Analysis of Variance

2021 ◽  
pp. 127-138
Author(s):  
Andy Hector
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Analysis Of Variance ◽  
Inbreeding Depression ◽  
Charles Darwin ◽  
Sums Of Squares ◽  
Anova Table ◽  
Maize Plants

Analysis of variance is introduced using a worked analysis of some data collected by Charles Darwin on inbreeding depression in experimental maize plants. ANOVA is used to compare the heights of a group of cross-pollinated plants with a group of self-fertilized seedlings. The least squares process is explained, including the calculation of sums of squares and variances and the calculation of F-ratios. The organization of the results of a linear model into an ANOVA table is explained. The R code necessary to perform the analysis is worked through and explained in terms of the underlying statistical concepts, and the interpretation of the R output is demonstrated.

Comparison of plasma progesterone profiles in cyclic, pregnant, pseudopregnant and hysterectomized pigs between 8 and 27 days after oestrus

1988 ◽  
Vol 119 (1) ◽  
pp. 111-116 ◽  
Author(s):  
G. J. King ◽  
R. Rajamahendran
Keyword(s):  
Least Squares ◽  
Analysis Of Variance ◽  
The Other ◽  
Corpora Lutea ◽  
Plasma Progesterone ◽  
The Third ◽  
Secretory Potential ◽  
The Mean

ABSTRACT Plasma progesterone concentrations were compared in cyclic (n = 12), pregnant (n =12), oestradiol-induced pseudopregnant (n=12) and hysterectomized gilts (n=10) between days 8 and 27 after oestrus. The results were grouped into periods covering days 8–13, 14–20 and 21–27 and analysed by least-squares analysis of variance. Plasma progesterone concentrations were significantly (P<0·001) higher in hysterectomized compared with other groups between days 8 and 13. Progesterone concentrations declined rapidly after day 14 in cyclic females and gradually in the other groups. Throughout the third and fourth weeks the mean progesterone concentrations for hysterectomized animals were consistently higher than for pseudopregnant animals (P<0·05). The pregnant group means were below but not significantly different from the hysterectomized means in both of the last two periods. The greater progesterone concentrations in hysterectomized gilts indicated that secretion is high without any conceptus-produced or -mediated luteotrophin, and corpora lutea in cyclic, pregnant or pseudopregnant gilts may never reach full secretory potential. J. Endocr. (1988) 119, 111–116

A new vision on ordinary least squares estimation of parameters of linear model

2021 ◽  
Author(s):  
K. Lakshmi ◽  
B. Mahaboob ◽  
D. Sateesh Kumar ◽  
G. Balagi Prakash ◽  
T. Nageswara Rao
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Ordinary Least Squares ◽  
Least Squares Estimation ◽  
Estimation Of Parameters ◽  
New Vision

scholarly journals Least Squares Estimations for the General Linear Model Parameters with Epsilon Skew Normal Error Term

2020 ◽  
pp. 636-645
Author(s):  
Hussain Karim Nashoor ◽  
Ebtisam Karim Abdulah
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Least Squares Method ◽  
General Linear Model ◽  
Ordinary Least Squares ◽  
Skewed Distribution ◽  
General Linear ◽  
Average Error ◽  
Model Parameters ◽  
Skew Normal

Examination of skewness makes academics more aware of the importance of accurate statistical analysis. Undoubtedly, most phenomena contain a certain percentage of skewness which resulted to the appearance of what is -called "asymmetry" and, consequently, the importance of the skew normal family . The epsilon skew normal distribution ESN (μ, σ, ε) is one of the probability distributions which provide a more flexible model because the skewness parameter provides the possibility to fluctuate from normal to skewed distribution. Theoretically, the estimation of linear regression model parameters, with an average error value that is not zero, is considered a major challenge due to having difficulties, as no explicit formula to calculate these estimates can be obtained. Practically, values for these estimates can be obtained only by referring to numerical methods. This research paper is dedicated to estimate parameters of the Epsilon Skew Normal General Linear Model (ESNGLM) using an adaptive least squares method, as along with the employment of the ordinary least squares method for estimating parameters of the General Linear Model (GLM). In addition, the coefficient of determination was used as a criterion to compare the models’ preference. These methods were applied to real data represented by dollar exchange rates. The Matlab software was applied in this work and the results showed that the ESNGLM represents a satisfactory model. 

INFLUENCE OF MATRIX ERRORS ON PARAMETER ESTIMATES BY THE LEAST SQUARES METHOD

2021 ◽  
Author(s):  
V. A. Galanina ◽  
◽  
L. A. Reshetov ◽  
M. V. Sokolovskay ◽  
A. E. Farafonova ◽  
...  
Keyword(s):  
Least Squares ◽  
Linear Model ◽  
Least Squares Method ◽  
Statistical Characteristics ◽  
Parameter Estimates ◽  
Model Matrix ◽  
Least Squares Estimates

The paper investigates the effect of distorsions of the linear model matrix on the statistical characteristics of the least squares estimates.

Analysis of variance (ANOVA).

2021 ◽  
pp. 155-165
Author(s):  
Donald Quicke ◽  
Buntika A. Butcher ◽  
Rachel Kruft Welton
Keyword(s):  
Linear Model ◽  
Analysis Of Variance ◽  
Explanatory Variable ◽  
T Test ◽  
Specific Function ◽  
Real Numbers ◽  
Response Variable ◽  
Explanatory Variables ◽  
Student’S T ◽  
One Way Anova

Abstract Analysis of variance is used to analyze the differences between group means in a sample, when the response variable is numeric (real numbers) and the explanatory variable(s) are all categorical. Each explanatory variable may have two or more factor levels, but if there is only one explanatory variable and it has only two factor levels, one should use Student's t-test and the result will be identical. Basically an ANOVA fits an intercept and slopes for one or more of the categorical explanatory variables. ANOVA is usually performed using the linear model function lm, or the more specific function aov, but there is a special function oneway.test when there is only a single explanatory variable. For a one-way ANOVA the non-parametric equivalent (if variance assumptions are not met) is the kruskal.test.

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