Question

1. emily works as a customer - service representative answering customer emails. for eight days she records the amount of time she spends answering emails and the number of emails she can answer during that time. her results are shown in the scatter - plot with the least squares regression line and the residual plot.

a. the residual for 3 hours is 4.5. interpret this value.
b. the residual for 4 hours is 0. explain what this means.
c. here is a list of each residual, rounded to the nearest tenth.
-5.6, -4.8, -3, 0, 2, 2.6, 4.2, 4.6
the mean of the residuals is 0 and the standard deviation of the residuals is 4.017. interpret this standard deviation.

Explanation:

Step1: Recall residual definition

The residual is the difference between the observed value and the predicted value from the regression line.

Step2: Interpret residual of 4.5 for 3 hours

A residual of 4.5 for 3 hours means that the actual number of emails Emily answered in 3 hours is 4.5 more than the number of emails predicted by the least - squares regression line.

Step3: Interpret residual of 0 for 4 hours

A residual of 0 for 4 hours means that the actual number of emails Emily answered in 4 hours is equal to the number of emails predicted by the least - squares regression line.

Step4: Interpret standard deviation of residuals

The standard deviation of the residuals (4.017) measures the average amount by which the residuals deviate from the mean residual (which is 0). A standard deviation of 4.017 indicates that, on average, the residuals are about 4.017 units away from 0. This gives an idea of how well the least - squares regression line fits the data. A smaller standard deviation would indicate a better fit.

Answer:

a. The actual number of emails answered in 3 hours is 4.5 more than the predicted number.
b. The actual number of emails answered in 4 hours is equal to the predicted number.
c. On average, the residuals deviate from 0 by about 4.017 units, indicating the average amount by which the observed values differ from the predicted values by the regression line.