The figure below shows a scatterplot of some data together with a l.pdf

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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.

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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.

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