scholarly journals Conditional Prediction Intervals for Linear Regression

2009 ◽  
Author(s):  
Peter McCullagh ◽  
Vladimir Vovk ◽  
Ilia Nouretdinov ◽  
Dmitry Devetyarov ◽  
Alex Gammerman
Keyword(s):  
Linear Regression ◽  
Prediction Intervals ◽  
Conditional Prediction

A Note on Shortest Prediction Intervals for Log-Linear Regression

Technometrics ◽  
1971 ◽  
Vol 13 (4) ◽  
pp. 889-894
Author(s):  
Alastair J. Scott ◽  
Michael J. Symons
Keyword(s):  
Linear Regression ◽  
Prediction Intervals ◽  
Log Linear

Regression

2021 ◽  
pp. 71-84
Author(s):  
Andy Hector
Keyword(s):  
Linear Regression ◽  
Hypothesis Testing ◽  
Linear Model ◽  
Confidence Intervals ◽  
Linear Models ◽  
Model Analysis ◽  
Prediction Intervals ◽  
Explanatory Variables ◽  
Worked Example

This chapter extends the use of linear models to relationships with continuous explanatory variables, in other words, linear regression. The goal of the worked example (on timber hardness data) given in detail in this chapter is prediction, not hypothesis testing. Confidence intervals and prediction intervals are explained. Graphical approaches to checking the assumptions of linear-model analysis are explored in further detail. The effects of transformations on linearity, normality, and equality of variance are investigated.

Predicting defoliation by Choristoneura biennis (Lepidoptera: Tortricidae)

2003 ◽  
Vol 135 (6) ◽  
pp. 903-907 ◽  
Author(s):  
V.G. Nealis ◽  
R. Turnquist
Keyword(s):  
British Columbia ◽  
Life Cycle ◽  
Linear Regression ◽  
Picea Glauca ◽  
Spruce Budworm ◽  
White Spruce ◽  
Prediction Intervals ◽  
Abies Lasiocarpa ◽  
Independent Data ◽  
Subalpine Fir

AbstractThe 2-year-cycle spruce budworm, Choristoneura biennis Free. (Lepidoptera: Tortricidae), causes defoliation of spruce – subalpine fir forests in British Columbia, Canada. Historical and newly obtained data were used to develop a linear regression relating percent defoliation in the 2nd feeding year of the life cycle to the percentage of shoots damaged in the previous, 1st feeding year of the life cycle. The resulting regression was tested with independent data and correctly predicted (95% prediction intervals) defoliation in 14 of 15 stands. Patterns of defoliation were similar on white spruce, Picea glauca (Moench) Voss (Pinaceae), and subalpine fir, Abies lasiocarpa (Hook.) Nutt. (Pinaceae), and hence the regression can be used for either mixed or pure stands of either species.

Unbiased Estimation of the MSE Matrix of Stein-Rule Estimators, Confidence Ellipsoids, and Hypothesis Testing

1990 ◽  
Vol 6 (1) ◽  
pp. 63-74 ◽  
Author(s):  
R.A.L. Carter ◽  
M.S. Srivastava ◽  
V.K. Srivastava ◽  
A. Ullah
Keyword(s):  
Linear Regression ◽  
Least Squares ◽  
Linear Regression Model ◽  
Unbiased Estimation ◽  
Confidence Sets ◽  
Coverage Probabilities ◽  
Coefficient Vector ◽  
The Mean ◽  
Conditional Prediction ◽  
Confidence Ellipsoids

We first present an unbiased estimator of the MSE matrix of the Stein-rule estimator of the coefficient vector in a normal linear regression model. The Steinrule estimator can be used with both its estimated MSE matrix and with the least-squares MSE matrix to form confidence ellipsoids. We derive the approximate expected squared volumes and coverage probabilities of these confidence sets and discuss their ranking. These results can be applied to the conditional prediction of the mean of the endogenous variable. We also consider the power of F-tests which employ the Stein-rule estimator in place of the least-squares estimator.

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