Question

Use the image to answer the 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.

Find the residual of the data point (2,15.27)
. Round the answer to the nearest thousandths.

Answer 1

To calculate the residual of a data point in a regression model, you need to find the difference between the observed value (the y-coordinate of the data point) and the predicted value (the y-coordinate predicted by the regression line) at the same x-coordinate.

Given the data point (2, 15.27):
- The observed value (y) is 15.27 (the actual y-value at x = 2).
- You need to determine the predicted value (y') at x = 2 using the regression line.

Assuming you have the equation of the regression line from the plotted points, you can input 2 into that equation to find the predicted value.

Let's denote the predicted value as \( y' \).

The residual can be calculated using the following formula:
\[
\text{Residual} = \text{Observed value} - \text{Predicted value} = y - y'
\]

Now, let's substitute for \( y \) and \( y' \):
\[
\text{Residual} = 15.27 - y'
\]

If you provide the equation of the regression line or the predicted value for \( x = 2 \), I can help you compute the residual. Please share that information for the final calculation!