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The trend line for the following dataset is y=5x+3.4

with a correlation coefficient of 0.87. Complete the table to find the residual of each point.(2 points)
This table shows actual data points, corresponding trend line points, and residuals, with a correlation coefficient of 0.87.
Actual Point & nbsp; Point on Trend Line Residual
(1,9)
(
) (
)
(2,12.3)
(
) (
)
(3,18.625)
(
) (
)

1 answer

To find the residuals for each data point in the given dataset, we need to perform the following steps:

  1. Use the trend line equation \(y = 5x + 3.4\) to calculate the predicted value (point on the trend line) for each corresponding \(x\) value.
  2. Calculate the residual for each point using the formula: \[ \text{Residual} = \text{Actual value} - \text{Predicted value} \]

Let's go through this step-by-step for each point in your dataset:

For the first point (1, 9):

  1. Calculate the predicted \(y\) using the trend line: \[ y = 5(1) + 3.4 = 5 + 3.4 = 8.4 \]

  2. Calculate the residual: \[ \text{Residual} = 9 - 8.4 = 0.6 \]

For the second point (2, 12.3):

  1. Calculate the predicted \(y\): \[ y = 5(2) + 3.4 = 10 + 3.4 = 13.4 \]

  2. Calculate the residual: \[ \text{Residual} = 12.3 - 13.4 = -1.1 \]

For the third point (3, 18.625):

  1. Calculate the predicted \(y\): \[ y = 5(3) + 3.4 = 15 + 3.4 = 18.4 \]

  2. Calculate the residual: \[ \text{Residual} = 18.625 - 18.4 = 0.225 \]

Now we can fill in the values in the table.

| 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 |

Completed table:

| 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 |

Let me know if you need any more help!