regression fallacy

Examples of regression fallacy in the following topics:

• The Regression Fallacy

  • The regression fallacy fails to account for natural fluctuations and rather ascribes cause where none exists.
  • The regression (or regressive) fallacy is an informal fallacy.
  • It is frequently a special kind of the post hoc fallacy.
  • Incidentally, some experiments have shown that people may develop a systematic bias for punishment and against reward because of reasoning analogous to this example of the regression fallacy.
  • Assuming athletic careers are partly based on random factors, attributing this to a "jinx" rather than regression, as some athletes reportedly believed, would be an example of committing the regression fallacy.

• Ecological Fallacy

  • Ecological fallacy can refer to the following statistical fallacy: the correlation between individual variables is deduced from the correlation of the variables collected for the group to which those individuals belong.
  • Running regressions on aggregate data is not unacceptable if one is interested in the aggregate model.
  • Choosing to run aggregate or individual regressions to understand aggregate impacts on some policy depends on the following trade off: aggregate regressions lose individual level data but individual regressions add strong modeling assumptions.
  • Ecological fallacy can also refer to the following fallacy: the average for a group is approximated by the average in the total population divided by the group size.
  • A striking ecological fallacy is Simpson's paradox, diagramed in .

• Logical Fallacies

  • A fallacy is an error in reasoning; there are two basic categories of fallacies--formal and informal.
  • A fallacy is an error in reasoning.
  • There are two basic categories of fallacies--formal and informal.
  • An argument that contains a formal fallacy will always be invalid.
  • Some of the more frequent common logical fallacies are:

• The Collins Case

  • The Collins' case is a prime example of a phenomenon known as the prosecutor's fallacy—a fallacy of statistical reasoning when used as an argument in legal proceedings.
  • At its heart, the fallacy involves assuming that the prior probability of a random match is equal to the probability that the defendant is innocent.
  • For example, if a perpetrator is known to have the same blood type as a defendant (and 10% of the population share that blood type), to argue solely on that basis that the probability of the defendant being guilty is 90% makes the prosecutors's fallacy (in a very simple form).
  • The basic fallacy results from misunderstanding conditional probability, and neglecting the prior odds of a defendant being guilty before that evidence was introduced.
  • The Collins case is a classic example of the prosecutor's fallacy.

• Multiple Regression Models

  • Multiple regression is used to find an equation that best predicts the $Y$ variable as a linear function of the multiple $X$ variables.
  • You use multiple regression when you have three or more measurement variables.
  • One use of multiple regression is prediction or estimation of an unknown $Y$ value corresponding to a set of $X$ values.
  • Multiple regression is a statistical way to try to control for this; it can answer questions like, "If sand particle size (and every other measured variable) were the same, would the regression of beetle density on wave exposure be significant?
  • As you are doing a multiple regression, there is also a null hypothesis for each $X$ variable, meaning that adding that $X$ variable to the multiple regression does not improve the fit of the multiple regression equation any more than expected by chance.

• Polynomial Regression

  • For this reason, polynomial regression is considered to be a special case of multiple linear regression.
  • Although polynomial regression is technically a special case of multiple linear regression, the interpretation of a fitted polynomial regression model requires a somewhat different perspective.
  • This is similar to the goal of non-parametric regression, which aims to capture non-linear regression relationships.
  • Therefore, non-parametric regression approaches such as smoothing can be useful alternatives to polynomial regression.
  • An advantage of traditional polynomial regression is that the inferential framework of multiple regression can be used.

• Regression Analysis for Forecast Improvement

  • Regression Analysis is a causal / econometric forecasting method.
  • In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function, which can be described by a probability distribution.
  • Familiar methods, such as linear regression and ordinary least squares regression, are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data.
  • Nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinite-dimensional.
  • The performance of regression analysis methods in practice depends on the form of the data generating process and how it relates to the regression approach being used.

• Estimating and Making Inferences About the Slope

  • You use multiple regression when you have three or more measurement variables.
  • When the purpose of multiple regression is prediction, the important result is an equation containing partial regression coefficients (slopes).
  • When the purpose of multiple regression is understanding functional relationships, the important result is an equation containing standard partial regression coefficients, like this:
  • Where $b'_1$ is the standard partial regression coefficient of $y$ on $X_1$.
  • A graphical representation of a best fit line for simple linear regression.

• Evaluating Model Utility

  • Multiple regression is beneficial in some respects, since it can show the relationships between more than just two variables; however, it should not always be taken at face value.
  • It is easy to throw a big data set at a multiple regression and get an impressive-looking output.
  • But many people are skeptical of the usefulness of multiple regression, especially for variable selection, and you should view the results with caution.
  • You should examine the linear regression of the dependent variable on each independent variable, one at a time, examine the linear regressions between each pair of independent variables, and consider what you know about the subject matter.
  • You should probably treat multiple regression as a way of suggesting patterns in your data, rather than rigorous hypothesis testing.

• Predictions and Probabilistic Models

  • Regression models are often used to predict a response variable $y$ from an explanatory variable $x$.
  • In regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function, which can be described by a probability distribution.
  • Regression analysis is widely used for prediction and forecasting.
  • Performing extrapolation relies strongly on the regression assumptions.
  • Here are the required conditions for the regression model: