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!