The following table shows a tech product's sales during the financial years 2005–2009. (t is time in years since 2005.)
Year t	0	1	2	3	4
Sales S
(millions)	22.8	39.4	51.7	54.8	54.1
(a)
Find a quadratic regression model for these data. (Round coefficients to three significant digits.)
S(t) =

To find the quadratic regression model for the data, we assume the model has the form:

\[
S(t) = at^2 + bt + c
\]

We can use the given data to determine the coefficients \(a\), \(b\), and \(c\) by performing quadratic regression. The data provided is:

\[
\text{t (years)}: 0, 1, 2, 3, 4
\]
\[
\text{Sales S (millions)}: 22.8, 39.4, 51.7, 54.8, 54.1
\]

I will calculate the quadratic regression model for this dataset.

Let's compute the coefficients.The quadratic regression model for the given data is:

\[
S(t) = -3.129t^2 + 20.314t + 22.703
\]

Would you like more details on how this was computed or any further clarification?

Here are five related questions:
1. How does quadratic regression compare to linear regression in modeling trends?
2. Can this model be used to predict future sales beyond 2009?
3. How can we assess the accuracy of the quadratic model?
4. What is the significance of each coefficient in the quadratic equation?
5. How would the model change if we had sales data for more years?

**Tip:** Quadratic models are useful when data shows a non-linear trend, such as an initial increase followed by leveling off or a decline.

The following table shows a tech product's sales during the financial years 2005–2009. (t is time in years since 2005.)
Year t: 0, 1, 2, 3, 4
Sales S (millions): 22.8, 39.4, 51.7, 54.8, 54.1
(a) Find a quadratic regression model for these data. (Round coefficients to three significant digits.)
S(t) = 

Find the quadratic regression model for sales data from 2005 to 2009 using a statistical approach. Explore how to compute coefficients in the quadratic equation S(t) = -3.129t^2 + 20.314t + 22.703 with detailed steps. Suitable for Grades 10-12, this problem involves concepts in quadratic equations and regression analysis.

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