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Question

Four points are plotted on the first quadrant of a coordinate plane. The x-axis ranges from 0 to 10 in increments of 1 and the y-axis ranges from 0 to 17 in increments of 1. A line is drawn that almost passes through all the points.
The other points are (1,16.88) and (3,15.2) and (4,14.59)
Y = -0.694x + 17.22
Find the residual of the data point (2,15.27)
. Round the answer to the nearest thousandths.

(1 point)
The residual of the data point (2,15.27)
is
.
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Answer 1

To find the residual of the data point (2, 15.27), we need to follow these steps:

1. Calculate the predicted y-value using the regression equation \( Y = -0.694x + 17.22 \) for \( x = 2 \).
2. Subtract the predicted y-value from the actual y-value (15.27) to find the residual.

Step 1: Calculate the predicted y-value

Using the equation: \[ Y = -0.694(2) + 17.22 \]

Calculating this: \[ Y = -1.388 + 17.22 = 15.832 \]

Step 2: Calculate the residual

The residual is calculated as follows: \[ \text{Residual} = \text{Actual y-value} - \text{Predicted y-value} \] \[ \text{Residual} = 15.27 - 15.832 \] \[ \text{Residual} = -0.562 \]

Rounding to the nearest thousandths: \[ \text{Residual} \approx -0.562 \]

Thus, the residual of the data point \( (2, 15.27) \) is -0.562.