« Previous Next »
The importance of regression residuals in regression diagnosis is crucial, and we'll go over it more detail later. Because residuals can be calculated using the observed responses yi's and the fitted values ŷi’s, they are observable. It should be emphasized that the regression model's error component εi is unobservable. As a result, regression error is unobservable while regression residual is. The amount by which an observation departs from its expected value is known as regression error; the latter is based on the entire population from which the statistical unit was picked at random. The expected value, which is the population's average, is usually unobservable.
If the average height of 21-year-old male is 5 feet 9 inches, and one randomly chosen male is 5 feet 11 inches tall, then the “error” is 2 inches; if the randomly chosen man is 5 feet 7 inches tall, then the “error” is −2 inches. It's as if measuring a man's height was an attempt to determine the population average, and any discrepancy between the average and man's height was a measurement error.
In contrast, a residual is an observable estimate of unobservable error. A random sample of n men's heights is measured in the simplest instance. The population average is estimated using the sample average. The gap between each man's height in the sample and the unobservable population average is called an error, while the difference between each man's height in the sample and the observable sample average is called a residual. We can utilize residuals to estimate the unobservable model error since residuals are observable.
Because a linear regression model isn't always appropriate for the data, you need define residuals and examine residual plots to see if the model is appropriate. The residual (e) is the difference between the observed value of the dependent variable (y) and the predicted value (ŷ). There is one residual for each data point.
On this topic, your comments/suggestions are highly appreciated. Type it in the comment section below. You can follow to this blog to receive notifications of new posts.
« Previous Next »
0 Comments