https://file.aiquickdraw.com/mathbot/file/172719110257787g6cl11.jpg

Let's work through the problem step by step.

### Information Given:
- **Equation of the line of best fit**: \( y = 0.8x + 8.09 \)
  - Where \( x \) is the number of years of experience, and \( y \) is the hourly pay rate.
  
### Table:
- We are asked to find the **predicted hourly pay rate** using the line of best fit for two values of experience: **6.8 years** and **8.9 years**.
- We also need to compute the **residual** for each of these values, which is given by the formula:
  \[
  \text{Residual} = \text{Observed value} - \text{Predicted value}
  \]
  
### Steps to Solve:
1. **Observed hourly pay rate**: Directly from the table:
   - For \( x = 6.8 \) years, the observed hourly pay rate is \( 12.40 \) dollars.
   - For \( x = 8.9 \) years, the observed hourly pay rate is \( 13.90 \) dollars.
   
2. **Predicted hourly pay rate**: Using the line of best fit formula \( y = 0.8x + 8.09 \), plug in the values for \( x = 6.8 \) and \( x = 8.9 \).

3. **Residual**: Compute the difference between the observed and predicted values.

Let me compute the predicted values and residuals.Here are the results for the table:

- **For \( x = 6.8 \) years**:
  - Observed hourly pay rate: **12.40** dollars
  - Predicted hourly pay rate: **13.53** dollars
  - Residual: **-1.13** dollars

- **For \( x = 8.9 \) years**:
  - Observed hourly pay rate: **13.90** dollars
  - Predicted hourly pay rate: **15.21** dollars
  - Residual: **-1.31** dollars

Would you like any further details or clarification on these calculations?

Here are five related questions to expand on the topic:
1. How is the line of best fit determined from a scatter plot?
2. What does a negative residual indicate in this context?
3. How could you assess if the line of best fit is a good predictor?
4. What methods could be used to improve the fit of the line to the data?
5. How would outliers affect the line of best fit?

**Tip**: A residual closer to 0 means the line of best fit predicts the data point more accurately!

The table and scatter plot show the number of years of experience and the hourly pay rate. The equation of the line of best fit is given as y = 0.8x + 8.09. Fill in the blanks with the observed pay rate, predicted pay rate, and residuals for 6.8 and 8.9 years of experience.

Learn how to apply linear regression to predict hourly pay rate from years of experience. Calculate residuals using the equation of the best-fit line y = 0.8x + 8.09. Suitable for high school students in Grades 9-12.

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