Math Problem Statement

Who drew the line of best fit correctly to make predictions? Based on the scatterplot, what is the best prediction of the number of games a baseball team won if the team practiced 3 hours each week during the season?

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:

  1. How do you calculate the slope of the line of best fit?
  2. What factors could cause the two students to draw different lines of best fit?
  3. How can we use correlation coefficients to evaluate the strength of the relationship?
  4. Why is it important to use the line of best fit for making predictions in data analysis?
  5. 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