Use a graphing utility to find the equation of the line of best fit. Round to two decimal places, if necessary.
-Ten students in a graduate program were randomly selected. Their grade point averages (GPAs) when they entered the program were between 3.5 and 4.0. The following data were obtained regarding their GPAs on entering the program
Versus their current GPAs. $\begin{array}{cc}
\text { Entering GPA } & \text { Current GPA } \
\hline 3.5 & 3.6 \
3.8 & 3.7 \
3.6 & 3.9 \
3.6 & 3.6 \
3.5 & 3.9 \
3.9 & 3.8 \
4.0 & 3.7 \
3.9 & 3.9 \
3.5 & 3.8 \
3.7 & 4.0
\end{array}$
A) $y = 0.50 x + 5.81$
B) $y = 0.03 x + 3.67$
C) $y = 0.02 x + 4.91$
D) $y = 0.33 x + 2.51$

Question

Quizplus · Accepted Answer

Using a graphing utility to plot the given data points and then applying a linear regression function, the line of best fit can be calculated. The coefficients (slope and y-intercept) are determined by the utility based on minimizing the sum of the squared differences between the observed values and the values predicted by the linear model. The option that closely matches the output of such a calculation, given the data provided, is $y = 0.03 x + 3.67$, which suggests a slight positive correlation between entering GPA and current GPA with a small slope, indicating a modest increase in GPA over time.

Use a Graphing Utility to Find the Equation of the Line