The following table gives the data for the hours students spent on homework and their grades on the first test. The equation of the regression line for this data is $\widehat{y}=50.793+0.901 x$. This equation is appropriate for making predictions at the 0.01 level of significance. If a student spent 9 hours on their homework, make a prediction for their grade on the first test. Round your prediction to the nearest whole number.
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\hline \multicolumn{10}{|c|}{ Hours Spent on Homework and Test Grades } \\
\hline Hours Spent on Homework & 38 & 26 & 33 & 47 & 8 & 34 & 49 & 43 & 11 & 25 \\
\hline Grade on Test & 85 & 70 & 76 & 92 & 54 & 79 & 97 & 89 & 62 & 87 \\
\hline
\end{tabular}
Answer
Final Answer: The predicted grade for a student who spent 9 hours on their homework is \(\boxed{59}\).
Step 1 ：Given the regression line equation \(\widehat{y}=50.793+0.901 x\), we are asked to predict the grade of a student who spent 9 hours on their homework.
Step 2 ：Substitute x (the number of hours spent on homework) with 9 in the equation to predict the grade of the student.
Step 3 ：\(\widehat{y}=50.793+0.901 \times 9\)
Step 4 ：Calculate \(\widehat{y}\) to get the predicted grade.
Step 5 ：\(\widehat{y}=58.902\)
Step 6 ：Round \(\widehat{y}\) to the nearest whole number to get the final predicted grade.
Step 7 ：\(\widehat{y}_{rounded}=59\)
Step 8 ：Final Answer: The predicted grade for a student who spent 9 hours on their homework is \(\boxed{59}\).
