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### 📊 Analyzing Relationships Between Variables

#### 🔹 Linear Relationships (Continuous Variables)

- What test would I use to test the linear relationship between two continuous variables?

→ Pearson R Correlation Test

- What equation provides the line that best fits the data?

→ Regression Analysis

→ Must know the Regression Line Equation:

\( Y = \beta_0 + \beta_1X + \varepsilon \)

#### 🔹 Joint Variation

- Occurs when a variable varies directly or inversely with multiple variables.

#### 🔹 Partial Correlation

- Understand what partial correlations are and when to use them.

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### 🧹 Data Handling

- Listwise Deletion: Deletes entire row if any value is missing.

- Pairwise Deletion: Only excludes cases with missing values for the specific variables being analyzed.

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### 📏 Standardization and Covariance

- Know the importance of standardization:

→ Useful for interpreting effect sizes and comparing across variables.

→ Covariance alone doesn’t give meaningful scale.

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### 📊 Categorical Variables & Hypothesis Testing

- Test hypotheses with categorical variables:

→ Use Non-Parametric Tests (e.g., Chi-square)

- Matching tests to analysis types:

- Pearson R Correlation → Continuous variables

- Logistic Regression → Binary outcome

- Chi-Square Test → Categorical data

- Multiple Linear Regression → Multiple predictors, continuous outcome

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### 📈 Regression & Interpretation

- Standardized Beta Coefficients:

→ Interpret as change in standard deviation units of Y for each SD unit increase in X.

- Intercept (β₀):

→ Value of Y when all predictors = 0.

- Dummy Coding:

→ Used to code categorical variables in regression.

→ For K groups, use K - 1 dummy variables.

- When to use Binary Outcome:

→ If the dependent variable has only 2 categories (e.g., Yes/No), use Logistic Regression.

- Odds Ratio Interpretation Example:

→ Odds Ratio = 0.4 → 55% less likely (1 - 0.4 = 0.6 → 60%, approximate to 55% depending on context).

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### 🧮 Statistical Concepts to Know

- Power of a Test:

→ Probability of correctly rejecting the null.

→ Influenced by sample size, effect size, alpha level.

- Sum of Square Differences (SS):

→ Measure of total variability in the data.

- Model Sum of Squares:

→ Variability explained by the model.

- R² (R-squared):

→ Proportion of variance in Y explained by the predictors.

- Standard Deviation:

→ Measures spread or dispersion of a dataset.

- Know what Y and Beta-0 are:

→ \( Y \): Outcome variable

→ \( \beta_0 \): Intercept (baseline value of Y when X=0)

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