7.1: Scatter Diagram

A graphical display of bivariate data using points (xi, yi) plotted on a coordinate plane, where the pattern of points r

Correlation and Regression

7.1: Scatter Diagram

Pearson's product-moment correlation coefficient r = Σ[(x - x̄)(y - ȳ)] / √[Σ(x - x̄)² × Σ(y - ȳ)²]. Values range from -

Correlation and Regression

7.2: Pearson Correlation Coefficient

The product moment correlation coefficient (PMCC) calculated as r = Σ(x - x̄)(y - ȳ) / √[Σ(x - x̄)² × Σ(y - ȳ)²], rangin

Correlation and Regression

7.2: Pearson Correlation Coefficient

A rank-based correlation coefficient calculated as rs = 1 - (6Σd² / n(n² - 1)), where d is the difference in ranks for e

Correlation and Regression

7.3: Least Squares Regression

A regression method that finds the line y = a + bx minimizing Σ(observed y - predicted y)², where b = Σ(x - x̄)(y - ȳ) /

Correlation and Regression

7.3: Least Squares Regression

Using the regression equation to estimate y for an x-value within the range of x-values in the original data.

Correlation and Regression

7.3: Least Squares Regression

Using the regression equation to estimate y for an x-value outside the range of x-values in the original data.

Correlation and Regression

7.3: Least Squares Regression

The vertical distance from each data point to the regression line, calculated as ei = yi - ŷi, where ŷi = a + bxi is the

Correlation and Regression

7.4: Scatter Diagram with Regression Line

A scatter diagram plots pairs of observations as points on a graph. The least squares regression line y = a + bx minimiz

Correlation and Regression

7.4: Scatter Diagram with Regression Line

For a regression line ŷ = a + bx, the residual for observation (x, y) is e = y - ŷ = y - (a + bx). The sum of residuals

Correlation and Regression

7.4: Scatter Diagram with Regression Line

Regression diagnostics include: residual plots (checking for patterns, outliers, heteroscedasticity), normal probability

Correlation and Regression