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Advanced Correlation and Regression Analysis

A comprehensive guide to correlation, regression, and their applications in health research

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Advanced Correlation and Regression Analysis
From Theory to Health Research Applications
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Advanced Correlation and Regression Analysis
From Theory to Health Research Applications
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Part 1: Fundamentals of Correlation
Section summary or transition context...
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Learning Objectives
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    Understand the role of correlation in research
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    Differentiate dependent and independent variables
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    Interpret correlation strength and direction
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    Apply correlation to health-related data
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Why Correlation Matters in Research
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    Identifies relationships between variables
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    Guides hypothesis testing in studies
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    Informs predictive modeling in health sciences
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    Helps validate assumptions in experimental design
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Dependent vs Independent Variables
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    Independent: the variable you manipulate
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    Example: hours of sleep per night
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    Often denoted as X
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    Dependent: the outcome you measure
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    Example: mental health score
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    Often denoted as Y
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Types of Correlation
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Three scatter plots showing positive, negative, and zero correlation
Three scatter plots showing positive, negative, and zero correlation
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Correlation Strength and Direction
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    Range of r: -1 to +1
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    r = +1: perfect positive linear relationship
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    r = -1: perfect negative linear relationship
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    r = 0: no linear relationship
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    0.3 to 0.5: moderate, 0.5 to 1.0: strong
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“
A scatter plot is a visual story of how two variables dance together.
Adapted from statistical education literature
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Correlation in Health Research
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    Example: BMI and diabetes risk (r = 0.65)
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    Example: Stress levels and blood pressure (r = 0.50)
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    Example: Vaccination rates and disease incidence (r = -0.70)
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    Limitation: does not prove causation
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Part 2: Pearson Correlation
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Pearson Correlation Concept
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    Measures linear relationship between two continuous variables
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    Assumes normality and linearity
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    Sensitive to outliers
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    Formula: r = Cov(X,Y) / (σX * σY)
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Thank You and Q&A
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Key takeaways: correlation vs regression • Practice with health datasets for mastery • Explore advanced topics: multiple regression, logistic regression

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