What are externally studentized residuals?
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 calculate externally studentized residuals?
A studentized residual is calculated by dividing the residual by an estimate of its standard deviation. The standard deviation for each residual is computed with the observation excluded. For this reason, studentized residuals are sometimes referred to as externally studentized residuals.
What are the degrees of freedom in an externally studentized residuals for an observation in a multiple linear regression?
To do that we rely on the fact that, in general, studentized residuals follow a t distribution with (n–k–2) degrees of freedom. Three of the studentized residuals — –1.7431, 0.1217, and, 1.6361 — are all reasonable values for this distribution.
How do you find the standardized residual?
The standardized residual is found by dividing the difference of the observed and expected values by the square root of the expected value. The standardized residual can be interpreted as any standard score. The mean of the standardized residual is 0 and the standard deviation is 1.
How do you show that residuals are independent?
Rule of Thumb: To check independence, plot residuals against any time variables present (e.g., order of observation), any spatial variables present, and any variables used in the technique (e.g., factors, regressors). A pattern that is not random suggests lack of independence.
What Semistudentized residuals?
• When you divide the residuals by MSE , you have semi-studentized residuals. • Slightly better than regular residuals, can use them in the same ways we used residuals. Page 6.
What do we use internally studentized residuals for what do we use externally studentized residuals for?
The good thing about internally studentized residuals is that they quantify how large the residuals are in standard deviation units, and therefore can be easily used to identify outliers: An observation with an internally studentized residual that is larger than 3 (in absolute value) is generally deemed an outlier.
How do you calculate studentized residuals in R?
If the standardized residual is ri, then the studentized residual ti is: ti=ri(n−k−2n−k−1−r2i)1/2, The motivation behind studentized residuals comes from their use in outlier testing.