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