Jason found the trend line y=6.6x+13.4

Question

for a dataset. One of the points in the dataset is (4,43.6)
. Which of the following is an accurate conclusion that Jason can make about the trend line? (1 point)
Responses

The residual of the data point (4,43.6)
is −354.4
.
The residual of the data point left parenthesis 4 comma 43.6 right parenthesis is negative 354.4 .

The data point (4,43.6)
is 3.8 units above the trend line.
The data point left parenthesis 4 comma 43.6 right parenthesis is 3.8 units above the trend line.

The residual of the data point (4,43.6)
is −3.8
.
The residual of the data point left parenthesis 4 comma 43.6 right parenthesis is negative 3.8 .

The data point (4,43.6)
is 297.16 units below the trend line.

Answer 1

To determine the accurate conclusion about the trend line and the data point \((4, 43.6)\), we need to calculate the value of \(y\) on the trend line when \(x = 4\).

The trend line is given by the equation: \[ y = 6.6x + 13.4 \]

Substituting \(x = 4\) into the equation: \[ y = 6.6(4) + 13.4 = 26.4 + 13.4 = 39.8 \]

Now, we have the value of \(y\) at \(x = 4\) on the trend line: \[ y = 39.8 \]

The actual data point is \((4, 43.6)\). To find the residual, we use the formula: \[ \text{Residual} = \text{Actual} - \text{Predicted} \] \[ \text{Residual} = 43.6 - 39.8 = 3.8 \]

Since the residual is positive, this means the data point is above the trend line by 3.8 units.

Therefore, the correct response is: The data point \((4, 43.6)\) is 3.8 units above the trend line.