To complete the residual table, we follow these steps:

Steps:

1. Use the trend line equation $y = 3.5x + 10$ to calculate the predicted $y$-values for each $x$ (number of laps).
2. Subtract the predicted $y$-value from the actual $y$-value (time) to compute the residual for each $x$:
   $\text{Residual} = \text{Actual} - \text{Predicted}$

Given Data:

• $x$ values: $7, 8, 9, 10, 11$
• Actual $y$-values: $35.5, 37, 41.5, 45, 49.5$

Step-by-Step Computation:

1. Calculate predicted $y$-values: Using $y = 3.5x + 10$:

   • For $x = 7$:
     $y = 3.5(7) + 10 = 24.5 + 10 = 34.5$
   • For $x = 8$:
     $y = 3.5(8) + 10 = 28 + 10 = 38$
   • For $x = 9$:
     $y = 3.5(9) + 10 = 31.5 + 10 = 41.5$
   • For $x = 10$:
     $y = 3.5(10) + 10 = 35 + 10 = 45$
   • For $x = 11$:
     $y = 3.5(11) + 10 = 38.5 + 10 = 48.5$

2. Calculate residuals: $\text{Residual} = \text{Actual} - \text{Predicted}$

   • For $x = 7$:
     $35.5 - 34.5 = 1.0$
   • For $x = 8$:
     $37 - 38 = -1.0$
   • For $x = 9$:
     $41.5 - 41.5 = 0.0$
   • For $x = 10$:
     $45 - 45 = 0.0$
   • For $x = 11$:
     $49.5 - 48.5 = 1.0$

Completed Residual Table:

Let me know if you need further clarifications or calculations!

Related Questions:

1. What does the residual represent in this context?
2. How do positive and negative residuals affect the trend line's accuracy?
3. How can you check if the trend line is a good fit for the data?
4. How is a residual plot used to evaluate a regression line?
5. What adjustments can be made if residuals indicate a poor fit?

Tip: Residuals close to 0 indicate that the trend line predicts the data well; large residuals suggest a poor fit!