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 y = 49.884 +0.925x. This equation is appropriate for making predictions at the 0.01 level of significance. If a student spent 46 hours on their homework, make prediction for their grade on the first test. Round your prediction to the nearest whole number. Hours Spent on Homework and Test Grades 30 Hours Spent on Homework 26 27 35 38 13 41 40 48 6 Grade on Test 84 71 76 95 63 80 90 86 47 88
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 y = 49.884 +0.925x. This equation is appropriate for making predictions at the 0.01 level of significance. If a student spent 46 hours on their homework, make prediction for their grade on the first test. Round your prediction to the nearest whole number. Hours Spent on Homework and Test Grades 30 Hours Spent on Homework 26 27 35 38 13 41 40 48 6 Grade on Test 84 71 76 95 63 80 90 86 47 88
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![### Predicting Student Grades Based on Homework Hours
The following data represents the hours students spent on homework and their respective grades on the first test. The regression line equation for this dataset is:
\[ \hat{y} = 49.884 + 0.925x \]
This equation is applicable for making predictions at the 0.01 level of significance. Using this equation, if a student spent 46 hours on homework, we can predict their test grade. Remember to round your prediction to the nearest whole number.
#### Hours Spent on Homework and Test Grades
| Hours Spent on Homework | 26 | 27 | 35 | 38 | 13 | 41 | 40 | 48 | 6 | 30 |
|-------------------------|----|----|----|----|----|----|----|----|----|----|
| Grade on Test | 84 | 71 | 76 | 95 | 63 | 80 | 90 | 86 | 47 | 88 |
**Prediction Calculation Example:**
For a student who spent 46 hours on homework:
\[ \hat{y} = 49.884 + 0.925(46) \]
First, calculate the value inside the parentheses:
\[ 0.925 \times 46 = 42.55 \]
Next, add this value to 49.884:
\[ \hat{y} = 49.884 + 42.55 = 92.434 \]
Therefore, the predicted grade for a student who spent 46 hours on homework is approximately 92, when rounded to the nearest whole number.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F40f20eb5-0e51-4d3d-b863-3f4dfc0cabab%2F12bdd689-0f35-4af7-9f6a-23f548f091ad%2F1hxqvb_processed.png&w=3840&q=75)
Transcribed Image Text:### Predicting Student Grades Based on Homework Hours
The following data represents the hours students spent on homework and their respective grades on the first test. The regression line equation for this dataset is:
\[ \hat{y} = 49.884 + 0.925x \]
This equation is applicable for making predictions at the 0.01 level of significance. Using this equation, if a student spent 46 hours on homework, we can predict their test grade. Remember to round your prediction to the nearest whole number.
#### Hours Spent on Homework and Test Grades
| Hours Spent on Homework | 26 | 27 | 35 | 38 | 13 | 41 | 40 | 48 | 6 | 30 |
|-------------------------|----|----|----|----|----|----|----|----|----|----|
| Grade on Test | 84 | 71 | 76 | 95 | 63 | 80 | 90 | 86 | 47 | 88 |
**Prediction Calculation Example:**
For a student who spent 46 hours on homework:
\[ \hat{y} = 49.884 + 0.925(46) \]
First, calculate the value inside the parentheses:
\[ 0.925 \times 46 = 42.55 \]
Next, add this value to 49.884:
\[ \hat{y} = 49.884 + 42.55 = 92.434 \]
Therefore, the predicted grade for a student who spent 46 hours on homework is approximately 92, when rounded to the nearest whole number.
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