# All Questions

28k views

### Algorithms for automatic model selection

I would like to implement an algorithm for automatic model selection. I am thinking of doing stepwise regression but anything will do (it has to be based on linear regressions though). My problem ...
41k views

### Is normality testing 'essentially useless'?

A former colleague once argued to me as follows: "we usually apply normality tests to the results of processes that, under the null, generate random variables that are only asymptotically or ...
281k views

### What is the meaning of p values and t values in statistical tests?

After taking a statistics course and then trying to help fellow students, I noticed one subject that inspires much head-desk banging is interpreting the results of statistical hypothesis tests. It ...
22k views

### Can a probability distribution value exceeding 1 be OK?

On the Wikipedia page about naive Bayes classifiers, there is this line: $p(\mathrm{height}|\mathrm{male}) = 1.5789$ (A probability distribution over 1 is OK. It is the area under the bell curve ...
130k views

### Difference between logit and probit models

What is the difference between Logit and Probit model? I'm more interested here in knowing when to use logistic regression, and when to use Probit. If there is any literature which defines it using ...
13k views

### What if residuals are normally distributed, but y is not?

I've got a weird question. Assume that you have a small sample where the dependent variable that you're going to analyze with a simple linear model is highly left skewed. Thus you assume that $u$ is ...
123k views

### Making sense of principal component analysis, eigenvectors & eigenvalues

In today's pattern recognition class my professor talked about PCA, eigenvectors & eigenvalues. I got the mathematics of it. If I'm asked to find eigenvalues etc. I'll do it correctly like a ...
80k views

### When conducting multiple regression, when should you center your predictor variables & when should you standardize them?

In some literature, I have read that a regression with multiple explanatory variables, if in different units, needed to be standardized. (Standardizing consists in subtracting the mean and dividing ...
69k views

### How to understand degrees of freedom?

From Wikipedia, there are three interpretations of the degrees of freedom of a statistic: In statistics, the number of degrees of freedom is the number of values in the final calculation of a ...
14k views

### Is $R^2$ useful or dangerous?

I was skimming through some lecture notes by Cosma Shalizi (in particular, section 2.1.1 of the second lecture), and was reminded that you can get very low $R^2$ even when you have a completely linear ...
129k views

### In linear regression, when is it appropriate to use the log of an independent variable instead of the actual values?

Am I looking for a better behaved distribution for the independent variable in question, or to reduce the effect of outliers, or something else?
39k views

### How can a regression be significant yet all predictors be non-significant?

My multiple regression analysis model has a statistically significant F value however all beta values are statistically non-significant. All the regression assumptions are met. No multicollinearity ...
2k views

### Is there a difference between 'controlling for' and 'ignoring' other variables in multiple regression?

The coefficient of an explanatory variable in a multiple regression tells us the relationship of that explanatory variable with the dependent variable. All this, while 'controlling' for the other ...
67k views

### Interpretation of R's lm() output

the help pages in R assume I know what those numbers mean. I don't :) I'm trying to really intuitively understand every number here. I will just post the output and comment on what I found out. There ...
16k views

### Assessing approximate distribution of data based on a histogram

Suppose I want to see whether my data is exponential based on a histogram (i.e. skewed to the right). Depending on how I group or bin the data, I can get wildly different histograms. One set of ...
29k views

### How to deal with perfect separation in logistic regression?

If you have a variable which perfectly separates zeroes and ones in target variable, R will yield the following "perfect or quasi perfect separation" warning message: ...
9k views

### How can adding a 2nd IV make the 1st IV significant?

I have what is probably a simple question, but it is baffling me right now, so I am hoping you can help me out. I have a least squares regression model, with one independent variable and one ...
27k views

### Including the interaction but not the main effects in a model

Is it ever valid to include a two-way interaction in a model without including the main effects? What if your hypothesis is only about the interaction, do you still need to include the main effects?
25k views

### Best practice when analysing pre-post treatment-control designs

Imagine the following common design: 100 participants are randomly allocated to either a treatment or a control group the dependent variable is numeric and measured pre- and post- treatment Three ...
17k views

### Interpretation of log transformed predictor

I'm wondering if it makes a difference in interpretation whether only the dependent, both the dependent and independent, or only the independent variables are log transformed. In the case of ...
5k views

### What is the benefit of breaking up a continuous predictor variable?

I'm wondering what the value is in taking a continuous predictor variable and breaking it up (e.g., into quintiles), before using it in a model. It seems to me that by binning the variable we lose ...
29k views

### When is it ok to remove the intercept in lm()?

I am running linear regression models and wondering what the conditions are for removing the intercept term of lm()? In comparing results from two different lm ...
2k views

### Is there an intuitive interpretation of $A^TA$?

For a given data matrix $A$, it seems like $A^TA$ plays an important role in statistics. For example, it is an important part of the analytical solution of ordinary least squares. Or, for PCA, its ...
71k views

### What are the differences between Factor Analysis and Principal Component Analysis?

It seems that a number of the statistical packages that I use wrap these two concepts together. However, I'm wondering if there are different assumptions or data 'formalities' that must be true to use ...
4k views

