Regression & Correlation

Correlation Coefficient ($r$)

Measures the strength and direction of a linear relationship. Ranges from -1 to +1.

• $r = 1$: Perfect positive correlation.
• $r = -1$: Perfect negative correlation.
• $r = 0$: No linear correlation.

Simple Linear Regression

Fitting a straight line to the data to predict $Y$ based on $X$.

Method of Least Squares: Minimizes the sum of squared errors (residuals).

Coefficient of Determination ($R^2$)

The percentage of variation in $Y$ that is explained by $X$.

If $r = 0.8$, then $R^2 = 0.64$. This means 64% of the change in $Y$ is due to $X$.

Advanced Topics

• Multiple Regression (More than one X)
• Forecasting (Time Series)