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 $\hat{y} = 50.793 + 0.901 x$ . 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.
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Final Answer: The predicted grade for a student who spent 9 hours on their homework is $59$ .

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Step 1 ：Given the regression line equation $\hat{y} = 50.793 + 0.901 x$ , 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 ： $\hat{y} = 50.793 + 0.901 \times 9$

Step 4 ：Calculate $\hat{y}$ to get the predicted grade.

Step 5 ： $\hat{y} = 58.902$

Step 6 ：Round $\hat{y}$ to the nearest whole number to get the final predicted grade.

Step 7 ： ${\hat{y}}_{r o u n d e d} = 59$

Step 8 ：Final Answer: The predicted grade for a student who spent 9 hours on their homework is $59$ .

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