Residuals and More

Enter the number of data points into the box. Then enter the data from the class activity you gathered in Lesson 6 into the spreadsheet (For this activity everyone will use the same data set). Then plot the points. For each point, you will draw in a residual segment, which is the vertical segment between the point and the line. The length of that segment is called the residual. Residual = y-value of data point – y-value on line of regression Notice that if the point is above the line, the residual will be positive; if the point is below the line the residual will be negative. Find the lengths of the residuals and add them together. We want to evaluate how well a line fits the data. If the sum of the residuals is close to zero, that might indicate a perfect line. Note that sum of the residuals may equal 0 for lines that are not very close, if the positive lengths and negative lengths cancel each other out. To eliminate that issue, we will be looking at squares of each residual. Draw in the squares for each residual and approximate their areas. Find the sum of the areas. Notice that the areas are all positive, so now everything is counted, no residual squares will cancel out.