We have examined several lines that have yielded different SSEs. The lines, however, had one thing in common: they all had a slope of 1, so they were all parallel. Keep in mind that the slope of a line is often described as the ratio of rise to run. The formula for slope is: slope = (change in Y) / (change in X). Now, let's investigate a line with a different slope to describe the trend in the data.
One such line, with slope 0.75, passes through (164, 164) and (188, 182) and near many of the other data points; its equation is YL = 0.75X + 41. Let's compare this line to line YL = X - .7, which is the best fit we have found so far.
Note that these two lines are not parallel since they have different slopes.
Here is the scatter plot of the 24 people and the graph of the lines YL = .75X + 41 and YL = X - .7:
Here is the table to find the SSE for the line YL = .75X + 41:
The SSE for the line YL = .75X + 41 is 616.8 (as compared to 770.56). So this new line, with its different slope, turns out to be a better fit for the data set. Note 3