Use the equation of the line of best fit, y = -0.76x + 26.04, to answer the questions below. (a) What is the predicted time spent doing homework for a student who doesn't spend any... Use the equation of the line of best fit, y = -0.76x + 26.04, to answer the questions below. (a) What is the predicted time spent doing homework for a student who doesn't spend any time watching TV? (b) For an increase of one hour in the time spent watching TV, what is the predicted decrease in the time doing homework? (c) What is the predicted time spent doing homework for a student who spends 18 hours watching TV?
Understand the Problem
The question is asking us to use the provided equation of the line of best fit to compute the predicted time spent on homework based on the time spent watching TV for different scenarios. Specifically, we need to derive answers for three distinct parts involving calculations based on the equation.
Answer
(a) 26.04 hours (b) 0.76 hours (c) 12.36 hours
Answer for screen readers
(a) 26.04 hours
(b) 0.76 hours
(c) 12.36 hours
Steps to Solve
- Understanding the Equation of Best Fit
The equation given is ( y = -0.76x + 26.04 ). Here, ( y ) is the time spent doing homework (in hours) and ( x ) is the time spent watching TV (in hours).
- Part (a): Predicted Homework Time for 0 Hours of TV
To find the predicted time spent doing homework when a student doesn't spend any time watching TV, substitute ( x = 0 ) into the equation:
$$ y = -0.76(0) + 26.04 $$
This simplifies to:
$$ y = 26.04 $$
- Part (b): Decrease in Homework Time for 1 Hour Increase in TV
For an increase of one hour in TV watching, substitute ( x = 1 ):
$$ y = -0.76(1) + 26.04 $$
This gives:
$$ y = -0.76 + 26.04 = 25.28 $$
Now, to find the decrease:
$$ \text{Decrease} = 26.04 - 25.28 = 0.76 $$
- Part (c): Predicted Homework Time for 18 Hours of TV
Substituting ( x = 18 ):
$$ y = -0.76(18) + 26.04 $$
Calculating this:
$$ y = -13.68 + 26.04 = 12.36 $$
(a) 26.04 hours
(b) 0.76 hours
(c) 12.36 hours
More Information
The results indicate how time spent watching TV negatively impacts the time a student can dedicate to homework. The predictions are derived from the linear regression analysis, which attempts to model the relationship between two variables.
Tips
- Forgetting to substitute the correct values: Always double-check the values substituted into the equation.
- Incorrectly calculating the decrease: Ensure you subtract the predicted homework time after the increase in TV watching from the original prediction.
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