(Score for Question 3: of 10 points)
3. The table shows the test scores and the sleep averages of several students.
\begin{tabular}{|l|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline Test Score (\%) & 88 & 75 & 76 & 92 & 96 & 94 & 83 & 90 & 99 & 65 & 77 & 88 & 82 & 83 & 94 & 97 \
\hline Average Sleep (h) & 7 & $ 6.5 $ & 6 & $ 7.5 $ & 8 & 7 & $ 6.5 $ & 8 & $ 8.5 $ & 5 & 7 & 9 & 8 & $ 8.5 $ & $ 8.5 $ & 9 \
\hline
\end{tabular}
(a) Write the least squares regression equation that models the data.
Let $ x= $ the test score and $ y= $ average sleep.
(b) Use the equation to determine the approximate test score of a student who sleeps an average of 8 hours a night.
Show your work.
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