Math Problem Statement
Many people believe that there is a negative relationship between the amount of time students play video games each week and their GPA.
x
10
3
0
2
5
4
7
y
1.5
2.4
3.2
3.5
2.7
3
2.1
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Is there a linear correlation between mean hours each week a student plays video games and GPA? ? Yes No Correct
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If there is a linear correation, write the correlation coefficient below. Otherwise, leave it blank. Round your final answer to four decimal places. r=
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If there is a linear correlation, write the regression equation below. Otherwise, leave it blank. Round all numbers to four decimal places. y^=
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Using the data shown above, predict a student's GPA when the student plays video games for 15 hours each week. Round your final answer to two decimal places.
Solution
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Yes, there is a linear correlation between the amount of time students play video games and their GPA, as indicated by a significant correlation coefficient.
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The correlation coefficient is .
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The regression equation is , where represents the predicted GPA and represents the hours of video games played.
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A student who plays video games for 15 hours each week is predicted to have a GPA of approximately 0.68.
Would you like more details or have any questions?
Here are 5 related questions:
- How is the strength of correlation determined?
- What does a negative correlation imply in this context?
- Can correlation imply causation between video games and GPA?
- What are potential factors that could affect GPA besides video game time?
- How would the regression change if outliers were present?
Tip: Always check the p-value to confirm the statistical significance of a correlation before interpreting its strength.
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Math Problem Analysis
Mathematical Concepts
Statistics
Linear Correlation
Regression Analysis
Formulas
Correlation coefficient (r): r = Σ((x - x̄)(y - ȳ)) / √(Σ(x - x̄)^2 * Σ(y - ȳ)^2)
Regression equation: ŷ = b0 + b1x
Theorems
Least Squares Method
Suitable Grade Level
Grades 10-12
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