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What are studentized residuals in R?
A studentized residual is simply a residual divided by its estimated standard deviation. In practice, we typically say that any observation in a dataset that has a studentized residual greater than an absolute value of 3 is an outlier.
What is a Studentized deleted residual?
Studentized deleted residuals (or externally studentized residuals) is the deleted residual divided by its estimated standard deviation. Studentized residuals are going to be more effective for detecting outlying Y observations than standardized residuals.
How do you standardize residuals?
How to Calculate Standardized Residuals in Excel
- A residual is the difference between an observed value and a predicted value in a regression model.
- It is calculated as:
- Residual = Observed value – Predicted value.
What are the values of studentized deleted residuals?
Three of the studentized deleted residuals — -1.7431, 0.1217, and, 1.6361 — are all reasonable values for this distribution. But, the studentized deleted residual for the fourth (red) data point — -19.799 — sticks out like a very sore thumb.
What is the studentized residual for the Red Data Point?
As you can see, the studentized residual (” TRES1 “) for the red data point is t4 = -19.7990. Now we just have to decide if this is large enough to deem the data point influential. To do that we rely on the fact that, in general, studentized residuals follow a t distribution with ( n – k –2) degrees of freedom.
What does solid line in studentized residuals mean?
The solid line represents the estimated regression line for all four data points, while the dashed line represents the estimated regression line for the data set containing just the three data points — with the red data point omitted. Observe that, as expected, the red data point “pulls” the estimated regression line towards it.
What is the standard deviation of studentized residuals?
In this case, the ti are all either +1 or −1, with 50% chance for each. The standard deviation of the distribution of internally studentized residuals is always 1, but this does not imply that the standard deviation of all the ti of a particular experiment is 1.