Week 10A Correlation Simple Regression(1) - Tagged
Page 1: Introduction to Correlations and Regression
Dr. Ryan Blything, PY2501 Research Methods & Data Analysis
Week 10 Lecture A focuses on:
Correlations (recap)
Simple Regression
Link to discussion platform: https://vevox.app/#/m/113082976
Page 2: Statistical Tests Overview
Types of ANOVA:
One-Way ANOVA (more than 2 levels)
One-Way Repeated Measures ANOVA
One-Way Independent Groups ANOVA
Decision Tree helps determine which test statistic to use based on:
Continuous DV
Nominal IV
Multiple Regression is introduced in this context, characterizing:
N-way Independent Groups ANOVA
N-way Repeated Measures ANOVA
Mixed Designs
Page 3: Structure of Lecture
Part 1: Correlation Recap
Definition of correlation
Understanding correlation coefficient
Part 2: Introduction to Regression
Differences between regression and correlation
Goals of regression analysis
Part 3: Preview of Multiple Regression
Distinction between Simple and Multiple Regression
Page 4: Importance of Learning Regression
Foundation for understanding various statistical analyses.
Frequently utilized by psychologists, particularly in final year projects.
Regression concepts underpin algorithms in machine learning and AI, which are integral to future technological advancements.
Page 5: Recap of Correlation
Strength of correlations:
Strong positive correlation
Moderate positive correlation
Weak positive correlation
No correlation
Weak negative correlation
Moderate negative correlation
Strong negative correlation
Perfect positive/negative correlation
Page 6: Correlational Analysis
Examines relationships between two continuous variables:
Examples of variables:
Advertising budget and album downloads
Meditation hours and average heartbeat
Fuel efficiency and car weight
Age of child and vocabulary skills
Provides a test statistic to support hypotheses.
Page 7: Correlation Coefficient Details
Defines strength and direction:
Range from -1 (perfect negative) to +1 (perfect positive)
Rationale for varying coefficients and their interpretations.
Example correlations:
Negative relationship between height and limbo-dancing ability.
Positive relationship between children’s age and height.
Page 8: Understanding Correlation Strength
Different scatter levels impact correlation strength:
Same slope can yield varying strength indicated by how tightly data points cluster.
More scatter = smaller correlation coefficient.
Page 9: Quick Quiz on Correlation
Suitable situation for correlation analysis.
Implication of a correlation coefficient of -0.5.
Comparing two scatterplot clusters and their correlation coefficients.
Page 10: Interpreting Correlation Coefficient
Using Jamovi for calculation:
Correlation coefficient indicated between -1 and +1.
P-value interpretation:
p > 0.05: correlation not significant.
p < 0.05: correlation significant.
Page 11: Example of Correlation
Navarro & Foxcroft example of correlation:
Dad's sleep hours vs. Newborn's sleep:
Pearson’s r = .63, p < .001 (positive and significant correlation).
Page 12: Extended Example Correlations
Examines relationships including:
Dad's Grumpiness versus sleep and newborn sleep (all significant correlations reported).
Page 13: Main Assumptions of Pearson’s r Correlation
Key assumptions must be met:
Linearity
No outliers detected
Normally distributed data
Alternatives when assumptions are violated:
Spearman’s rho test.
Page 14: Quick Quiz on Correlation Interpretation
Exercises on understanding significance in correlation results in Jamovi.
Page 15: Break Before Regression
Transition to discussing Simple Regression.
Page 16: Comparing Correlation and Regression
Key difference: Regression provides more information for prediction.
Page 17: When to Use Correlation vs. Regression
Deciding factors:
Correlation useful for direction/strength analysis.
Regression utilized for predicting outcomes and establishing cause-effect relationships.
Page 18: Prediction Through Regression
Regression aims to predict outcomes (Y) from predictors (X).
Example: Exam anxiety affecting performance results.
Page 19: Key Statistics in Regression Analysis
Essential statistics to report include:
Beta estimate,
T statistic,
F statistic,
R-squared values.
Page 20: Reporting Regression Results
Interpretation of statistics in context:
Example shows how anxiety impacts exam score prediction.
Page 21: Assessing Regression Fit
F statistic role in regression output interpretation.
Page 22: Variance Explained by Regression Model
Reporting R-squared and adjusted R-squared to convey variance.
Page 23: Summarizing Regression Reporting
Example reporting format with essential statistics provided.
Page 24: Quick Quiz on Regression Analysis
Exercises relating to the understanding of regression's function and outcomes.
Page 25: Additional Quick Quiz
More assessment on regression outputs and their meanings.
Page 26: Break Before Conclusion
Awaiting further details on multiple regression in next lecture.
Page 27: Reminder of Regression Key Takeaways
Key statistics reiterated for clarity on regression analysis outputs.
Page 28: Simple vs. Multiple Regression
Definitions of Simple Regression and the complexity of Multiple Regression introduced.
Page 29: Preview of Multiple Regression
Upcoming focus: detailed analysis of regression model components.
Page 30: Final Takeaway Messages
Correlation clearly shows relationship strength but lacks predictive capability.
Regression gives deeper insights, predicting outcomes while assessing model fit.
Page 31: Contact Information and Reminder
Dr. Blything's email for further questions: r.blything@aston.ac.uk
Highlights on assignments and quizzes to be looked into.