To determine the best linear function that models the relationship between the number of times Brent's friends post on social media and their grade point averages (GPA), you would typically perform a linear regression analysis on the data collected from the scatter plot. The resulting equation would generally be in the form:
\[ y = mx + b \]
where:
- \( y \) is the predicted GPA,
- \( x \) is the number of social media posts,
- \( m \) is the slope of the line (the rate of change of GPA with respect to the number of posts),
- \( b \) is the y-intercept (the predicted GPA when the number of posts is zero).
The slope \( m \) represents the change in GPA for each additional post made on social media. If the slope is positive, it means that, on average, as the number of posts increases, the GPA tends to increase. Conversely, if the slope is negative, it indicates that as the number of posts increases, the GPA tends to decrease. The magnitude of the slope quantifies this relationship, showing how much the GPA changes with each additional social media post.
To summarize, once Brent finds the line of best fit from his scatter plot, he will have an equation that models the data, and the slope will provide insight into how social media activity relates to academic performance among his friends.
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