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 (4,14.59)
. Round the answer to the nearest thousandths.
The residual of the data point (4,14.59)
is
.
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 (4,14.59)
. Round the answer to the nearest thousandths.
The residual of the data point (4,14.59)
is
.
Answers
GPT-4o mini
To find the residual for the data point (4, 14.59), you need to determine the predicted value of y at \(x = 4\) using the line drawn through the points and then subtract that predicted value from the actual value.
1. **Find the predicted value**: This value will be determined using the line of best fit (trend line) that you mentioned is drawn through the points. However, without the specific equation of that line, we cannot compute the predicted value directly. You usually obtain the equation of the line in the format \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
2. **Calculate the residual**: Once you have \(y_{\text{predicted}}\) at \(x = 4\), you can calculate the residual using the formula:
\[
\text{Residual} = y_{\text{actual}} - y_{\text{predicted}}
\]
where \(y_{\text{actual}}\) is 14.59 in this case.
3. **Round to the nearest thousandth**: After you've calculated the residual, round your result to three decimal places.
Since I do not have the actual line of best fit equation from your description, you'll need to calculate \(y_{\text{predicted}}\) for \(x = 4\) and then proceed with finding the residual as described. If you provide the line equation, I can help you find \(y_{\text{predicted}}\) and the residual.
1. **Find the predicted value**: This value will be determined using the line of best fit (trend line) that you mentioned is drawn through the points. However, without the specific equation of that line, we cannot compute the predicted value directly. You usually obtain the equation of the line in the format \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
2. **Calculate the residual**: Once you have \(y_{\text{predicted}}\) at \(x = 4\), you can calculate the residual using the formula:
\[
\text{Residual} = y_{\text{actual}} - y_{\text{predicted}}
\]
where \(y_{\text{actual}}\) is 14.59 in this case.
3. **Round to the nearest thousandth**: After you've calculated the residual, round your result to three decimal places.
Since I do not have the actual line of best fit equation from your description, you'll need to calculate \(y_{\text{predicted}}\) for \(x = 4\) and then proceed with finding the residual as described. If you provide the line equation, I can help you find \(y_{\text{predicted}}\) and the residual.