# Correlation and Regression

A scatterplot displays the form, direction, and strength of the relationship between two quantitative variables. Straight-line (linear) relationships are particularly important because a straight line is a simple pattern that is quite common. The

**correlation**measures the direction and strength of the linear relationship. The**least-squares regression line**is the line that makes the sum of the squares of the vertical distances of the data points from the line as small as possible (these vertical distances, from each data point to the least-squares regression line, are called the**residual**values). This applet lets you explore how the correlation and least-squares regression line changes as points are added or subtracted from a scatterplot.**Directions:**Drag the blue points to the orange graphing area to create a scatterplot of data points. Click again on a previously-added point and drag the point to move it around. The correlation coefficient for the data you enter will be shown on the left. Click the checkboxes to show the least-squares regression line for your data, the mean values of

*X*and

*Y*, and/or the residual values for each data point. Start over completely by clicking on the reset icon in the upper right corner. Click "Draw your own line" to select starting and ending points for your own line on the plot. The "relative sum of squares" for your line, as compared to the least-squares regression line, will then be calculated and shown. This value ("Relative SS") indicated how close the line you've drawn is to the "ideal" least-squares regression line. A value of 1.0 indicates that the residual sum of squares for your line is exactly the same as the residual sum of squares for the least-squares line. The higher this value gets, the larger the residual SS for your line is relative to the least-squares line. (Note: If your plot includes only 1 or 2 points, the least-squares residual SS is either not calculable or is 0, so "Relative SS" cannot be calculated. Add 3 or more points to calculate the Relative SS value.)

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