Problem
Question 9 of 15 , Step 1 of 1 Correct 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} Copy Data Answer Keypad How to enter your answer (opens in new window) Keyboard Shortcut Tutor Skip Try Similar Submit Answer
Solution
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 \(\boxed{78}\).