### What is meant by a “random variable”?

What do they mean when they say "random variable"?
5k views

### Interpretation of simple predictions to odds ratios in logistic regression

I'm somewhat new to using logistic regression, and a bit confused by a discrepancy between my interpretations of the following values which I thought would be the same: exponentiated beta values ...
51k views

79k views

### Why square the difference instead of taking the absolute value in standard deviation?

In the definition of standard deviation, why do we have to square the difference from the mean to get the mean (E) and take the square root back at the end? Can't we just simply take the absolute ...
54k views

### How should I transform non-negative data including zeros?

If I have highly skewed positive data I often take logs. But what should I do with highly skewed non-negative data that include zeros? I have seen two transformations used: $\log(x+1)$ which has the ...
62k views

### What is the difference between linear regression on y with x and x with y?

The Pearson correlation coefficient of x and y is the same, whether you compute pearson(x, y) or pearson(y, x). This suggests that doing a linear regression of y given x or x given y should be the ...
13k views

### Using principal component analysis (PCA) for feature selection

I'm new to feature selection and I was wondering how you would use PCA to perform feature selection. Does PCA compute a relative score for each input variable that you can use to filter out ...
5k views

### Simulation of logistic regression power analysis - designed experiments

This question is in response to an answer given by @Greg Snow in regards to a question I asked concerning power analysis with logistic regression and SAS ...
6k views

### Why do statisticians say a non-significant result means “you can't reject the null” as opposed to accepting the null hypothesis?

Traditional statistical tests, like the two sample t-test, focus on trying to eliminate the hypothesis that there is no difference between a function of two independent samples. Then, we choose a ...
4k views

### Converting similarity matrix to (euclidean) distance matrix

In Random forest algorithm, Breiman (author) constructs similarity matrix as follows: Send all learning examples down each tree in the forest If two examples land in the same leaf increment ...
42k views

### PCA on correlation or covariance?

What are the main differences between performing principal component analysis (PCA) on the correlation matrix and on the covariance matrix? Do they give the same results?
15k views

### R's lmer cheat-sheet

There's a lot of discussion going on on this forum about the proper way to specify various hierarchical models using lmer. I thought it would be great to have all ...
18k views

### Why does a 95% CI not imply a 95% chance of containing the mean?

It seems that through various related questions here, there is consensus that the "95%" part of what we call a "95% confidence interval" refers to the fact that if we were to exactly replicate our ...
12k views

### What is a complete list of the usual assumptions for linear regression?

What are the usual assumptions for linear regression? Do they include: a linear relationship between the independent and dependent variable independent errors normal distribution of errors ...
6k views

### Relationship between SVD and PCA. How to use SVD to perform PCA?

Principal component analysis (PCA) is usually explained via an eigen-decomposition of the covariance matrix. However, it can also be performed via singular value decomposition (SVD) of the data matrix ...
36k views

### Which pseudo-$R^2$ measure is the one to report for logistic regression (Cox & Snell or Nagelkerke)?

I have SPSS output for a logistic regression model. The output reports two measures for the model fit, Cox & Snell and ...
8k views

### How to choose between t-test or non-parametric test e.g. Wilcoxon in small samples

Certain hypotheses can be tested using Student's t-test (maybe using Welch's correction for unequal variances in the two-sample case), or by a non-parametric test like the Wilcoxon paired signed rank ...
32k views

### Under what conditions should Likert scales be used as ordinal or interval data?

Many studies in the social sciences use Likert scales. When is it appropriate to use Likert data as ordinal and when is it appropriate to use it as interval data?
6k views

### What, precisely, is a confidence interval?

I know roughly and informally what a confidence interval is. However, I can't seem to wrap my head around one rather important detail: According to Wikipedia: A confidence interval does not ...
41k views

### Is there any reason to prefer the AIC or BIC over the other?

The AIC and BIC are both methods of assessing model fit penalized for the number of estimated parameters. As I understand it, BIC penalizes models more for free parameters than does AIC. Beyond a ...
80k views

### How exactly does one “control for other variables”?

Here is the article that motivated this question: Does impatience make us fat? I liked this article, and it nicely demonstrates the concept of “controlling for other variables” (IQ, career, income, ...
17k views

### Does an unbalanced sample matter when doing logistic regression?

Okay, so I think I have a decent enough sample, taking into account the 20:1 rule of thumb: a fairly large sample (N=374) for a total of 7 candidate predictor variables. My problem is the following: ...
10k views

### How to generate correlated random numbers (given means, variances and degree of correlation)?

I'm sorry if this seems a bit too basic, but I guess I'm just looking to confirm understanding here. I get the sense I'd have to do this in two steps, and I've started trying to grok correlation ...
16k views

### Removal of statistically significant intercept term boosts $R^2$ in linear model

In a simple linear model with a single explanatory variable, $\alpha_i = \beta_0 + \beta_1 \delta_i + \epsilon_i$ I find that removing the intercept term improves the fit greatly (value of $R^2$ ...
2k views

### Does down-sampling change logistic regression coefficients?

If I have a dataset with a very rare positive class, and I down-sample the negative class, then perform a logistic regression, do I need to adjust the regression coefficients to reflect the fact that ...
85k views

### Pearson's or Spearman's correlation with non-normal data

I get this question frequently enough in my statistics consulting work, that I thought I'd post it here. I have an answer, which is posted below, but I was keen to hear what others have to say. ...

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