Regression test is an important test that has been used extensively in data analysis.Can anybody tell me the differences between logistic regression test and linear regression test? When would we use each?
The UCLA statistical consulting websites are fantastic for reviewing methods: http://www.ats.ucla.edu/stat/. Suggest starting here: http://www.ats.ucla.edu/stat/sas/whatstat/default.htm
I find it so unfortunate that the UCLA pages are just about tests. They just say: "if you have this and this variables, then you should use this and this test". But they title it "What statistical analysis should I use?"... *analysis! A test is as much a statistical analysis as pushing the throttle is driving.
I have to chorus with Dr. Wilhelm: please, I mean please, don't go testing like crazy. Hypothesis testing, no matter what approach (frequentist, Bayesian, decision-theoretic) is a very serious subject, for it involves carefully laying out a hypothesis and checking the *scientific* validity of the underlying assumptions.
That said, the use of each "test" is very much tied to the type of data (response or dependent variable) you have at hand. As already pointed out, for dichotomous outcomes it MAY be suitable to perform logistic regression and then use the several available tests to assess the statistical effect of a given covariate (predictor, dependent variable). When your variable is continuous AND approximately normal (Gaussian), you can apply standard linear regression and, once more, one of the several goodness-of-fit measures and the associated tests for statistical significance.
I strongly recommend you go through some basica material. Not only you'll be able to better choose the appropriate method to analyse your data, but also will learn a lot more about the modeling process. Sometimes people forget the regression analysis is a multiple stage process, that goes from variable selection/transformation to goodness-of-fit tests and predictive power assessment.
I hope this helps.
Cheers,
Luiz
Some links:
http://www.montefiore.ulg.ac.be/~kvansteen/GBIO0009-1/ac20092010/Class8/Using%20R%20for%20linear%20regression.pdf # learning with R is quite useful
Logistic regression is more appealing than linear regression as it requires few assumptions about the distribution of your data and can accomodate any form of independent variables. But be careful of colinearity between independent variables, and the direction of coding of the categories of your independent variables
Also sample size should be suitable for the number of variables in your multiple logistic model (as a rule of thumb 20 units for every one independent variable)
LR allows estimating the probability that a particular outcome of a dependent nominal variable (y) will occur based on information from one or more explanatory variables. The technique ultimately finds the equation that best predicts the probability p of getting a particular value of y, with p taking values from 0.0 to 1.0.
Unlike the least-squares method used in linear regression, logistic regression finds the intercept and slopes of the best-fitting equation by means of the maximum-likelihood method, which is a computer-intensive technique that finds the values of the parameters under which you would be most likely to get the observed results.
To put it more plainly, the above LR equation consists of values of the independent variables plus weights estimated by the model to predict the outcome of the dependent variable.
As consequence, once logistic regression has been ran, and the intercept and coefficients have been found, one is in the position to derive the probability of the outcome of y by plugging those parameters and any known value of the various independent variables into the logistic regression equation.
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