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9
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2answers
191 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. ...
8
votes
0answers
76 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 ...
0
votes
0answers
18 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. ...
1
vote
1answer
19 views

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 ...
0
votes
0answers
15 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 ...
0
votes
1answer
27 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 ...
2
votes
0answers
26 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 ...
0
votes
0answers
14 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 ...
2
votes
0answers
50 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 ...
0
votes
0answers
21 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 ...
1
vote
0answers
36 views

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 ...
0
votes
0answers
16 views

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 ...
1
vote
0answers
40 views

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 ...
10
votes
0answers
111 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 ...
0
votes
1answer
53 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 ...
1
vote
0answers
44 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 ...
1
vote
0answers
48 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 ...
1
vote
1answer
71 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 ...
1
vote
0answers
92 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 ...
0
votes
0answers
62 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 ...
3
votes
2answers
119 views

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 ...
0
votes
0answers
73 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 ...
0
votes
0answers
22 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, ...
0
votes
1answer
132 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. ...
2
votes
1answer
292 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 ...
0
votes
1answer
34 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 ...
1
vote
0answers
60 views

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 ...
0
votes
0answers
154 views

How to calculate prediction intervals from a multiple linear regression with simulated future Xs

I am using a multiple linear regression model to generate 80% prediction intervals based on simulations of future X values. While I understand how to calculate prediction intervals typically (such as ...
0
votes
0answers
43 views

How to calculate prediction intervals in major axis regression using R

Need help in calculation of prediction intervals in major axis regression (MA). I'm using 'lmodel2' package for calculation of the MA, but I don't understand how to calculate prediction intervals ...
1
vote
2answers
349 views

Prediction interval for a fitted log-normal distribution

What I am trying to do is to fit a log-normal distribution to a data-set, and then determine confidence and prediction intervals for the fitted distribution - not just for the mean and sd estimates. ...
1
vote
0answers
67 views

Which statistics to use calculating prediction interval of dummy linear regression?

I have performed a linear regression and found a model of the form: $$ \hat{Y} = \alpha + \beta_1 x+ \delta_{high} + \delta_{low} + \epsilon\\ $$ Where: $\beta_1$ is a continuously distributed ...
1
vote
0answers
45 views

Inverse prediction of percentile

Suppose we consider a linear normal regression $y\sim$Normal($\mu,\sigma$) and $\mu=a+bx$. I have seen documentations for methods for obtaining a confidence interval for $x$ for a specific mean value ...
2
votes
0answers
47 views

Multiple regression prediction interval comparison

Here's my situation. I have a multiple linear regression which I've used to come up with a prediction interval to predict a value y for a given (x1,x2,x3,x4,x5,x6). It reads something like lower: ...
1
vote
0answers
75 views

Inventory control - first order quantity of periodic order quantities model

I Have read "Manufacturing Planning and Control for Supply Chain Management 6th Edition" by F.Robert Jacobs. I found the problem on the Periodic Order Quantities (POQ). As I know POQ calculation is ...
8
votes
2answers
244 views

Can we make probabilistic statements with prediction intervals?

I've read through the many excellent discussions on the site regarding interpretation of confidence intervals and prediction intervals, but one concept is still a bit puzzling: Consider the OLS ...
2
votes
0answers
107 views

Forecasting call volumes over short intervals using R

I am trying to do a basic forecast of call volumes using the forecast library for R. I am not having too much trouble forecasting on a daily or monthly interval, however when I try to forecast on an ...
0
votes
0answers
67 views

Confidence and prediction intervals

The difference between confidence and prediction intervals has been explained in plain English on Cross Validated: Difference between confidence intervals and prediction intervals However, when ...
3
votes
2answers
832 views

Can a mathematically sound prediction interval have a negative lower bound?

I have used R to form a 95% prediction interval for the number of endemic species on an island. My lower bound is negative – is that mathematically sound? In the linear model used in the prediction ...
1
vote
0answers
28 views

Joint vs. marginal prediction intervals for path forecasts (with k-family wise error rate)

I am trying to become comfortable with the bootstrapping of joint prediction regions described in this paper: http://www.nccr-finrisk.uzh.ch/media/pdf/wp/WP748_A3.pdf This calculates the prediction ...
1
vote
0answers
170 views

Prediction Intervals for General Linear Model

How do I derive prediction intervals for a general linear model? My general linear model written in matrix form is, $$ \mathbf{Y} = \mathbf{X} \mathbf{B} + \mathbf{R}$$ with each of the rows of ...
2
votes
1answer
137 views

Prediction interval on untransformed scale

I am attempting to use simple linear regression to construct a 95% prediction interval for a continuous response variable (Y) using a continuous input variable (X). When examining my data, I realized ...
3
votes
2answers
114 views

What does error refer to in linear regression notation?

I regularly see linear regression models written in this notation: $y = a + \beta X + error$ I've never really pinned down what $error$ actually refers to. In the linear regression plotted below, ...
12
votes
1answer
1k views

Shape of confidence interval for predicted values in linear regression

I have noticed that the confidence interval for predicted values in an linear regression tends to be narrow around the mean of the predictor and fat around the minimum and maximum values of the ...
8
votes
2answers
648 views

Shape of confidence and prediction intervals for nonlinear regression

Are the confidence and prediction bands around a non-linear regression supposed to be symmetrical around the regression line? Meaning they do not take on the hour-glass shape as in the case of the ...
2
votes
0answers
56 views

Which confidence interval should I use to bound actual values around a predicted value?

I have a 'black box' model that outputs model predictions, but I don't know what actually goes on inside the model. I also have a bunch of data that I can pass through the model so that I can compare ...
0
votes
0answers
114 views

Prediction intervals predict.Arima r

I would like to ask how the long-term (multiple step ahead) prediction intervals are calculated by function predict.Arima in R. I am particularly interested in ...
0
votes
0answers
44 views

Why do matching algorithms use point estimates rather than intervals?

I'm developing a matching algorithm, and I am wondering why websites choose using point estimates, e.g. "You match 60% with person X". Given that there will be most likely be missing data, rather ...
1
vote
2answers
160 views

Estimate the sum of predicted variables by a linear model in R

I have a dataset with 3000 sub-regions with data about their population by income range and their value spending in a commodity. I made a OLS model with log-log transformation using ...
2
votes
0answers
52 views

Prediction interval in principal component regression

I would like to obtain a prediction interval from a model returned by the R package 'pls'. The predict method does not seem to be able to return this value. I wonder if anyone has a suggested ...
5
votes
1answer
177 views

Does more variables mean tighter confidence intervals?

Assume that the true (but unknown) relationship in a population between $Y$ and $X1, X2, X3, X4$ is $$Y=\beta_0 + \beta_1 X_1 + \beta_2 X_2 + \beta_3 X_3 + \beta_4 X_4.$$ Further assume that I have a ...