The scatterplot shows data with a line claimed to be the least squares line fitted to the data. However, the least squares line must pass through the average x and y values given as 4.4 and 9.9, respectively. The plotted line does not pass through this point, so it cannot be the true least squares line fitted to the data.

1. The ?figure below shows a scatterplot of some data together with a line that
purports to have been ?fitted by least squares. The averages of the x and y
values are 4:4 and 9:9 respectively. The line in the ?figure cannot be the least
squares line. Say why not AND provide a justi?cation for your answer.
Solution
From the definition of a least square regression we know that the regression line has
to go through the averages of x and y. From the prompt we are told that the average of x and y is
4.4 and 9.9 respectively. From the graph that we are given of the regression line and x=4.4 and
y=9.9 we see that the regression does not go through this point. Therefore we can be certain that
the current regression is not attained through the least squares method.