Question

Mari suspects that there is a relationship between the number of text messages high school students send and their academic achievement. To explore this, she asks a random sample of 52 students at her school how many text messages they sent yesterday and what their grade point average (GPA) was during the most recent marking period. Her data are summarized in the scatter plot below. The line of best fit is also shown as y=3.8-0.005x.

what is the GPA of someone who texted 200 and 90 times?

Answer 1

Interpretation of the slope: For students at this school, the predicted GPA decreases by 0.005 for each additional text message sent OR the GPA decreases by 0.005, on average, for each additional text message sent.

Interpretation of intercept: The model predicts that students at this school who send no text messages have, on average, a GPA of 3.8.

Explanation:

The purpose of this task is to assess the ability to interpret the slope and intercept of the line of best fit in context. There are two common errors that students make when interpreting the slope. Students may not make it clear that the slope is the predicted change (not necessarily an actual change) in GPA associated with an increase of 1 in the number of text messages sent. They also often do not communicate that the slope describes the change

You might want to point out that it is not always reasonable to interpret the intercept as the predicted y value when x = 0, as this often involves extrapolation far beyond the range of the x values in the data set. In this example, however, it is appropriate because there are observations with x = 0 in the data set.

You can also point out that the interpretation of the slope and intercept represents a generalization from the sample of 52 students to the population of all students at the school. This is appropriate because the sample was a random sample of students from the school.

Although this task is short and looks simple, some of the points brought out in this task are subtle. It might be a good strategy to engage in a whole class discussion of the correct interpretations.

Answer 2

The GPA of someone who texted 200 and 90 times would be approximately 2.8 and 3.4, respectively.

Based on the scatter plot and the equation of the line of best fit, the GPA of someone who texted 200 times would be approximately 2.8, and the GPA of someone who texted 90 times would be approximately 3.4.

This is because the line of best fit shows a negative correlation between the number of text messages sent and GPA. This means that as the number of text messages sent increases, the predicted GPA decreases.

To calculate the predicted GPA for someone who texted 200 times, we can simply plug the value of 200 into the equation of the line of best fit:

Predicted GPA = 3.8 - 0.005 * 200 = 2.8

To calculate the predicted GPA for someone who texted 90 times, we can simply plug the value of 90 into the equation of the line of best fit:

Predicted GPA = 3.8 - 0.005 * 90 = 3.4

It is important to note that these are just predicted values based on the line of best fit. The actual GPA of someone who texted 200 or 90 times could vary depending on a number of other factors, such as their study habits, homework completion, and test scores.