Intervals which cover the (future or otherwise unknown) value of some random variable with some prespecified probability. See https://en.wikipedia.org/wiki/Prediction_interval

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Forecasting values along with corresponding years [migrated]

I have a sample data set (named as s3) in the following manner: ...
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32 views

Prediction Interval: Propagate error associated with variable in R

I have a linear dataset with known values of X & Y in R. I treat the dataset as a linear model. I have a data point with a known value of X and an unknown value of Y. The X value has an ...
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28 views

R - lm how to get standard deviation coefficients

I have a very simple problem but I cannot find the answer anywhere. I run a linear model with lm() and I want the standard deviation coefficients in order to compute the confidence interval. I know ...
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36 views

Empirical Prediction interval for time series forecast based on quantile regression

As Gardner notes "almost all point forecasts are wrong", so prediction intervals (PI) are necessary to quantify uncertainty and help us make informed decisions. There exists theoretical PI, and in ...
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Is it possible to get a prediction interval for logistic regression via a latent variable?

carbocation asked how to compute prediction intervals for logistic regression. The answer was that prediction intervals don't make sense for logistic regression because the response variable only ...
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21 views

How does R calculate prediction intervals in the forecast package?

I have a large dataset with different factors that I want to forecast to the future. These forecasts I will then later on use as inputs for a Monte Carlo simulation. My idea would be to use arima ...
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69 views

R: glm(…,family=poisson) plot confidence and prediction intervals [closed]

I could not find many information on how to plot a confidence interval and a prediction interval for a Poisson regression (for example with glm()). What are some ...
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24 views

Why does the upper prediction interval region gets larger than lower prediction interval when data are transformed?

I present here two examples one with transformed data and the other without any transformation. In the transformed data case, the upper interval gets enormous large, whereas not in the untransformed ...
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35 views

ensemble of three regressors to find pointwise prediction intervals in instance-based online learning setting

Here is my online learning scenario: Data point $x_n$ arrives Response of the data point, $\hat{y}_n$, is predicted. Real response, $y_n$, is obtained Regression algorithm is updated incrementally ...
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37 views

Derivation of prediction interval for simple linear regression

For simple linear regression $y_i = \beta_0 + \beta_1 x_i + e$, how does one derive the prediction interval for some $x$? I thought the prediction error was just the mean square error for regression ...
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37 views

Multiple regression model and prediction/confidence interval for two values of a coefficient

Hi i've been working on this model of house prices based on multiple independent variables. I got the out put out throught gretl. ...
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1answer
58 views

Using predict() in R to predict the y-value for multiple occurrences of the same x-value

If I have a linear model and want to use predict() to predict the mean and confidence interval of multiple ($m$) new observations of a given x-value ($x_h$), how do ...
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35 views

Restricting a set of predictions to a range of values of non-negative numbers

I am not even sure how to even phrase this question so if anyone could help that would be great. I am analyzing facebook activity and I wish to predict a particular activity (comments, for instance). ...
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Data Interval Determination

I run a TV programme for 30 mins. That TV programme has, say 5 keywords, associated with it. I then measure the number of clicks those keywords received over that 30 min time window. The problem is ...
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60 views

Does it make sense to generate prediction intervals for the estimates of a logistic regression?

Say I have a binary outcome of 0 or 1 and suppose I were to use logistic regression model to estimate the probability a new sample will have an outcome of 1. I have read answers (for example here: ...
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1answer
48 views

Prediction intervals in ARIMAX accounting for forecast uncertainty in future $X$?

I have a problem with my SPSS software and ARIMAX forecasts. Consider a series $Y$ that depends on a different series $X$, which is not known in advance with certainty, but must be forecasted itself. ...
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250 views

Prediction interval for lmer() mixed effects model in R

I want to get a prediction interval around a prediction from a lmer() model. I have found some discussion about this: ...
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52 views

Prediction Intervals for Incremental OLS regression

I am implementing incremental OLS regression algorithm where the data points arrive one at a time. As the regression parameters are determined by the formula, $(X'X)^{-1} X'y$ and the Sherman-Morrison ...
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31 views

prediction interval formula

I have a model $Y_i= \beta_0 + \beta_1X_i+\beta_2X_i^2+\beta_3X_i^3+\epsilon_i$ with $\epsilon_i\sim\mathcal{N}(0,\sigma^2)$. Is the following formula correct for calculating the width of a 95% ...
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89 views

How to calculate the prediction interval for an OLS multiple regression?

What is the algebraic notation to calculate the prediction interval for multiple regression? It sounds silly, but I am having trouble finding a clear algebraic notation of this.
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36 views

Estimating the variance of a sum of predictions

I have $N$ plots that were used to estimate a relationship between three predictor variables, $X_1$, $X_2$, $X_3$, and an outcome, $Y$, using a generalized linear (lognormal) model. The resulting ...
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Regression: Should I use the prediction interval obtained given n=9 and an outlier (Cook's D= 0.558) present?

The data I'm working with has 9 observations. I'm using only one predictor variable. Using SAS, I fit the model and checked the residuals. The typical model assumptions appear to be met, but there ...
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1answer
80 views

finding prediction interval for any type of regression

I am working on a project where I need to estimate some real-valued values given some features in an online fashion. I evaluate various online learning methods. My estimations has to be bounded by a ...
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230 views

Does a prediction interval have to contain the mean?

I am having a huge problem with a conceptual problem that I came up with. Say a company has a distribution that is highly skewed. Something similar to an exponential or lognormal only more extreme. ...
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247 views

How to calculate prediction intervals for LOESS?

