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15 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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25 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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0answers
30 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
50 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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0answers
31 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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0answers
16 views

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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2answers
49 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
38 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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1answer
146 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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0answers
38 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 ...
0
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1answer
24 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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1answer
55 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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31 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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0answers
16 views

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
66 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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2answers
216 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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1answer
184 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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0answers
20 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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1answer
21 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 ...
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0answers
33 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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1answer
36 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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0answers
33 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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0answers
24 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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0answers
70 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
35 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
42 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
25 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
55 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 ...
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0answers
158 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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1answer
61 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
49 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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0answers
52 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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1answer
79 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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0answers
141 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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69 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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2answers
128 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
80 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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0answers
25 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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1answer
164 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
388 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
36 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
69 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
216 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 ...
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0answers
48 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 ...
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2answers
439 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
76 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
49 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 ...
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0answers
55 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
100 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
266 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 ...