Linear Regression & Correlation Worksheet
Explore linear modeling of (x, y) data by moving the data points up and down. You'll see how the correlation coefficient r describes the linearity of the data, and how the least-squares regression line fits the data. The point indicating the mean of the x-coordinates ("x-bar") and the mean of the y-coordinates ("y-bar") is shown. (Points are constrained to move up and down only.)
Move the points so the slope of the least-squares line is negative. What happens to the sign on the correlation coefficient? Adjust the points so they fall in a line. What is the correlation coefficient? Does the point (x-bar, y-bar) ever come off of the least-squares line?