What is the predicted midterm score for a student who studies for 18 hours? What is the predicted midterm score for a student who doesn't spend any time studying? For an increase o... What is the predicted midterm score for a student who studies for 18 hours? What is the predicted midterm score for a student who doesn't spend any time studying? For an increase of one hour in the time spent studying, what is the predicted increase in the midterm score?
Understand the Problem
The question is asking us to use the given line of best fit equation to predict midterm scores based on students' study hours and to determine the increase in predicted score for an increase in study time.
Answer
(a) 85.04, (b) 15.56, (c) 3.86
Answer for screen readers
(a) 85.04
(b) 15.56
(c) 3.86
Steps to Solve
- Predicting the Midterm Score for 18 Hours of Study
To find the predicted midterm score for a student who studies for 18 hours, we use the line of best fit equation:
$$ y = 3.86x + 15.56 $$
Substituting ( x = 18 ):
$$ y = 3.86(18) + 15.56 $$
- Calculate the Result
Now, let's calculate the value:
$$ y = 3.86 \times 18 + 15.56 $$ $$ y = 69.48 + 15.56 $$ $$ y = 85.04 $$
Thus, the predicted midterm score for a student who studies for 18 hours is 85.04.
- Predicting the Midterm Score for 0 Hours of Study
Next, we predict the midterm score for a student who doesn’t study (0 hours):
Substituting ( x = 0 ):
$$ y = 3.86(0) + 15.56 $$
- Calculate the Result
Now, calculating this value:
$$ y = 0 + 15.56 $$ $$ y = 15.56 $$
So, the predicted midterm score for a student who doesn’t study is 15.56.
- Finding the Increase in Midterm Score for an Additional Hour of Study
The predicted increase in the midterm score for each additional hour of study is represented by the coefficient of ( x ) in the equation, which is 3.86.
(a) 85.04
(b) 15.56
(c) 3.86
More Information
The predictions are based on a linear relationship between study hours and midterm scores. The slope of the line (3.86) indicates the change in the midterm score for each additional hour of study.
Tips
- Incorrect Substitution: Make sure to substitute the correct values into the equation.
- Ignoring Units: Remember that ( x ) represents hours of study and ( y ) represents the score.
- Rounding Too Soon: Ensure to keep calculations exact until the final answer, as requested.
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