# Regression

A Tour of Machine Learning Algorithms. Originally published by Jasonb on MachineLearningMastery.com.

From the Ensemble Methods section Learning Style There are different ways an algorithm can model a problem based on its interaction with the experience or environment or whatever we want to call the input data. It is popular in machine learning and artificial intelligence text books to first consider the learning styles that an algorithm can adopt. Which regression technique to apply? What do practitioners need to know about regression?

Fabio Rojas writes: In much of the social sciences outside economics, it’s very common for people to take a regression course or two in graduate school and then stop their statistical education.

This creates a situation where you have a large pool of people who have some knowledge, but not a lot of knowledge. As a result, you have a pretty big gap between people like yourself, who are heavily invested in the cutting edge of applied statistics, and other folks.So here is the question: What are the major lessons about good statistical practice that “rank and file” social scientists should know?

Six quick tips to improve your regression modeling. It’s Appendix A of ARM: A.1.

Fit many models Think of a series of models, starting with the too-simple and continuing through to the hopelessly messy. Generally it’s a good idea to start simple. Or start complex if you’d like, but prepare to quickly drop things out and move to the simpler model to help understand what’s going on. Some useful predictors. Dummy variables So far, we have assumed that each predictor takes numerical values.

But what about when a predictor is a categorical variable taking only two values (e.g., "yes" and "no"). Such a variable might arise, for example, when forecasting credit scores and you want to take account of whether the customer is in full-type employment. Selecting predictors. When there are many possible predictors, we need some strategy to select the best predictors to use in a regression model.

A common approach that is not recommended is to plot the forecast variable against a particular predictor and if it shows no noticeable relationship, drop it. This is invalid because it is not always possible to see the relationship from a scatterplot, especially when the effect of other predictors has not been accounted for. Another common approach which is also invalid is to do a multiple linear regression on all the predictors and disregard all variables whose $p$-values are greater than 0.05.

To start with, statistical significance does not always indicate predictive value. Can We do Better than R-squared? If you're anything like me, you've used Excel to plot data, then used the built-in “add fitted line” feature to overlay a fitted line to show the trend, and displayed the “goodness of fit,” the r-squared (R2) value, on the chart by checking the provided box in the chart dialog.

The R2 calculated in Excel is often used as a measure of how well a model explains a response variable, so that “R2 = 0.8” is interpreted as “80% of the variation in the 'y' variable is explained by my model.” What Regression Really Is. Bookmark this one, will you, folks?

If there’s one thing we get more questions about and that is more abused than regression, I don’t know. So here is the world’s briefest—and most accurate—primer. There are hundreds of variants, twists and turns, and tweaks galore, but here is the version most use unthinkingly. Take some thing in which you want to quantify the uncertainty. Call it y: y can be somebody’s income, their rating on some HR form, a GPA, their blood pressure, anything. Some heuristics about local regression and kernel smoothing. In a standard linear model, we assume that .

Alternatives can be considered, when the linear assumption is too strong. That’s Smooth. Some heuristics about spline smoothing. Let us continue our discussion on smoothing techniques in regression.

Assume that . where is some unkown function, but assumed to be sufficently smooth. For instance, assume that. Evaluating model performance - A practical example of the effects of overfitting and data size on prediction. Following my last post on decision making trees and machine learning, where I presented some tips gathered from the "Pragmatic Programming Techniques" blog, I have again been impressed by its clear presentation of strategies regarding the evaluation of model performance.

I have seen some of these topics presented elsewhere - especially graphics showing the link between model complexity and prediction error (i.e. "overfitting") - but this particular presentation made me want to go back to this topic and try to make a practical example in R that I could use when teaching. Effect of overfitting on prediction The above graph shows polynomial fitting of various degrees to an artificial data set - The "real" underlying model is a 3rd-degree polynomial (y ~ b3*x^3 + b2*x^2 + b1*x + a).

Nevertheless, a more robust analysis of prediction error is through a cross-validation - by splitting the data into training and validation sub-sets. Code to reproduce example: Created by Pretty R at inside-R.org. Strategy for building a “good” predictive model. By Ian Morton. Ian worked in credit risk for big banks for a number of years. He learnt about how to (and how not to) build “good” statistical models in the form of scorecards using the SAS Language. Read original post and similar articles here . I thing Ian's list below is a good starting point. This Cold Weather - A Good Reason to have a Flu Jab. Author: Andrew McCulloch Recently we noted here that there is a strong seasonal pattern in mortality in England and Wales with the number of deaths rising sharply in the winter months.

The figure below shows the number of deaths (using the left-hand axis) and the average temperature (using the right-hand axis) for each week in England and Wales in 2011. The figure shows that there were around 12500 deaths in the first week of 2011 but only around 8500 deaths per week during the summer months. Unsurprisingly, the average temperature follows a trend which is nearly the inverse of that followed by the number of deaths, and looking at the variation throughout the year in the number of deaths and the average temperature, it might seem clear that rising winter mortality is due to the cold. Researchers have found it hard, however, to agree on the exact relationship between temperature and mortality. President Ford receives a flu jab, 1976. Image: Wikimedia Commons/Gerald R. Statistical Formulas in R. Please direct questions and comments about these pages, and the R-project in general, to Dr.

Tom Philippi. Using Norms to Understand Linear Regression. Introduction In my last post, I described how we can derive modes, medians and means as three natural solutions to the problem of summarizing a list of numbers, (x_1, x_2, \ldots, x_n), using a single number, s. In particular, we measured the quality of different potential summaries in three different ways, which led us to modes, medians and means respectively.

Each of these quantities emerged from measuring the typical discrepancy between an element of the list, x_i, and the summary, s, using a formula of the form, \sum_i |x_i – s|^p, where p was either 0, 1 or 2. The L_p Norms. Rtips fit models to data. The brain of a fruit fly, Drosophila melanogaster, stained to visualize a set of approximately 50 neurons. Among the visualized neurons is a pair that controls a specific component of feeding behaviour. What does model.matrix() return? When NOT to Center a Predictor Variable in Regression. There are two reasons to center predictor variables in any time of regression analysis–linear, logistic, multilevel, etc.

Regression - Should I keep the interaction term. How is 95% CI calculated using confint in R. R - Linear Models. 4 Linear Models Let us try some linear models, starting with multiple regression and analysis of covariance models, and then moving on to models using regression splines. Linear Regression in SPSS - Procedure, assumptions and reporting the output. Introduction Linear regression is the next step up after correlation.

Interpreting the Intercept in a Regression Model. When is it ok to remove the intercept in lm()? Interpreting interaction coefficient in R (Part1 lm) Interaction are the funny interesting part of ecology, the most fun during data analysis is when you try to understand and to derive explanations from the estimated coefficients of your model. Interpreting the drop1 output in R. Predictors, responses and residuals: What really needs to be normally distributed? Introduction Many scientists are concerned about normality or non-normality of variables in statistical analyses. Correlation - What is the difference between doing linear regression on y with x versus x with y.

Multicollinearity. Roughly speaking, Multicollinearity occurs when two or more regressors are highly correlated. What are 'aliased coefficients'? Regression diagnostic plots. 19 October 2011 After you perform a regression, calling plot() or plot.lm() on that regression object brings up four diagnostic plots that help you evaluate the assumptions of the regression. How to create confounders with regression: a lesson from causal inference. Subsets vs pooling in regressions with interactions. A novel method for modelling interaction between categorical variables.

## GLM

Mixed Models. Robustness of simple rules. Data calls the model’s bluff. The Titanic Effect.