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Problem Summary:

• We are given a quadratic regression equation for predicting the profit $\hat{y}$ of a company based on the number of years $x$: $\hat{y} = -0.34x^2 + 4.43x + 3.46$
• We need to find the predicted profit for year 4.

Calculation:

Plugging $x = 4$ into the equation:

$\hat{y} = -0.34(4)^2 + 4.43(4) + 3.46$

I'll perform the calculation.The predicted profit for year 4 using the given quadratic regression equation is approximately $15.74 million.

The correct answer is Option B: $15.74 million.

Would you like more details or have any other questions? Here are some related questions you might find interesting:

1. How do you derive a quadratic regression equation from data points?
2. What are the key components of a quadratic equation?
3. How does the coefficient of $x^2$ influence the shape of a quadratic graph?
4. What is the importance of using regression analysis in business forecasting?
5. How can residuals help in assessing the accuracy of a regression model?

Tip: Always check the fit of the regression model by analyzing residuals and ensuring no systematic patterns remain unmodeled.