Question
Mandla found the equation of the regression line relating hours worked per week, \( x \), and the number of units, \( y \), community college students take per term to be: \( \hat{y}=18-0.2 x \) To estimate the number of units that a community college student who works 20 hours per week will take, we calculate: \( 18-0.2(20) \) Find this number.
Ask by Daniel Fowler. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
A student who works 20 hours per week is estimated to take 14 units.
Solution
To estimate the number of units, substitute x = 20 into the equation:
ŷ = 18 - 0.2(20)
First, calculate 0.2 multiplied by 20:
0.2 × 20 = 4
Then, subtract 4 from 18:
18 - 4 = 14
Thus, a community college student who works 20 hours per week is estimated to take 14 units.
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Simplify this solution Extra Insights
To estimate the number of units a community college student who works 20 hours per week will take, we substitute \( x = 20 \) into the regression equation \( \hat{y} = 18 - 0.2x \): \[ \hat{y} = 18 - 0.2(20) = 18 - 4 = 14. \] So, a community college student who works 20 hours per week is estimated to take 14 units per term. Additionally, this regression line suggests that for every additional hour a student works, the number of units they take decreases by 0.2. It’s a useful tool for understanding the balance between work commitments and academic workload. Students can leverage this information for planning their schedules effectively!
