# Prediction variance of a central composite design with missing observation

Kohei Fujiwara, Shun Matsuura

Research output: Contribution to journalArticle

### Abstract

Central composite design has been widely used in response surface methods. This article studies how much the variance of a predicted response is inflated when an observation is missing in a central composite design. A mathematical expression is derived for the inflation amount of the prediction variance. It turns out that, for rotatable central composite designs, the inflation amount of the prediction variance depends only on the Euclidean norms and the inner product of the two vectors of factor values at which the observation is missing and the response is predicted. Several numerical examples are presented to show relationships between the inflation amount of the prediction variance and the angle formed by the two vectors.

Original language English Communications in Statistics - Theory and Methods https://doi.org/10.1080/03610926.2019.1625925 Published - 2019 Jan 1

### Fingerprint

Prediction Variance
Missing Observations
Inflation
Composite
Response Surface Method
Euclidean norm
Scalar, inner or dot product
Angle
Numerical Examples
Design
Observation

### Keywords

• Central composite design
• missing data
• prediction variance
• response surface method
• rotatable design

### ASJC Scopus subject areas

• Statistics and Probability

### Cite this

In: Communications in Statistics - Theory and Methods, 01.01.2019.

Research output: Contribution to journalArticle

title = "Prediction variance of a central composite design with missing observation",
abstract = "Central composite design has been widely used in response surface methods. This article studies how much the variance of a predicted response is inflated when an observation is missing in a central composite design. A mathematical expression is derived for the inflation amount of the prediction variance. It turns out that, for rotatable central composite designs, the inflation amount of the prediction variance depends only on the Euclidean norms and the inner product of the two vectors of factor values at which the observation is missing and the response is predicted. Several numerical examples are presented to show relationships between the inflation amount of the prediction variance and the angle formed by the two vectors.",
keywords = "Central composite design, missing data, prediction variance, response surface method, rotatable design",
author = "Kohei Fujiwara and Shun Matsuura",
year = "2019",
month = "1",
day = "1",
doi = "10.1080/03610926.2019.1625925",
language = "English",
journal = "Communications in Statistics - Theory and Methods",
issn = "0361-0926",
publisher = "Taylor and Francis Ltd.",

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T1 - Prediction variance of a central composite design with missing observation

AU - Fujiwara, Kohei

AU - Matsuura, Shun

PY - 2019/1/1

Y1 - 2019/1/1

N2 - Central composite design has been widely used in response surface methods. This article studies how much the variance of a predicted response is inflated when an observation is missing in a central composite design. A mathematical expression is derived for the inflation amount of the prediction variance. It turns out that, for rotatable central composite designs, the inflation amount of the prediction variance depends only on the Euclidean norms and the inner product of the two vectors of factor values at which the observation is missing and the response is predicted. Several numerical examples are presented to show relationships between the inflation amount of the prediction variance and the angle formed by the two vectors.

AB - Central composite design has been widely used in response surface methods. This article studies how much the variance of a predicted response is inflated when an observation is missing in a central composite design. A mathematical expression is derived for the inflation amount of the prediction variance. It turns out that, for rotatable central composite designs, the inflation amount of the prediction variance depends only on the Euclidean norms and the inner product of the two vectors of factor values at which the observation is missing and the response is predicted. Several numerical examples are presented to show relationships between the inflation amount of the prediction variance and the angle formed by the two vectors.

KW - Central composite design

KW - missing data

KW - prediction variance

KW - response surface method

KW - rotatable design

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