Problem
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}
Solution
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 \(\boxed{59}\).
