Question

1. The following information was taken from an estimated regression equation:                                              
                                              
Number of observations: 7                                              
Number explanatory variables: 1                                              
SSE = 2.88535                                              
Residual One = -1.064                                              
Residual Two = 1.93                                              
                                              
(a) Calculate the standard residual associated with each of the residuals presented above.                                              
Would these residuals be considered outliers? Briefly explain.                                              
                                              
Standard Residual = Residual/Standard Error (SE)  

Answer 1

a) To calculate the standard residual we first need to calculate the Standard Error. n= 7 , k= 1, SSE = 2.88535

SE = SSE/(n-k)

SE = 2.88535/(7-1)

SE = 2.88535/6

SE = 0.48

Standard Residual for Residual 1 = (-1.064)/0.48 = (-2.2166)

Standard Residual for Residual 2 = (1.93)/0.48 = 4.02

Whether or not these residuals are outliers would be only identified by the data given. To identify remove the extreme data points that carry the residual. If the slope of regression equation changes significantly on its removal, one can safely mark them as outliers.