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Questions and Answers
What is an explanatory variable?
What is an explanatory variable?
A variable that explains or influences changes in a response variable.
What is a response variable?
What is a response variable?
A measurement for the outcome of a study.
A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The explanatory variable is on the ______ axis and the response variable is on the ______ axis.
A scatterplot shows the relationship between two quantitative variables measured on the same individuals. The explanatory variable is on the ______ axis and the response variable is on the ______ axis.
x, y
What are the four key aspects to describe when interpreting scatterplots?
What are the four key aspects to describe when interpreting scatterplots?
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Does association (correlation) imply causation?
Does association (correlation) imply causation?
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What does correlation measure?
What does correlation measure?
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Correlation is affected by outliers.
Correlation is affected by outliers.
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What variables are considered in correlation analysis?
What variables are considered in correlation analysis?
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How does the year 2008's revenue affect the correlation in the study on arcade games and computer science doctorates?
How does the year 2008's revenue affect the correlation in the study on arcade games and computer science doctorates?
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Study Notes
Explanatory and Response Variables
- Explanatory Variable: Influences changes in the response variable; also known as the independent variable.
- Response Variable: Outcome measurement of a study; referred to as the dependent variable.
- Some studies aim to demonstrate causal relationships, whereas others show merely associative relationships.
Scatterplots
- Tool to visualize the relationship between two quantitative variables measured on the same individuals.
- Plots explanatory variable on the x-axis and response variable on the y-axis; axes must be labeled and scaled.
- Each data point represents an individual’s measurements.
Interpreting Scatterplots
- Direction: Can be positive, negative, or absent.
- Unusual Features: Identify outliers or clusters.
- Form: Can be linear or nonlinear.
- Strength: Classify as weak, moderate, or strong.
- Describe associations using these characteristics in context.
Example Study on Manatees
- Data on boats registered in Florida and corresponding manatee deaths from 1977-2007.
- Analyze scattered points for any trends or patterns.
Old Faithful Eruptions Analysis
- Compare duration of eruption against the interval between eruptions.
- Evaluate direction, form, strength, outliers, and predictive information needed for future eruptions.
Important Concept: Association and Causation
- Association (correlation) does not imply causation. Consider other influencing factors in the observed relationship.
Measuring Linear Association
- Experiment with scatterplots to achieve different correlation coefficients, e.g., targeting r ≈ 0.7.
- Correlation coefficient is sensitive to outliers and must be interpreted in context.
Facts about Correlation
- Correlation applies only to pairs of quantitative variables.
- No distinction between explanatory and response variables in calculating correlation.
- Correlation (r) is unitless and not affected by units.
- Measures strength of linear relationships but can be skewed by outliers.
- Correlation alone cannot serve as a complete summary of data.
Gaming and Education Example
- Relationship studied between arcade revenue and computer science doctoral degrees awarded.
- Question correlation: Does playing video games influence degree attainment?
- Year 2008 data point may significantly affect correlation interpretation; consider implications of outlier influence.
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