Statistics 2501
                    Influential Observations in Regression

 
 NOTE: This topic is to accompany the analysis of residuals, covered in
section 11.13 of the 8th edition of our text (or 11.8 of the 7th edition).


 Suppose a restaurant has collected a random sample of 5 customers and
compared the amount of their bill to the tip left. The restaurant owner,
who remembered the valuable course called Stats 2501 he took, decided to
use a simple linear regression model to try and predict the tip from the
price of the meal. The data are below:

 Meal Price (x): 11.25 14.48 15.60 11.55 15.88 
        Tip (y):  1.25  1.88  1.88  1.50  2.50 

 Plot the data in the space below. Describe the relationship.














 The owner found the least squares line to be

      y = -0.813  +  0.190x


 Next, a new observation was included in the dataset:
 meal price = 41.98, tip = 0.00

  Put this point on your plot above.

  The owner found the regression line with this new point included:

     y = 2.5428  -  0.0565x

  What happened?

  This is an influential observation: its inclusion causes a dramatic
change in our regression line, i.e. slope changes from positive to
negative.

  - these points are often far from other points in the X-direction
  - often have residuals close to zero (you can verify this in this 
    example).