I have some data that I fitted using a LOESS model in R, giving me this: The data has one predictor and one response, and it is heteroscedastic. I also added confidence intervals. The problem is ...
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25 views

Can auto-predicted values ever improve linear regression?

You want to predict values of $y$ using a linear model of the following form: $ y = \beta_0 + \beta_1x_1 + \beta_2x_2 + \beta_3x_3$ $y$ is significantly dependent upon all three variables. ...
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Determining approximate prediction interval using moments

Given the values of mean, and the next 3 central moments of a continuous random variable X > 0 with unknown pdf, is it possible to derive an approximate interval $(a,b)$ within which X will fall with ...
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44 views

How is a most probable Hessian used to calculate Bayesian Prediction Intervals?

I'm using the MATLAB Neural Network Toolbox to use Bayesian Regularization (trainbr.m) to train a neural network which has one input, one hidden, and one output layer. I use this network for ...
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41 views

Prediction intervals for “single future response”?

Faraway (2002, 39-41) states, "There are two kinds of predictions that can be made for a given $x_0$ ... Most times, we will want the first case which is called “prediction of a future value” while ...
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49 views

Prediction intervals for mixture models for time series forecasting - is it really an average of the prediction intervals of the averaged models?

I'm trying to find out how to do forecasting with a mixture model (averaging the forecasts of an ets, an arima and an ...
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42 views

Multi-step ahead forecasting with generalized additive models

I would like to build forecast models using generalized additive models (GAM) with AR(p) correlation specification and explanatory covariates, using similar methods to those described in this blog ...
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82 views

Prediction Intervals for Robust Regression: Formulation and are they larger than for OLS?

I have created regression models using robust regression - in particular, LTS and MM-estimators (using the R package robustbase). I am now looking to creation prediction intervals. The standard ...
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45 views

Usage of standard deviation in random forests regression (for expected improvement)

It seems to me that the awareness of this problem is not high enough. Often the standard deviation (so the sd from each prediction of each tree in the forest) from the random forest regression is ...
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How to forecast a 95% prediction interval for a variable?

I have a data set containing the height of 1000 students for 4 years (one measurement for each student for each year), from 2011 to 2014. I want to forecast the mean height for these students for the ...
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GBM Prediction Interval Issue

I need to get prediction interval for GBM model (loss='ls'). I'm using this example as a basis http://scikit-learn.org/stable/auto_examples/ensemble/plot_gradient_boosting_quantile.html My model ...
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Calculate prediction interval for SAR model (errorsarlm function in R)

I would like to predict prediction interval for a SAR model (function errorsarlm in R - package spdep). While the function predict.lm allows to set interval='prediction' parameter to predict the upper ...
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193 views

Prediction interval based on cross-validation (CV)

In the text books and youtube lectures I learned a lot about iterative models such as boosting, but I never saw anything about deriving a prediction interval. Cross validation is used for the ...
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64 views

Matrix Inversion Error

I a Multiple linear regression model, from published literature, I am implementing a spreadsheet to generate new predictions based on the published model. the literature stated Coefficients and the ...
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54 views

approaches for computing confidence band and prediction band for general regression analysis and predictive models

In linear regression model, the predict in R is able to calculate the confidence band and ...
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58 views

difference between confidence interval and prediction interval in the context of regression analysis and predictive modeling

When building prediction models, I always see the following concept 1) Confidence interval for regression model 2) Prediction interval 3) Confidence interval for predicted value I can understand ...
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97 views

Interval estimation

I am looking for pointer/advises on producing interval estimation (as opposed to point wise) assuming the noise on my data is not constant. To make is simpler, let's assume the following linear model ...
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172 views

Using an RMSE with derived confidence interval, to generate a prediction interval for an estimate

Previous questions have asked about creating prediction intervals for estimates derived from random forests or boosted regression trees, in a similar way to is easily achieved with linear regression ...
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72 views

Is a confidence interval a prediction interval for the sample mean?

I am learning about different intervals and trying to get my head around them. Given that a sample mean from a sample size $n$ has a pdf equal to $f(x)$, the 95% prediction interval [a,b] is an ...
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cross-validation to predict distribution of errors on finite test sets

In one use of k-fold cross-validation for evaluating classifiers, one trains k models, each on n(k-1)/k examples, and tests each on n/k examples. The average accuracy on those k test sets of size n/k ...
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81 views

Prediction interval using predict and NeweyWest in R

I have a basic linear regression model I fitted to a time series. Unfortunately I have to account for autocorrelation and heteroskedasicity in the model and I have done so with the NeweyWest function ...
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27 views

confidence interval for aggregated expectation from logistic regression

My model steps: 1.I fitted a logistic regression model $Y\sim X$; 2.then get the probability $P(Y=1)$ for each record; 3.then I summed the probability $R = \sum_i(P_i(Y=1))$ to be the expected return, ...
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185 views

GBM Bootstrap Prediction Interval Code Error

based on code presented in thread: How to find a GBM Prediction Interval I am trying to apply this to my dataset. Below is my full code, and I am having issues with the bootstrap function. ...
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1answer
429 views

How to find a GBM Prediction Interval

I am working with GBM models using the caret package and looking to find a method to solve the prediction intervals for my predicted data. I have searched extensively but only come up with a few ...
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1answer
38 views

R- predict payment day (1-31)

I need to predict payment day of the month (1-31) for each client (I have at most 9 month of payments and on average is 5). I have both categorical variables and numerical. I tried to use rpart to do ...
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How to find the variance for a mean response in a multiple linear regression model

The question is the following: Our regression model can be written as $y_i = \beta^Tx_i + \epsilon_i, 1 \leq i \leq n$. Find the $100(1- \alpha)\%$ confidence interval for the mean response ...