In: Statistics and Probability
1.
Suppose, random variables X and Y denote neural and behave respectively.
(d)
We leave out the outlier (155.2,1.94).
Least square regression line is given by
We have,
We add the obtained least square regression line for predicting y from x in our plot as follows.
(e)
For x=155.2, predicted value of y is given by
This is very close to our observed value 1.94. Adding any point near to regression line increases value of correlation coefficient. Being very closed to our calculated regression line, it will have little effect on the least-squares line.
So, adding the outlier will increase the correlation but will have little effect on the least-squares line.
(f)
With the outlier-
Correlation coefficient is given by
Least square regression line is given by
We have,
Without the outlier-
Correlation coefficient is given by
Least square regression line is given by
We have,
Clearly, obtained least-squares lines for predicting y from x with and without outlier are very close. Thus these results verifies expectations from (e).