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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

  1. Foundation for understanding various statistical analyses.

  2. Frequently utilized by psychologists, particularly in final year projects.

  3. 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

  1. Suitable situation for correlation analysis.

  2. Implication of a correlation coefficient of -0.5.

  3. 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:

    1. Linearity

    2. No outliers detected

    3. 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.