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2
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13 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
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0answers
8 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
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0answers
36 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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0answers
14 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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0answers
24 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 ...
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0answers
14 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 ...
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0answers
31 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 ...
9
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0answers
92 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
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1answer
49 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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0answers
43 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
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0answers
36 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
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1answer
65 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
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0answers
67 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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0answers
53 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
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2answers
111 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 ...
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0answers
68 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
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0answers
21 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
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1answer
120 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
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1answer
244 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
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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 ...
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0answers
52 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 ...
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0answers
134 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
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0answers
36 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
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2answers
297 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. ...
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0answers
63 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 ...
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0answers
38 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
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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: ...
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0answers
68 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 ...
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2answers
234 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
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0answers
102 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 ...
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0answers
63 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 ...
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2answers
793 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
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0answers
26 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 ...
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0answers
154 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
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1answer
122 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
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2answers
112 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
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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
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2answers
580 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
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0answers
54 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 ...
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0answers
104 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
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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
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2answers
152 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
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0answers
50 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
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1answer
172 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 ...
0
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3answers
970 views

Why do we estimate the mean response in Confidence interval but predict individual outcome in prediction?

I have tried to understand the differences. Just to be clear, I think I understand the two sources of variation in prediction comes from the variation in the distribution of the location of Y and ...
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0answers
179 views

Question about prediction bands for non-linear regression computation?

I am interested in computing prediction bands for a non-linear regression (log-logistic function with 3 parameters). I have read the Prism help page: The calculation of the confidence and ...
0
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0answers
40 views

Leave-out data approach to get intervals for predictive performance of a regression model

When measuring predictive performance of a regression model, I am thinking about using repeated data splitting (or leave-out data at random) instead of using bootstrapping. By "repeated data ...
6
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0answers
188 views

Detecting outliers using 95% PI around a natural spline fit

Please see the picture below: I wanted to mark the points that are not consistent with their adjacent points as outlier. What I did was to fit a natural spline fit to 1000 observations (the purple ...
3
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1answer
141 views

Prediction interval = credible interval?

I am wondering if prediction interval and credible interval evaluate the same thing. For instance with a linear regression, when you estimate the prediction interval of a fitted values, you estimate ...
1
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1answer
1k views

Calculating Prediction Interval

I have the following data located here. I am attempting to calculate the 95% confidence interval on the mean purity when the hydrocarbon percentage is 1.0. In R, I enter the following. ...