The image presents a problem where a cubic regression model is sought for a company's annual profits, measured in millions of dollars, over several years. The table provides profits from 2006 to 2010, with profits and years listed as follows:

• Years (relabelled as $x$ starting from 0 for 2006):
  $x = 0 \ (2006), \ 1 \ (2007), \ 2 \ (2008), \ 3 \ (2009), \ 4 \ (2010)$

• Profits (in millions of dollars):
  $P = 87.6, \ 85.4, \ 83.1, \ 81.5, \ 80.3$

The goal is to find the cubic regression model and determine the coefficient of the $x^2$ term in the model. The available options are:

• A) $-0.15$
• B) $-0.2320$
• C) $-0.2697$
• D) $-0.40$
• E) None of the above

I will now fit a cubic regression model to this data and calculate the coefficient for the $x^2$ term. Let's proceed.The coefficient of the $x^2$ term in the cubic regression model is approximately $-0.0571$. Since none of the provided options match this value, the correct answer is:

E) None of the above.

Would you like more details or have any questions? Here are five related questions you might want to explore:

1. How is a cubic regression model calculated from data points?
2. Can we use other types of regression (e.g., linear, quadratic) for this data set?
3. How do you interpret the coefficients of a cubic regression model in real-world scenarios?
4. What is the role of higher-order terms (like $x^3$, $x^2$) in a polynomial model?
5. How would the predictions change if we extended the model to predict future profits?

Tip: Always ensure your model fits the trend in the data before trusting its predictions—using a polynomial of too high a degree can lead to overfitting.