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The fitted value is also called the event probability or predicted probability. Event probability is the chance that a specific outcome or event occurs. The event probability estimates the likelihood of an event occurring, such as drawing an ace from a deck of cards or manufacturing a non-conforming part. The probability of an event ranges from 0 (impossible) to 1 (certain).
In binary logistic regression, a response variable has only two possible values, such as the presence or absence of a particular disease. The event probability is the likelihood that the response for a given factor or covariate pattern is 1 for an event (for example, the likelihood that a woman over 50 will develop type-2 diabetes).
Each performance in an experiment is called a trial. For example, if you flip a coin 10 times and record the number of heads, you perform 10 trials of the experiment. If the trials are independent and equally likely, you can estimate the event probability by dividing the number of events by the total number of trials. For example, if you flip 6 heads out of 10 coin tosses, the estimated probability of the event (flipping heads) is:
Number of events ÷ Number of trials = 6 ÷ 10 = 0.6
In ordinal and nominal logistic regression, a response variable may have three or more categories. The event probability is the likelihood that a given factor or covariate pattern has a specific response category. Cumulative event probability is the likelihood that the response for a given factor or covariate pattern falls into category k or below, for each possible k, where k equals the response categories, 1…k.
The residual is a measure of how well the observation is predicted by the model. Observations that are poorly fit by the model have large residuals. Minitab calculates the residuals for each distinct factor/covariate pattern.
Plot the residuals to determine whether your model is adequate and meets the assumptions of regression. Examining the residuals can provide useful information about how well the model fits the data. In general, the residuals should be randomly distributed with no obvious patterns and no unusual values. If Minitab determines that your data include unusual observations, it identifies those observations in the Fits and Diagnostics for Unusual Observations table in the output. For more information on unusual values, go to Unusual observations.
The standardized residual equals the value of a residual (ei) divided by an estimate of its standard deviation.
Use the standardized residuals to help you detect outliers. Standardized residuals greater than 2 and less than −2 are usually considered large. The Fits and Diagnostics for Unusual Observations table identifies these observations with an 'R'. When an analysis indicates that there are many unusual observations, the model usually exhibits a significant lack-of-fit. That is, the model does not adequately describe the relationship between the factors and the response variable. For more information, go to Unusual observations.
Standardized residuals are useful because raw residuals might not be good indicators of outliers. The variance of each raw residual can differ by the x-values associated with it. This unequal scale causes it to be difficult to assess the sizes of the raw residuals. Standardizing the residuals solves this problem by converting the different variances to a common scale.
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