To find the linear regression equation for this data, we need to calculate the slope ($m$) and the y-intercept ($b$) for a line in the form:

$y = mx + b$

Steps to solve:

1. Calculate the slope $m$ using: $m = \frac{n \sum(xy) - \sum x \sum y}{n \sum(x^2) - (\sum x)^2}$ where $n$ is the number of data points.

2. Calculate the y-intercept $b$ using: $b = \frac{\sum y - m \sum x}{n}$

3. Substitute values into $y = mx + b$ to form the regression equation.

4. Project the number of cases for 2011, which corresponds to $x = 9$ (since 2011 is 9 years after 2002).

Let's calculate this step-by-step.The linear regression equation that represents this data is:

$y = 39.7x + 1127.8$

Using this equation to project the number of new cases for the year 2011 ($x = 9$), we find:

$y = 39.7 \times 9 + 1127.8 \approx 1485$

Thus, the projected number of new cases for 2011 is approximately 1485.

Would you like a more detailed breakdown of these steps? Here are some related questions for further exploration:

1. How do we interpret the slope and y-intercept in the context of this problem?
2. What is the significance of using linear regression for predictions?
3. Could we use a different type of regression if the data showed a non-linear pattern?
4. How does rounding affect the accuracy of our predictions?
5. What assumptions are we making with linear regression here?

Tip: Always check the correlation of your data points to see if a linear model is the best fit for predictions.