# 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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### 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 ...
264k views

### Correlations with unordered categorical variables

I have a dataframe with many observations and many variables. Some of them are categorical (unordered) and the others are numerical. I'm looking for associations between these variables. I've been ...
17k views

### Correlation coefficient between a (non-dichotomous) nominal variable and a numeric (interval) or an ordinal variable

I've already read all the pages in this site trying to find the answer to my problem but no one seems to be the right one form me... First I explain you the kind of data I'm working with... Let's ...
7k views

### $P[X=x]=0$ when $X$ is continuous variable

I know that for continuous variable $P[X=x]=0$. But i can't visualize that if $P[X=x]=0$, there is infinite number of possible $x$'s. And also why do their probabilities get infinitely small ?
178k views

### Correlation between a nominal (IV) and a continuous (DV) variable

I have a nominal variable (different topics of conversation, coded as topic0=0 etc) and a number of scale variables (DV) such as the length of a conversation. How can I derive correlations between ...
25k views

### How to choose between ANOVA and ANCOVA in a designed experiment?

I am conducting an experiment which has the following: DV: Slice consumption (continuous or could be categorical) IV: Healthy message, unhealthy message, no message (control) (3 groups in which ...
49k views

### Does it ever make sense to treat categorical data as continuous?

In answering this question on discrete and continuous data I glibly asserted that it rarely makes sense to treat categorical data as continuous. On the face of it that seems self-evident, but ...
10k views

### When should we discretize/bin continuous independent variables/features and when should not?

When should we discretize/bin independent variables/features and when should not? My attempts to answer the question: In general, we should not bin, because binning will lose information. Binning is ...
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### What is the difference between discrete data and continuous data?

What is the difference between discrete data and continuous data?
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### Why should binning be avoided at all costs?

So I've read a few posts about why binning should always be avoided. A popular reference for that claim being this link. The main getaway being that the binning points (or cutpoints) are rather ...
19k views

### How to correctly assess the correlation between ordinal and a continuous variable?

I'd like to estimate the correlation between: An ordinal variable: subjects are asked to rate their preference for 6 types of fruit on a 1-5 scale (ranging from very disgusting to very tasty) On ...
2k views

### Computationally efficient estimation of multivariate mode

Short version: What's the most computationally efficient method of estimating the mode of a multidimensional data set, sampled from a continuous distribution? Long version: I've got a data set that I ...
4k views

### Uniform random variable as sum of two random variables

Taken from Grimmet and Stirzaker: Show that it cannot be the case that $U=X+Y$ where $U$ is uniformly distributed on [0,1] and $X$ and $Y$ are independent and identically distributed. You should not ...
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### How can the probability of each point be zero in continuous random variable? [duplicate]

I know this is duplicated but I think the question is a bit different and needs different answer. How can CDF be continuous and have derivative at each point that is not equal to zero but the ...
48k views

### Can I use multiple regression when I have mixed categorical and continuous predictors?

It looks like you can use coding for one categorical variable, but I have two categorical and one continuous predictor variable. Can i use multiple regression for this in SPSS and if so how? thanks!
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### Determining an optimal discretization of data from a continuous distribution

Suppose you have a data set $Y_{1}, ..., Y_{n}$ from a continuous distribution with density $p(y)$ supported on $[0,1]$ that is not known, but $n$ is pretty large so a kernel density (for example) ...
26k views

### Correlation between dichotomous and continuous variable

I am trying to find the correlation between a dichotomous and a continuous variable. From my ground work on this I found that I have to use independent t-test and the precondition for it is that the ...
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### Probability that a continuous random variable assumes a fixed point

I'm in an introductory statistics class in which the probability density function for continuous random variables has been defined as $P\left\{X\in B\right\}=\int_B f\left(x\right)dx$. I understand ...
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### How to interpret interaction continuous variables in logistic regression?

I am struggling to understand and interpret the interaction term in a logistic regression. The explanatory variables are temperature (categorical), ...
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### Analyzing relationships between ordinal and continuous time series data

I have two sets of time series data - roleTrajectories & normalizedDegree. The former data set contains ordinal rankings of subjects' positions within a network at 13 time periods. The latter data ...
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### Clustering a dataset with both discrete and continuous variables

I have a dataset X which has 10 dimensions, 4 of which are discrete values. In fact, those 4 discrete variables are ordinal, i.e. a higher value implies a higher/better semantic. 2 of these discrete ...
67k views

### Predicting with both continuous and categorical features

Some predictive modeling techniques are more designed for handling continuous predictors, while others are better for handling categorical or discrete variables. Of course there exist techniques to ...
1k views

### Beta regression with “random effect” of source plot in two seasons

I am attempting to model the effect of several continuous and categorical predictors on a continuous proportion response variable. My experiment had 3 treatments, which were replicated in each of 9 ...
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### GLM with logit link and Gaussian family to predict a continuous DV between 0 and 1

