# Questions tagged [continuous-data]

A random variable $X$ is called continuous if its set of possible values is uncountable, and the chance that it takes any particular value is zero ($\text{P}(X = x) = 0$ for every real number $x$). A random variable is continuous if and only if its cumulative probability distribution function is a continuous function.

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### How to interpret a hazard ratio from a continuous variable — unit of difference?

I am reading an article which shows Hazard Ratios for continuous variables, but I'm not sure how to interpret the given values. My current understanding of hazard ratios is that the number ...
3k views

### Why reducing a regression model into a classification model by output discretization improves a model?

In regression problems, if the output is discretized into bins/categories/clusters and used as labels, the model is reduced to a classification model. My question is: what is the theoretical or ...
1k views

### Continuous dependent variable with upper and lower bounds: logit transformation appropriate?

I'm analyzing the relationship between a (log-transformed) continuous independent variable and a continuous dependent variable that has a lower and upper bound. If I scale the dependent variable to ...
330 views

### Estimating Continuous latent variables in a general Bayesian network

I am working on a problem where every node in the Bayesian network is continuous random variable and the structure of the network is known. This network comprises of both observed and latent nodes, ...
65 views

### What's the best way to find outliers in the time-series, encountering that it is a real-world mechanical process (process continuity)?

What's the best way to find outliers in the time-series, encountering continuity? I attached two time-series that I'm interested to filter. One is less noisy, and one is a bit noisier. I'm mostly ...
2k views

### Categorizing Continuous Random Variable in Logistic Regression

I have a Bernoulli response variable and I am going to fit a logistic regression. One of my independent variables is a continuous random variable and I would like to categorize it before fitting the ...
5k views

### Why Binning Variables in Predictive Analytics?

Lot of discussion in CrossValidated focuses on optimal binning methods, binning example etc. But I am trying to figure out what are the scenarios that I have to bin variables whereas it's better idea ...
2k views

### How to calculate odds ratio per unit decrease of continuous variable

I have a logistic regression model obtained in R comparing association between two index diagnoses (0 or 1) with Age (continuous) + ...
3k views

### discrete = countable and continuous = uncountable?

I want to understand what a discrete random variable and a continuous one are. Let $X: \Omega \rightarrow \mathbb{R}$ be a random variable (a function). If $\text{Image} (X)$ is a countable set, ...
426 views

### What is the definition of probability on a continuous distribution?

If I have a continuous distribution, $N$. I say $f$ is a sample from $N$, $f \sim N$. Now I want to determine the probability of $f$ having a value of $x$:  P(x)=\lim_{t\rightarrow0} {\frac{\text{...
2k views

### Interaction terms interpretation

How do you interpret an odds ratio of an interaction between two continuous variables $x_1, x_2$? Would you fix $x_2$ and let $x_1 = x$ and $x_1 = x+1$?
145 views

### Find P(Y=y | X=x) when X is a continuous random variable

could someone help me understand how to find the probability $\Pr(F=f_1 | X=x)$ by using the inputs below, where $X$ is a continuous random variable? Note: I know that probabilities of specific ...
2k views

### Feature selection using chi squared for continuous features

I'm looking at univariate feature selection. A method that is often described, is to look at the p-values for a $\chi^2$-test. However, I'm confused as to how this works for continuous variables. 1. ...
651 views

### Normality test for discrete values of a continuous variable

I have a dataset with several hundred pH measurements from a factory line. This dataset will be used to infer process capability using Minitab. On a physical basis, pH is a continuous scale (being ...
303 views

### How is it logically possible to sample a single value from a continuous distribution?

For example, suppose I am told that 10 data points come IID from a normal distribution with some mean and variance. Isn't the probability of realizing each of these values zero? Shouldn't the fact ...
58 views

### What statistical model can incorporate my categorical variable (2 levels) and 2 continuous variables?

I have some data which has a categorical variable (treatment) with 2 levels, control and 'mice added'. I have 2 continuous variables of plant density and elephant number/density. I have examined the ...
12k views

### How to analyse a continuous response having a bimodal distribution?

I am investigating unconscious racial prejudice as a predictor for guilty or not guilty judgements (Using SPSS). I have a continuous variable for unconscious racial prejudice (higher numbers equal ...
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### Can a negative binomial distribution be used to model a continuous distribution?

