Jason found the trend line y = 6.6x + 13.4 for a dataset. One of the points in the dataset is (4,43.6) which of the following is accurate conclusion that he can make about the trend line

Question

The residual of the data point (4,43.6) is -354.4
The data point (4,43.6) is 297.16 units below the trend line
The data point (4,43.6) is 3.8 units above the trend line
The residual of the data point (4,43.6) is -3.8

Answer 1

To analyze the relationship between the data point (4, 43.6) and the trend line \(y = 6.6x + 13.4\), we first need to calculate the predicted value of \(y\) for \(x = 4\):

1. Calculate the predicted value: \[ y = 6.6(4) + 13.4 = 26.4 + 13.4 = 39.8 \]

2. Determine the residual: The residual is the difference between the actual value and the predicted value. The actual value at \(x = 4\) is \(43.6\): \[ \text{Residual} = \text{Actual} - \text{Predicted} = 43.6 - 39.8 = 3.8 \]

From this analysis, we can conclude that:

• The residual of the data point (4, 43.6) is 3.8.
• This means the data point is 3.8 units above the trend line.

Now, let's evaluate the statements provided:

1. The residual of the data point (4,43.6) is -354.4: False
2. The data point (4,43.6) is 297.16 units below the trend line: False
3. The data point (4,43.6) is 3.8 units above the trend line: True
4. The residual of the data point (4,43.6) is -3.8: False

Thus, the accurate conclusion that Jason can make about the trend line is: The data point (4,43.6) is 3.8 units above the trend line.