

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5 Questions:

1. What software or method do you plan to use for regression analysis (e.g., Excel, Python, or calculator)?
2. Are the data points evenly spaced or random?
3. Is there more than one independent variable, or is this a single-variable cubic regression?
4. Would you like help understanding how to interpret regression coefficients?
5. Should we assess the quality of the fit (e.g., using $R^2$)?

Tip: Always standardize or scale variables when working with regression to make coefficients easier to interpret, especially with polynomials.