Question

Bivariate Data Sets Unit Test Part 2
4 of 104 of 10 Items





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.

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

To find the residual of a data point in a bivariate data set, you first need to find the predicted value from the line of best fit (or regression line) at the given x-value and then subtract that predicted value from the actual y-value of the data point.

In this case, you've provided the data point (2, 15.27). The actual value at x = 2 is 15.27. To find the residual, we need the predicted y-value that corresponds to x = 2 using the line of best fit.

1. Look at the line of best fit in the image you referred to.
2. Identify the predicted y-value (let's call it \( \hat{y} \)) for \( x = 2 \).
3. Use the formula for residual:
\[
\text{Residual} = \text{Actual y} - \text{Predicted y}
\]
4. Substitute the values:
\[
\text{Residual} = 15.27 - \hat{y}
\]

5. Round the answer to the nearest thousandths.

Since I don't have access to the specific line plotted in the image, you'll need to use that line to find \( \hat{y} \). Once you have it, you can plug it into the formula to get the final residual.

If you can provide the predicted y-value for (2), I can assist further in calculating the residual!