So I was studying the graph of averages for a scatterplot (when you plot the average of all y-values corresponding to a single x-value) and my book said that if the graph of averages falls on a straight line, then that line is the regression line. However, I'm not sure when the graph of averages would fall on a straight line. Would this only occur if the scatterplot itself had a correlation coefficient of 1 or -1?