Question 9 of 15 , Step 1 of 1
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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 $\widehat{y}=49.355+0.962 x$. This equation is appropriate for making predictions at the 0.01 level of significance. If a student spent 30 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 & 40 & 21 & 31 & 40 & 6 & 44 & 52 & 33 & 10 & 25 \\
\hline Grade on Test & 88 & 68 & 90 & 93 & 50 & 83 & 96 & 82 & 59 & 75 \\
\hline
\end{tabular}
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Final Answer: The predicted grade for a student who spent 30 hours on their homework is \(\boxed{78}\).
Step 1 ：Given the equation of the regression line is \(\widehat{y}=49.355+0.962 x\), where \(x\) is the hours spent on homework and \(\widehat{y}\) is the predicted grade on the test.
Step 2 ：Substitute \(x = 30\) into the equation to find the predicted grade: \(\widehat{y}=49.355+0.962 \times 30\).
Step 3 ：Calculate the value to get the predicted grade.
Step 4 ：Round the predicted grade to the nearest whole number.
Step 5 ：Final Answer: The predicted grade for a student who spent 30 hours on their homework is \(\boxed{78}\).
