Statistics and Probability - Regression

Bivariate Data: This involves the study of two variables to determine the relationship between them. The independent variable ($x$) is the explanatory variable, and the dependent variable ($y$) is the response variable.

Scatter Diagrams: A graphical representation of bivariate data. It helps identify the correlation (positive, negative, or none) and the strength (weak, moderate, or strong) of the relationship.

Pearson’s Product-Moment Correlation Coefficient ($r$): A numerical measure of the linear relationship between two variables. It ranges from $-1$ to $1$, where $r = 1$ is a perfect positive correlation, $r = -1$ is a perfect negative correlation, and $r = 0$ indicates no linear correlation.

The Least Squares Regression Line: The line of best fit that minimizes the sum of the squares of the vertical offsets (residuals). It is expressed in the form $y = ax + b$ or $y = mx + c$.

The Mean Point: The regression line always passes through the centroid or mean point $(\bar{x}, \bar{y})$.

Interpolation vs. Extrapolation: Interpolation is making a prediction within the range of the original data set (usually reliable). Extrapolation is making a prediction outside the range of data (often unreliable and should be treated with caution).