The table and scatter plot show the number of years of experience, x, and the hourly pay rate, y, for each of 11 cashiers in New York.

The equation of the line of best fit is y=0.9x+7.95.

Experience, x (in years)

Hourly pay rate, y (in dollars)

0.8

7.48

1.1

8.00

1.1

9.42

2.2

9.03

3.3

11.36

3.6

12.41

3.8

13.00

5.0

14.50

6.8

12.40

8.5

15.39

9.0

15.99


Hourly pay rate (in dollars)

Experience (in years)

Use 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.

Number of years of experience

5.0


6.8

Observed hourly pay rate (in dollars)

Predicted hourly pay rate (in dollars)

X

Residual (in dollars)




To fill in the blanks with the predicted hourly pay rate and the residuals, we will use the equation of the line of best fit and the observed data.

### Steps to Follow:

1. **Equation of the line of best fit**: 
   \[
   y = 0.9x + 7.95
   \]
   This equation predicts the hourly pay rate \( y \) based on the years of experience \( x \).

2. **Residual**:
   \[
   \text{Residual} = \text{Observed } y - \text{Predicted } y
   \]

Now, let’s calculate the predicted hourly pay rates and the residuals for \( x = 5.0 \) years and \( x = 6.8 \) years of experience.

### Calculations:

#### For \( x = 5.0 \) years:
- **Predicted \( y \)**:
  \[
  y = 0.9(5.0) + 7.95 = 4.5 + 7.95 = 12.45 \text{ dollars}
  \]
- **Observed \( y \)**: 14.50 dollars (from the table).
- **Residual**:
  \[
  \text{Residual} = 14.50 - 12.45 = 2.05 \text{ dollars}
  \]

#### For \( x = 6.8 \) years:
- **Predicted \( y \)**:
  \[
  y = 0.9(6.8) + 7.95 = 6.12 + 7.95 = 14.07 \text{ dollars}
  \]
- **Observed \( y \)**: 12.40 dollars (from the table).
- **Residual**:
  \[
  \text{Residual} = 12.40 - 14.07 = -1.67 \text{ dollars}
  \]

### Final Table:

| Number of years of experience (in years) | Observed hourly pay rate (in dollars) | Predicted hourly pay rate (in dollars) | Residual (in dollars) |
|------------------------------------------|---------------------------------------|----------------------------------------|------------------------|
| 5.0                                      | 14.50                                 | 12.45                                  | 2.05                   |
| 6.8                                      | 12.40                                 | 14.07                                  | -1.67                  |

Let me know if you need further details or explanations!

Here are 5 related questions for practice:
1. What is the predicted hourly pay rate for 3.3 years of experience?
2. Calculate the residual for a cashier with 9.0 years of experience and an observed hourly pay rate of 15.99 dollars.
3. What does a positive residual indicate in this context?
4. How would a different y-intercept (e.g., 8.5 instead of 7.95) affect the predicted pay rates?
5. Why is it important to compare observed values with predicted values in regression analysis?

**Tip**: Residuals can help identify if there are outliers in the data, where the observed values are much higher or lower than what the model predicts.

Learn how to calculate predicted hourly pay rates using linear regression with the equation of a line. Utilize residuals to assess model accuracy. Practice questions included.

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