To complete the table for the given dataset, we will need to calculate the corresponding points on the trend line and the residuals for each actual data point.
The trend line equation is given as \( y = 5x + 3.4 \). We will calculate the trend line points for each \( x \) value (1, 2, and 3), and then find the residuals using the formula:
\[ \text{Residual} = \text{Actual Value} - \text{Trend Line Value} \]
Let's calculate it step by step.
For \( x = 1 \):
- Actual Point: \( (1, 9) \)
- Trend line point: \( y = 5(1) + 3.4 = 5 + 3.4 = 8.4 \)
- Residual: \( 9 - 8.4 = 0.6 \)
For \( x = 2 \):
- Actual Point: \( (2, 12.3) \)
- Trend line point: \( y = 5(2) + 3.4 = 10 + 3.4 = 13.4 \)
- Residual: \( 12.3 - 13.4 = -1.1 \)
For \( x = 3 \):
- Actual Point: \( (3, 18.625) \)
- Trend line point: \( y = 5(3) + 3.4 = 15 + 3.4 = 18.4 \)
- Residual: \( 18.625 - 18.4 = 0.225 \)
Completed Table:
Now we can fill in the table as follows:
| Actual Point | Point on Trend Line | Residual | |--------------|---------------------|----------| | (1, 9) | (1, 8.4) | 0.6 | | (2, 12.3) | (2, 13.4) | -1.1 | | (3, 18.625) | (3, 18.4) | 0.225 |
This table gives the actual points, the values predicted by the trend line, and the calculated residuals for each point in the dataset.