Question on coefficient of determination

[kawsarkurban]

I am really confused with this question asked by my tutor, as I have no idea how to explain it, it says are there any point that you think might have an undue influence on the coefficient of determination, I said the data is outlier thus affects the average and the best fitted line is far away, I know I am wrong so please help me out thank you.

 

[Harry_the_cat]

The line of best fit minimises the sum of the squares of the vertical distances between the points and the line.

The vertical distance between the point (12.00, 40) and the line is large compared to the other distances and so influences the calculation of r² and r. It is effectively reducing the gradient of the line. It effectively pulls the line down on the right hand side.

If that point was removed, the gradient of the line would increase. thereby getting closer to the two points up the top. The r² value would increase if the point (12.00, 40) was removed from the data set and the new line of best fit would better fit the remaining data.