Origin of 'regression' The term "regression" was coined by Francis Galton in the 19th century to describe a biological phenomenon. The phenomenon was that the heights of descendants of tall ancestors tend to regress down towards a normal average (a phenomenon also known as regression toward the mean)(Galton, reprinted 1989).

In regression we can get biased estimators of slopes by doing stepwise regression. A variable is more likely to be kept in a stepwise regression if the estimated slope is further from 0 and more likely to be dropped if it is closer to 0, so this is biased sampling and the slopes in the final model will tend to be further from 0 than the true slope.

As an example, the data is X = 1,...,100. The value of Y is plotted on the Y axis. The red line is the linear regression surface. Personally, I don't find the independent/dependent variable language to be that helpful. Those words connote causality, but regression can work the other way round too (use Y to predict X).

2016年4月13日 · While sometimes linear regression is a good approximation for limited dependent variables (for example, in the case of binary logit/probit), oftentimes it is not. Enter Generalized Linear Models . In your case, because the outcome variable is count data, you have several choices:

I am having some difficulty attempting to interpret an interaction between two categorical/dummy variables. For example, lets say there is an interaction term between an individual's gender and he

The insight that since Pearson's correlation is the same whether we do a regression of x against y, or y against x is a good one, we should get the same linear regression is a good one. It is only slightly incorrect, and we can use it to understand what is actually occurring.

2024年3月21日 · I have a question regarding the choice between interaction term and subgroup analysis. Suppose that I want to study the association between education and income by sex. I can fit a model with an

2013年3月19日 · I start with my OLS regression: $$ y = \beta _0 + \beta_1x_1+\beta_2 D + \varepsilon $$ where D is a dummy variable, the estimates become different from zero with a low p-value. I then preform a Ramsey RESET test and find that i have some misspesification of the equation, i thus include squared x: $$ y = \beta _0 + \beta_1x_1+\beta_2x_1^2+\beta ...

2017年6月20日 · In practice, using a standard T-test to check the significance of a linear regression coefficient is common practice. The mechanics of the calculation make sense to me. Why is it that the T-distribution can be used to model the standard test statistic used in linear regression hypothesis testing? Standard test statistic I am referring to here:

You don't need to assume Normal distributions to do regression. Least squares regression is the BLUE estimator (Best Linear, Unbiased Estimator) regardless of the distributions. See the Gauss-Markov Theorem (e.g. wikipedia) A normal distribution is only used to show that the estimator is also the maximum likelihood estimator.