The table and scatter, plot show the time spent texting, x, and the time spent exercising, y, by each of 9 students last week.
The equation of the line of best fit is y=-0.4x+7.07.
Time spent texting, x (in hours)
Time spent exercising, y (in hours)
210
6.44
2.20
554
2.80
6.96
150
524
4.00
5.50
4.50
5.24
5.00
6.50
3.28
5.50
5.90
5:50
Time spent texting (in hours)
Vise the equation of the line of best fit, and use the table above, to fill in the blanks below.
Give exact answers, not rounded approximations.
Time spent texting (in hours)
5.00
5.90
Observed time spent exercising (in hours)
Predicted time spent exercising (in hours)
X
Residual (in hours)

To fill in the table with the predicted time spent exercising and the residuals, we'll follow these steps:

1. **Equation of the line of best fit**: \( y = -0.4x + 7.07 \)
   - This equation is used to predict the time spent exercising (in hours) based on the time spent texting (in hours).

2. **Predicted time spent exercising**:
   - Use the equation of the line of best fit to calculate the predicted value of \( y \) (time spent exercising) for each value of \( x \) (time spent texting).

3. **Residual**:
   - The residual is the difference between the observed time spent exercising and the predicted time spent exercising.
   - Residual = Observed \( y \) - Predicted \( y \)

Let's calculate the predicted values and residuals for the given time spent texting (5.00 hours and 5.90 hours).

### For \( x = 5.00 \) hours:
- **Predicted \( y \)**: 
  \[
  y = -0.4(5.00) + 7.07 = -2 + 7.07 = 5.07 \text{ hours}
  \]
- **Observed \( y \)**: From the table, the observed time spent exercising for 5.00 hours of texting is 6.50 hours.
- **Residual**:
  \[
  \text{Residual} = 6.50 - 5.07 = 1.43 \text{ hours}
  \]

### For \( x = 5.90 \) hours:
- **Predicted \( y \)**: 
  \[
  y = -0.4(5.90) + 7.07 = -2.36 + 7.07 = 4.71 \text{ hours}
  \]
- **Observed \( y \)**: From the table, the observed time spent exercising for 5.90 hours of texting is 5.90 hours.
- **Residual**:
  \[
  \text{Residual} = 5.90 - 4.71 = 1.19 \text{ hours}
  \]

### Summary Table:

| Time spent texting (in hours) | Observed time spent exercising (in hours) | Predicted time spent exercising (in hours) | Residual (in hours) |
|-------------------------------|-------------------------------------------|--------------------------------------------|---------------------|
| 5.00                           | 6.50                                      | 5.07                                       | 1.43                |
| 5.90                           | 5.90                                      | 4.71                                       | 1.19                |

Let me know if you would like more details or have further questions. 

Here are 5 related questions for practice:
1. What would be the predicted time spent exercising for 7 hours of texting?
2. If a student spent 2 hours texting, what is the predicted time spent exercising using the line of best fit?
3. How do you interpret a positive residual in this context?
4. What does the slope of -0.4 mean in terms of the relationship between texting and exercising?
5. How would the residuals change if the line of best fit had a steeper slope?

**Tip**: Residuals can help you understand the accuracy of your model—large residuals indicate that the model may not be fitting the data well in those areas.

Learn how to predict time spent exercising from time spent texting using the line of best fit equation y = -0.4x + 7.07. Detailed steps include calculating predicted values and residuals for specific texting times.

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