Can you run a GLM using a logit link with a continuous DV (between 0 and 1)? Generally it's suggested to use a binomial family with a logit link, but I'm guessing that is because the model assumes a ...
15k views

### How do you plot an interaction between a factor and a continous covariate?

I would like to plot on the same graph the interaction between my continuous predictor and my categorical moderator. I know how to do it when both are categorical (factor interaction), but don't ...
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### Rank transformed 2-way ANOVA

I know I'm asking a lot of questions these days! Sorry about that, but I'm trying to work through my grad thesis data collected over the last 4 years, and am repeatedly tripping on my beginner's grasp ...
6k views

### How to transform continuous data with extreme bimodal distribution

Is there a way to transform a continuous predictor variable (grant) that has a bimodal distribution into a normal distribution (see density plot below)? I have tried log(x+c), z-score and inverse ...
191 views

### Different Types of Data

According to my Elementary statistics for Business and Economics text book revised Edition 2012 . Under a section concerning the Different types of Data . This text book says that under Quantitative ...
505 views

### Expectation of 2 functions with one random variable

This may be a trivial question but I want to consult with you all. Let U be a continuous random variable taking values int he interval [0,2pi]. Let X = cos(U), Y = sin(U). Determine the Pearson ...
3k views

### Why is the Cauchy Distribution so useful?

Could anyone give me some practical examples of the Cauchy Distribution? What makes it so popular?
18k views

### Continuous and Categorical variable data analysis

I have three variables: distance (continuous, variable range negative infinity to positive infinity) isLand (discrete categorical/ Boolean, variable range 1 or 0) occupants (discrete categorical, ...
472 views

### Measure of association between non-dichotomous ordinal variable and continuous variable

I have to collect and then analyse a large dataset. A particular data input (continuous variable) is laborious to collect and I believe that an ordinal category (1,2,3,4) would correlate closely with ...
7k views

### Common Continuous Distributions with [0,1] support

Question I am looking to understand what possible common statistical continuous distributions exist with support [0,1]. Background In my work I often come across data which are bounded between 0 and ...
4k views

### Analogues of sensitivity and specificity for continuous outcomes

How can I calculate the sensitivity and specificity (or analogous measures) of a continuous diagnostic test in predicting a continuous outcome (e.g., blood pressure) without dichotomizing the outcome? ...
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### Why X=x is impossible for continuous random variables?

Background: When we consider a continuous random variable $X$ and consider some independent realisations of $X$, I am told that the realisations must be unique since $\text{Pr}(X=x)=0$. When we ...
2k views

### hurdle model with non-zero gaussian distribution in R

I have biomass data (continuous response variable). If sufficient data is collected, the log(Biomass) follows a normal distribution. However, I am separating the overall biomass by family (i.e., ...
518 views

### how to measure the correlation between non-normally distributed numeric variable and nominal variable?

I have two nominal variables and some numeric variables. The first nominal variable is a binary one. I want to measure the correlation between this binary variable and the other numeric variables. ...
498 views

### Gibbs sampling and mixed distribution

For a project, I need to simulate from a joint distribution with both continuous and discrete variables that are dependent. The conditional distribution of any variable given the rest is known. I ...
313 views

### Transforming continuous variable to ordinal for estimation with ordered logit

I currently have a continuous variable. However, I would like to transform it into 5 intervals using cutpoints of my choosing to carry out an ordered logit estimation. That is: Will this affect the ...
403 views

### Using counts of a continuous random variable to establish an unknown probability density function

The precision of a given measuring device defines a window over the probability density function of whatever is being measured. For instance, if a measuring tape is precise to 0.1 inches, then the ...
5k views

### Continuous generalization of the negative binomial distribution

Negative binomial (NB) distribution is defined on non-negative integers and has probability mass function$$f(k;r,p)={\binom {k+r-1}{k}}p^{k}(1-p)^{r}.$$ Does it make sense to consider a continuous ...
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### Integer Data: Categorical or Continuous?

I am wondering if integer predictor data should be treated as categorical (thus requiring encoding) or continuous. For example, if the range of a given predictor X ...
20k views

### interaction of categorical and continuous variables

I have a dependent variable that is continuous and I have two independent variables: one continuous and one categorical (with 2 categories) The interaction between the independent variables is ...
12k views

### Using poisson regression for continuous data?

Can the poisson distribution be used to analyze continuous data as well as discrete data? I have a few data sets where response variables are continuous, but resemble a poisson distribution rather ...
11k views

### Correct glmer distribution family and link for a continuous zero-inflated data set

Data set details: Zeros are "real" (volume) Data set is heavily left skewed (even when zeros are excluded) Response is continuous (volume) Can anyone recommend a distribution family and link that I ...