Module 6 · Regression & Correlation · Topic 1
Scatter Plot. A scatter plot displays the relationship between two quantitative variables by plotting data as points on an x-y coordinate plane. The explanatory variable goes on the x-axis, the response variable on the y-axis.
What to Look For. Examine the direction (positive, negative, none), form (linear, curved), and strength (how tightly clustered the points are). Also look for outliers and unusual patterns.
yhat = a + bx — Line that minimizes the sum of squared residuals.r = sum((x_i-xbar)(y_i-ybar)) / sqrt(sum((x_i-xbar)^2)sum((y_i-ybar)^2)) — Measures direction and strength of a linear association.Plotting study hours (x) vs exam score (y) for 30 students. If the points trend upward from left to right, there is a positive association: more study hours tend to correspond to higher scores.
Always start with a scatter plot before computing correlation or fitting a regression line. The plot may reveal nonlinearity or outliers that summary statistics alone would miss.
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