Math Problem Statement
Solution
Let's analyze the scatterplots to determine who drew the better line of best fit and to predict the number of games won if the team practiced 3 hours per week.
Step 1: Observing the Lines of Best Fit
- Justin's scatterplot shows a purple line. The slope appears steeper, suggesting that he predicts a higher number of games won per hour of practice.
- Brian's scatterplot has an orange line with a more moderate slope. His predictions suggest fewer games won compared to Justin for the same amount of practice.
Step 2: Checking Predictions for 3 Hours of Practice
Now, let's see what each line predicts for 3 hours of practice:
- In Justin's graph, if we trace from 3 hours of practice on the x-axis, the line of best fit crosses the y-axis at approximately 15 games.
- In Brian's graph, for 3 hours of practice, the line of best fit crosses the y-axis at around 13 games.
Step 3: Conclusion
The best prediction for the number of games won with 3 hours of practice is from Brian's line, which predicts 13 games. This suggests that Brian's line of best fit is more accurate than Justin's.
Therefore, the correct answer is: D. Brian; 13 games
Would you like further details on how to interpret scatterplots, lines of best fit, or have any additional questions?
Here are 5 related questions to deepen your understanding:
- How do you calculate the slope of the line of best fit?
- What factors could cause the two students to draw different lines of best fit?
- How can we use correlation coefficients to evaluate the strength of the relationship?
- Why is it important to use the line of best fit for making predictions in data analysis?
- Can the accuracy of the line of best fit be affected by outliers?
Tip: A steeper slope in a line of best fit means a higher rate of change; in this case, more games are won for each additional hour of practice.
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Math Problem Analysis
Mathematical Concepts
Scatterplots
Line of Best Fit
Linear Relationships
Prediction
Formulas
y = mx + b (slope-intercept form for linear equations)
Theorems
Least squares method for determining the line of best fit
Suitable Grade Level
Grades 6-8
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