Least-Squares Regression Line vs Scatterplot
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Least-squares regression line
Regression and correlation
The least-squares regression line is the straight line through a scatterplot that makes the sum of the squared residuals as small as possible.
The least-squares regression line is the best-fit line for predicting the response from the explanatory variable, chosen to minimize the total squared vertical distance from the points. Its equation is , where (read y-hat) is the predicted response, is the y-intercept, and is the slope. For example, predicts a score of 75 when hours of study. The line always passes through the point of averages .
Scatterplot
Graphs and displays
A scatterplot graphs paired values of two quantitative variables as points, showing the direction, form, and strength of their relationship.
A scatterplot plots each individual as a point, with the explanatory variable on the horizontal axis and the response variable on the vertical axis. You read it for direction (positive or negative), form (linear or curved), strength (tight or loose), and any outliers. For example, plotting hours studied against exam score for 30 students may show an upward, roughly linear cloud of points. When the pattern looks linear, a least-squares regression line can summarize it.