Question

georges asked five of his friends how long they studied for the last math test and what grade they received. he found a linear regression equation for the data to be y = 9.6x + 65.8. what does the 9.6 mean in the context of this equation?
a his friends on average studied 9.6 hours.
b if they studied 9.6 hours they would get a 0 on the test.
c they should study 9.6 hours in order to get an a on the test.
d for every hour they studied their grade would go up 9.6 points.

Explanation:

Step1: Analyze the linear regression equation \(y = 9.6x+65.8\)

In a linear regression equation \(y = mx + b\) (where \(m\) is the slope and \(b\) is the y - intercept), the slope \(m\) represents the rate of change. Here, \(x\) is the number of study hours and \(y\) is the grade.

Step2: Interpret the slope

The slope \(m = 9.6\) means that for every unit increase in \(x\) (i.e., for every additional hour of study), \(y\) (the grade) increases by \(9.6\) points.

Answer:

D. For every hour they studied their grade would go up 9.6 points.