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Errors and Residuals

Error and residuals in statistics are the measures of the deviation of an observed value of an element of a statistical sample from its theoretical value. The error of an observed value is the deviation of the observed value from the true function value. The residual of an observed value is the difference between the observed value and the estimated function value. The distinction is most important in regression analysis, where it leads to the concept of studentized residuals.

Suppose there is a series of observations from a univariate distribution and we want to estimate the mean of that distribution. The errors in this case are the deviations of the observations from the population mean, while the residuals are the deviation of the observations from the sample mean.

A statistical error is the amount by which an observation differs from its expected value. In the example above, the latter being based on the whole population from which the statistical unit was chosen randomly. The expected value I the mean of the entire population and therefore the statistical error cannot be observed either.

A residual is an observable estimate of the unobservable statistical error. Consider the previous example with men’s heights and suppose we have a random sample of n people. The sample mean could serve as a good estimator of the population mean. It should be noted that the sum of the residuals within a random sample is necessarily zero, and thus, the residuals are necessarily not independent. 

Binary logistic regression with SPSS

Task: Four hundred and sixty-seven lecturers completed questionnaire measures of Burnout (burnt out or not), Perceived Control (high score = low perceived control), Coping Style (high score = high ability to cope with stress), Stress from Teaching (high score = teaching creates a lot of stress for the person). Stress from Resea

SPSS Output

I have completed a Linear Multiple Regression in the SPSS and I need help with interpreting and writing the results using the APA format. The dataset (Child Aggression.sav) is from the Field's text. The variable used is Aggression (DV), to test to see if Sibling Aggression is a mediator of the relationship between Parenting Styl

Logistic Forward Multiple Regression Analysis Using SPSS

Logistic Regression: Discovering Statistics (4th ed) Using IBM SPSS Statistics Chapter 19, "Logistic Regression", and using IBM SPSS Statistics the following: 1. State the underlying assumptions for the statistical test. 2. State whether the assumptions have been met. a. If the assumptions were not met (either in actual

Chi squared test for independence and linear regression

1. Use the following data to: a) draw a scatter plot b) find the coefficient of correlation and test the significance at the .05 level c) find the regression line d) predict y' for x = 5 e) find the coefficients of determination and non-determination Number of alcoholic drinks - x Score on a Dexterity Test - y 2 15 1 1