In an experiment, a group gathers different rechargeable devices like phones, watches, electric toothbrushes, headphones, and cordless vacuums. They use each device until the battery runs out and record the initial battery life in hours. They use the devices for a year and then do the same experiment 1 year later, and record the battery life in hours again.

In this table, the first column shows battery life for 20 devices initially and the second column shows battery life 1 year later.

The scatter plot shows the battery life measurements for 20 devices together with the graph of .

The function described by the equation is a model of the relationship between the initial and later battery life for a device.

This model predicts the later battery life from the device's initial battery life. These predicted battery lives are shown in the third column of the table.

A scatterplot. Horizontal, from 10 to 50, by fives, labeled initial battery life (hours). Vertical, from 10 to 45, by fives, labeled later battery life (hours). Line  drawn, trend linearly upward and right with 20 data points above and below line.

1. Two devices that both have an initial battery life of 31 hours have different later battery life. What are their later battery lives? How can you see this in the table? How can you see this in the graph?

2. The model predicts that when the initial battery life is 31 hours, the later battery life will be 26.25. How can you see this in the graph? How can you see this using the equation?

3. One of the devices has an initial battery life of 29 hours. What does the model predict for its later battery life? How does that compare to the actual later battery life?

4. Find a device for which the model makes a very good prediction of the actual later battery life. How can you see this in the table? In the graph?

5. Find a device for which the model’s prediction is not very close to the actual later battery life. How can you see this in the table? In the graph?

Here is a scatter plot that shows lengths and widths of 20 different left feet.

A scatterplot. Horizontal, from 20 to 32, by 2's, labeled foot length in centimeters. Vertical, from 7 to 12, by 1’s, labeled foot width in centimeters. 20 dots trend upward and to the right.

1. Estimate the widths of the longest foot and the shortest foot.

2. Estimate the lengths of the widest foot and the narrowest foot.

3. Here is the same scatter plot together with the graph of a model for the relationship between foot length and width.

   

   A scatterplot. Horizontal, from 20 to 32, by 2's, labeled foot length in centimeters. Vertical, from 7 to 12, by 1’s, labeled foot width in centimeters. 20 dots trend upward and to the right. Line drawn, trends linearly upward and right with 11 dots above lie and 9 below. No dots lie on the line. The line begins at about point 21 point 9 comma 9 and ends at about 31 point 25 comma 11 point 5.

   Circle the data point that seems weird when compared to the model. What length and width does that point represent?