Topic 2: Regression Analysis

Correlation analysis

Measures strength and direction of a linear relationship between two variables.

Difference between Spearman and Pearson correlation

Pearson: linear, continuous data. Spearman: ranked/ordinal data.

Correlation vs. Chi-square

Correlation: continuous variables. Chi-square: categorical variables.

Correlation coefficient (r)

Ranges from -1 to 1. +1 = perfect positive, -1 = perfect negative, 0 = no correlation.

Scatterplot for different correlations

Strong = tight line; Weak = spread out. Positive = slopes up; Negative = slopes down.

Does correlation imply causation?

No, it only indicates association.

Correlation vs. regression

Correlation shows relationship strength; regression predicts a dependent variable from independent variables.

Outputs of correlation and regression

Correlation: r, p-value; Regression: beta (coefficients), intercept, p-values, R^2.

Regression line drawing method

Using Ordinary Least Squares (OLS).

Beta (regression coefficient)

Shows expected change in dependent variable per unit change in independent variable.

Interpret beta = 0.15 for data used (MB) and phone bill ($)

Each MB increases bill by $0.15 on average.

Difference between r and beta

r: correlation strength; beta: effect size in prediction.

Two sets of p-values in regression

For the overall model and for individual coefficients.

Interpretation of p-values in regression

p < .05: significant predictor; p > .05: not significant.

R^2 and its values

Proportion of variance explained. R^2 = 0 (none), 0.5 (moderate), 0.9 (strong), 1 (perfect).

Multicollinearity

High correlation among predictors; makes beta unstable but may keep R^2 high.

Logistic vs. Linear regression

Logistic: binary outcomes (Yes/No); Linear: continuous outcomes (e.g., sales).