Question

a student believes there is a correlation between the number of texts sent during class and gpa. the student collected data and found that the line of fit can be modeled by the equation $hat{y}=3.6 - 0.3x$. identify and interpret the slope in this scenario. the slope is -0.3. starting at 3.6, the gpa will increase by 0.3 for every text sent in class. the slope is -0.3. starting at 3.6, the gpa will decrease by 0.3 for every text sent in class. the slope is 3.6. starting at 0.3, the gpa will increase by 3.6 for every text sent in class. the slope is 3.6. starting at 0.3, the gp will decrease by 3.6 for every text sent in class.

Explanation:

Step1: Recall slope - intercept form

The equation of a line is $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept. In the given equation $\hat{y}=3.6 - 0.3x$ or $\hat{y}=-0.3x + 3.6$, the coefficient of $x$ is the slope. So, $m=-0.3$.

Step2: Interpret the slope

The slope represents the change in the dependent variable ($\hat{y}$, which is GPA here) for a one - unit change in the independent variable ($x$, which is the number of texts sent during class). Since the slope $m=-0.3$, for every one - unit increase in the number of texts sent during class ($x$ increases by 1), the predicted GPA ($\hat{y}$) decreases by 0.3. Starting at the y - intercept value of 3.6, the GPA will decrease by 0.3 for every text sent in class.

Answer:

The slope is -0.3. Starting at 3.6, the GPA will decrease by 0.3 for every text sent in class.