What does Studentized residuals measure?
In statistics, a studentized residual is the quotient resulting from the division of a residual by an estimate of its standard deviation. It is a form of a Student’s t-statistic, with the estimate of error varying between points. This is an important technique in the detection of outliers.
What is a deleted residual?
The basic idea is to delete the observations one at a time, each time refitting the regression model on the remaining n–1 observations. Then, we compare the observed response values to their fitted values based on the models with the ith observation deleted. This produces (unstandardized) deleted residuals.
How do you calculate standardized 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 is the formula for studentized deleted residuals?
That’s where “studentized deleted residuals” come into play. A studentized deleted (or externally studentized) residual is: That is, a studentized deleted (or externally studentized) residual is just an (unstandardized) deleted residual divided by its estimated standard deviation (first formula).
How are deleted residuals related to standard deviation?
Deleted residuals depend on the units of measurement just as the ordinary residuals do. We can solve this problem though by dividing each deleted residual by an estimate of its standard deviation. That’s where “studentized deleted residuals” come into play. A studentized deleted (or externally studentized) residual is:
How to calculate studentized residuals in Stat 462?
Consider the following plot of n = 4 data points (3 blue and 1 red): 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.
What do you mean by deleted residuals in ith?
Then, we compare the observed response values to their fitted values based on the models with the ith observation deleted. This produces (unstandardized) deleted residuals. Standardizing the deleted residuals produces studentized deleted residuals, also known as externally studentized residuals.