Data was collected on the amount of time that a random sample of 8 students spent studying for a test and the grades they earned on the test. A scatter plot and line of fit were created for the data.

Question

scatter plot titled students' data, with points plotted at 1 comma 75, 2 comma 70, 2 comma 80, 2 comma 90, 3 comma 80, 3 comma 100, 4 comma 95, and 4 comma 100, and a line of fit drawn passing through the points 0 comma 60 and 2 comma 80

Find the y-intercept of the line of fit and explain its meaning in the context of the data.
5; for each additional hour a student studies, their grade is predicted to increase by 5% on the test
10; for each additional hour a student studies, their grade is predicted to increase by 10% on the test
60; a student who studies for 0 hours is predicted to earn 60% on the test
80; a student who studies for 0 hours is predicted to earn 80% on the test

Answer 1

To find the y-intercept of the line of fit, you can use the two points given that the line passes through: (0, 60) and (2, 80).

From these points, you can see that when the study time (x) is 0, the predicted grade (y) is 60%. This means that the y-intercept, which represents the predicted grade when no hours are studied, is 60.

Now, let's interpret this in the context of the data:

The correct interpretation of the y-intercept is: 60; a student who studies for 0 hours is predicted to earn 60% on the test.

This suggests that if a student does not study at all, they are expected to score 60% on the test. This is a starting point for understanding how study time may influence test scores, indicating a baseline performance without any study effort.