Paper Title :Comparisons of Theil’s and Simple Regression on Normal and Non-Normal Data Set with Different Sample Sizes
Author :Esemokumo Perewarebo Akpos, Opara, Jude
Article Citation :Esemokumo Perewarebo Akpos ,Opara ,Jude ,
(2018 ) " Comparisons of Theil’s and Simple Regression on Normal and Non-Normal Data Set with Different Sample Sizes " ,
International Journal of Management and Applied Science (IJMAS) ,
pp. 70-74,
Volume-4,Issue-1
Abstract : This paper is on comparisons of Theil’s and simple regression on normal and non-normal data set with different
sample sizes. Data used for this study were collected from a real life practical conducted by the researchers in their homes on
the weight of soap and the number of days it had been used. Thus dependent variable(y) is weight (grams) of the soap and
independent variable is the number of days (x). To know the efficiency of one method over the other, the Akaike Information
Criterion (AIC), Bayesian Information Criterion (BIC), and Mean Square Error (MSE) were used. From the analysis, the
result revealed that there is a significant relationship between dependent and independent variables for both the parametric
OLS regression and non-parametric Theil’s regression with and without residual normality validity. Hence, an inverse
relationship between x and y, that is as the number of days increase, weight of the soap decreases. It can be concluded that
the parametric OLS regression performs better than its non-parametric Theil’s regression since their Residual standard error,
AIC and BIC values are all smaller for both the normal and non-normal real data. The result of the real life data was used for
data simulation of sample sizes of n = 30, 50, 100, 150, 200, 400, 500, 700, 900, 1000, and 1500, and the results revealed
that the parametric OLS regression performs better than its non-parametric Theil’s regression since their EMS, AIC and BIC
values are all smaller. It can be concluded that the regression line gave a good fit to the observed data since the line explains
over 99% of the total variation of the Y values around their mean for both models. Even though the both models are good in
this study, the OLS is more efficient. Therefore the researchers recommend that future research should look at a similar work
with both high and low coefficient of variation of different sample sizes with normal and non-normal data, and also with
more than one explanatory variable to examine the differences between the parametric and nonparametric Regression.
Keywords - Theil’s Regression, Simple Regression, Anderson-Darling technique, Akaike Information Criterion, Bayesian
Information Criterion, Error Mean Squares
Type : Research paper
Published : Volume-4,Issue-1
DOIONLINE NO - IJMAS-IRAJ-DOIONLINE-10716
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Published on 2018-03-27 |
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