To find $R^2$, we need to perform linear regression on the given data. $R^2$ (the coefficient of determination) measures how well the independent variable (number of salespeople) predicts the dependent variable (sales in $1000).

The formula for $R^2$ is:

$R^2 = 1 - \frac{\text{SS}_{\text{res}}}{\text{SS}_{\text{tot}}}$

Where:

• $\text{SS}_{\text{res}}$ is the sum of the squares of residuals (the difference between observed and predicted values),
• $\text{SS}_{\text{tot}}$ is the total sum of squares (the difference between observed values and their mean).

Let me calculate the $R^2$ value based on the provided data.The value of $R^2$ is approximately 96.31%.

This means that about 96.31% of the variation in sales (in $1000) can be explained by the number of salespeople. The higher the $R^2$ value, the better the model fits the data.

Do you want more details or have any questions about the process?

Here are 5 related questions to expand your understanding:

1. How is the $R^2$ value interpreted in a real-world context?
2. What other metrics can be used to assess the quality of a linear regression model?
3. How would adding more data points affect the $R^2$ value?
4. Can $R^2$ be used for non-linear models as well?
5. What are the limitations of using $R^2$ as a metric for model performance?

Tip: Always check residual plots to ensure that the linear regression model assumptions hold.