Number of sales people working	Sales (in $1000)
2	10
3	12
6	14
9	15
11	19
11	21
13	21
15	24
17	24
19	27
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Part 1
Data from a small bookstore are shown in the accompanying table. What is the value of Rsquared and what does it​ mean?
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Question content area bottom
Part 1
What is the value of Rsquared​?
Rsquaredequals
  
enter your response here​%
​(Round to two decimal places as​ needed.)

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.

Data from a small bookstore are shown in the accompanying table. What is the value of R-squared and what does it​ mean?

Learn how to calculate the R-squared value for a small bookstore's sales data using linear regression. This example walks through the formula for R-squared, which indicates how well the number of salespeople predicts sales in $1000. A detailed solution shows how 96.31% of the variation in sales can be explained by the independent variable. Suitable for students in Grades 11-12 or introductory college statistics courses.

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