With a small sample, a single point can have a large effect on the Pearson corre

Question

With a small sample, a single point can have a large effect on the Pearson correlation. Consider the following data: The points are shown as blue circles on the following graph. Which line appears to fit these data best? C B D A Now change the X value of the first data point in the table from 1 to 6. Drag the black X onto the graph to "cross out" the original data point, and drag the grey star onto the graph to plot the new position of the data point. Which line now appears to fit these data best? A B C D Compute the Pearson correlation for the new data. Use two decimal places for the SS and SP values, three for r.

Explanation / Answer

Ans: Scatter plot and line of best fit:

Line D fits the best.(Red)

Now,with change of first x value from 1 to 6,new scatter plot and best line fit:

Now, line C fits the best.(Purple)

Pearson cofficient:

r=(5*50-15*15)/(9.49*9.49)

r=25/90.06=0.28

r=0.28

x y xy x^2 y^2 1 6 6 36 36 36 2 4 1 4 16 1 3 1 4 4 1 16 4 1 3 3 1 9 5 3 1 3 9 1 Total 15 15 50 63 63 SSX 9.49 SSY 9.49

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