Question

What is the best interpretation of this \(y\)-intercept?

a. The model predicts that the study time will increase \[37\] hours for each additional point scored.

b. The model predicts that the score will increase \[37\] points for each additional hour of study time.

c. The model predicts that a student who scored \[0\] points studied for \[37\] hours.

d. The model predicts that students who didn't study at all will have an average score of \[37\] points.

Answer 1

The best interpretation of the y-intercept is option 'd', which indicates that the model predicts students who did not study will have an average score of 37 points on the exam.

Step-by-step explanation:

Among the given options, the best interpretation of the y-intercept in a regression equation context is 'd'. The y-intercept represents the value of the dependent variable, in this case the exam score, when the independent variable, which is the study time, equals zero. Therefore, the model predicts that students who didn't study at all will have an average score of 37 points.

It's important to remember that the y-intercept gives us the starting value of y when x equals zero. The intercept can have meaningful interpretations in many contexts, such as estimating the starting salary of a job based on years of experience where x is zero at the beginning of the experience. A y-intercept of a regression line also sets the starting point of the line on the y-axis in a scatter plot capturing the relationship between two variables.