I have a data set which is a set of continuous distances from some origin. I originally modeled this as a negative binomial distribution by rounding the data and using it as an input in the Matlab ...
2k views

### Probability that a quadratic equation with random coefficients has two real solutions?

In the following second order equation $ax^2+2bx+1.5=0$ where $a$ and $b$ are given by random points $(a,b)$ in the $[0,2]\times[0,1]$ rectangle, what is the probability of having two real solutions? ...
156 views

### Do financial return series have a probability mass function (pmf)?

Stock returns, computed from stock prices as $r_t = \ln (p_{t}) - \ln (p_{t-1})$, are real-valued and unbounded giving the impression that they are continuous random variables. But aren't they ...
542 views

### Ratio of Two Uniform Random Variables [duplicate]

If X1 X2 are independent Uniform variates on (0,1), Find the distribution of Z=X1/X2. I tried using the CDF method where P(X1<=zX2) is equal to z/2 when z is in(0,1). However, I am unable to find ...
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### Building Cox Model using forward likelihood-ratio testing - Appropriateness of adding continuous variables to model?

I am constructing Cox models that predict survival in a clinical trials cohort. After speaking to our statistician (who is away at the moment, hence this post), I was advised to take a forward ...
2k views

### Comparing odds ratios of continuous and discrete variables

I need to compare the ability of two methods to predict an event with a binary response. Each method produces a score, where the higher score indicates 1 and a lower score indicates 0. I am looking to ...
1k views

### Fitting continuous data with zeros to a discrete distribution

I have data on the abundance of a particular organism across a sampling area. However, instead of counts, I have the estimated biomass of the organism at at each sampling location (that is, the ...
2k views

### What is a continuous variable in statistics?

Continuous variables can be split into three categories according to statements over here: http://www.unesco.org/webworld/idams/advguide/Chapt1_3.htm. One category is Interval - scale Variables. It ...
465 views

### Interpretation of continuous by continuous interaction in binary regression model

I'm performing binary logistic regression in SPSS; y is dichotomous variable; and both Xs are continuous variables. I performed three models and I have troubles interpreting model with both ...
102 views

### Stratify Cox Proportional Hazard Model on continuous variable

I have a question regarding Cox proportional hazard models. I've been working with data with some time-varying variables and some that are fixed over time. In total 79 units are surveyed giving around ...
2k views

### Bayesian updating of continuous variables given mutual information

I have very little stats training, so this may be a very obvious and boring question, in which case I apologise. Given two real-valued continuous random variables A and B, and given prior probability ...
105 views

### Does treating trial number as a continuous variable for linear models lose information?

If I create a linear model where Trial number is one of the predictors, am I losing any information by treating it as continuous (when in fact it is actually discrete + ordinal)? I believe the answer ...
520 views

### Rayleigh Distribution Quartiles

The Rayleigh distribution has PDF f(x) =xe−$\frac{x^2}{2}$, x >0. Let X have the Rayleigh distribution. (a) Find P(1< X < 3).(b) Find the first quartile, median, and third quartile of X. ...
899 views

### Discretizing/Binning Continuous Variable by Continuous Response

I am trying to discretize a continuous variable that does not follow a linear relationship with our response variable. I am trying to find the optimal way to discretize this variable to better ...
162 views

### How to do time-series analysis for 2x2x2 factorial design?

I have a dataset with the following variables for the treatment (nutrition, fertilizer), that records algal growth in water across time (t0, t1...t10). In series with fertilizer marked as "nitrogen" , ...
265 views

### Binomial probability for a continuous variable

I have some data that look like this: dist <- c(125,12,26,21,52,123) exists <- c(0,1,0,0,1,0) df <- cbind(dist, exists) Basically its a bunch of ...
284 views

### Compute $P(Y<3X)$ using joint PDF

I'm given a joint pdf $f_{X,Y}(x,y)=2e^{-x-y}, 0<x<y, 0<y$ and asked to compute $P(Y<3X)$. To do this, I let $Y=3X$ (the boundary) and found that the region of integration is under this ...