scholarly journals What’s in a Coefficient? The “Not so Simple” Interpretation of R2, for Relatively Small Sample Sizes

2019 ◽  
Vol 7 (12) ◽  
pp. 27
Author(s):  
Nizar Zaarour ◽  
Emanuel Melachrinoudis
Keyword(s):  
Standard Deviation ◽  
Linear Regression ◽  
Small Sample ◽  
Coefficient Of Determination ◽  
Simple Linear Regression ◽  
Sample Sizes ◽  
Simple Interpretation ◽  
Small Sample Sizes ◽  
Level Of Significance ◽  
The Relationship

There are several misconceptions when interpreting the values of the coefficient of determination, R2, in simple linear regression. R2 is heavily dependent on sample size n and the type of data being analyzed but becomes insignificant when working with very large sample sizes. In this paper, we comment on these observations and develop a relationship between R2, n, and the level of significance α, for relatively small sample sizes. In addition, this paper provides a simplified version of the relationship between R2 and n, by comparing the standard deviation of the dependent variable, Sy, to the standard error of the estimate, Se. This relationship will serve as a safe lower bound to the values of R2. Computational experiments are performed to confirm the results from both models. Even though the focus of the paper is on simple linear regression, we present the groundwork for expanding our two models to the multiple regression case.

scholarly journals علاقة بين البيئة التعليمية ورغبة تعلم اللغة العربية

2021 ◽  
Vol 10 (1) ◽  
pp. 131
Author(s):  
Khaira Fatma ◽  
Aina Salsabila
Keyword(s):  
Standard Deviation ◽  
Linear Regression ◽  
Educational Environment ◽  
Quantitative Approach ◽  
Survey Method ◽  
Simple Linear Regression ◽  
Research Instrument ◽  
High Category ◽  
Class Viii ◽  
The Relationship

This study aims to determine the educational environment, interesting in learning Arabic and the relationship between both are in learning Arabic for students of class VIII ofMTsN 1 Lhokseumawe. This study uses a quantitative approach with a survey method to collect data. The research instrument is a questionnaire distributed online with the help of google form. The population amounted to 267 students and the sample is 25% of the population, there are 66 students. The data were analyzed using a simple linear regression formula with the help of the SPSS program. The results of this study indicate that the educational environment of class VIII students of MTsN 1 Lhokseumawe is in the high category with an average of 135.71 with a standard deviation of 10,185. Meanwhile, the average student’s interest in learning Arabic is in the high category, with an average of 71.67 and a standard deviation of 9,907. This study also found that there was no relationship between the two variables or no relationship between the educational environment and the students' interest in learning Arabic in class VIII MTsN 1 Lhokseumawe

The Relationship Between Sample Sizes and Effect Sizes in Systematic Reviews in Education

2009 ◽  
Vol 31 (4) ◽  
pp. 500-506 ◽  
Author(s):  
Robert Slavin ◽  
Dewi Smith
Keyword(s):  
Sample Size ◽  
Effect Size ◽  
Secondary Mathematics ◽  
Significant Negative Correlation ◽  
Small Sample ◽  
Effect Sizes ◽  
Sample Sizes ◽  
Large Samples ◽  
Small Sample Sizes ◽  
The Relationship

Research in fields other than education has found that studies with small sample sizes tend to have larger effect sizes than those with large samples. This article examines the relationship between sample size and effect size in education. It analyzes data from 185 studies of elementary and secondary mathematics programs that met the standards of the Best Evidence Encyclopedia. As predicted, there was a significant negative correlation between sample size and effect size. The differences in effect sizes between small and large experiments were much greater than those between randomized and matched experiments. Explanations for the effects of sample size on effect size are discussed.

Phase II Multiple Linear Regression Profile with Small Sample Sizes

2014 ◽  
Vol 31 (5) ◽  
pp. 851-861 ◽  
Author(s):  
Mahmoud A. Mahmoud ◽  
Abd El Naser Saad ◽  
Reham El Shaer
Keyword(s):  
Linear Regression ◽  
Multiple Linear Regression ◽  
Phase Ii ◽  
Small Sample ◽  
Sample Sizes ◽  
Small Sample Sizes

scholarly journals Study on Optimalization of Own-Source Revenue in Regencies and Municipals in Central Java Province

2017 ◽  
Vol 16 (1) ◽  
Author(s):  
Jalu Adi Prakoso ◽  
Suci Rahmawati Prima ◽  
M. Chrisna Satriagasa ◽  
M. Syahli IMNS
Keyword(s):  
Linear Regression ◽  
Linear Regression Analysis ◽  
Coefficient Of Determination ◽  
Positive Trend ◽  
Simple Linear Regression ◽  
Local Revenue ◽  
Central Java ◽  
The Government ◽  
The Relationship ◽  
Central Java Province

<p>Optimizing the management of potential areas would provide additional revenue for the region. This research aims to assess whether the government in the counties and cities in Central Java province has been optimally manage their potentials so as to provide benefits beupa increased local revenues derived from the wealth management area. Through the relationship between the variables of the original income (PAD) and the Gross Domestic Product (GRDP) in the counties and cities in Central Java is expected to be known whether each area has been optimal in obtaining local revenue. The data used is data sekuder form of data revenues and GRDP in counties and cities in the province of Central Java during the years 2011-2013 were berusmber from the Central Statistics Agency (BPS), the Supreme Audit Agency (BPK), Report of Realized APBD, and RPJMD Central Java.</p><p>Methods of data analysis in this research is to use a simple linear regression analysis (OLS Model) and design analysis group. The analysis showed the existence of ties between the GRDP and the PAD. The magnitude of the relationship analyzed by simple linear regression, where the results indicate a positive trend. That is, there is a directly proportional relationship anatara GRDP and PAD. The coefficient of determination of 99.9% explained that the GRDP variable can be explained by the variable revenue of 99.9%, while 0.1% is explained by other variables.</p><p>The analysis showed that the GRDP value of the coefficient b&gt; b PAD either at the district, town and overall. These results indicate that there has been no attempt by the government to manage PAD so as to generate the GRDP increase. The government can manage the outcome of PAD to be used in a way that increases the GRDP obtained. As for the test results to determine differences in optimizing the management of local revenue between districts and cities showed that the district can generate GRDP is greater with smaller PAD. It shows that the effort made by the district is more efficient than the effort undertaken by the municipality.</p><p>Spatial analysis shows a comparison of the GRDP against the PAD in each county and city in Central Java province is divided into four clusters. Each cluster has a distinct regional characteristics seen from economic activity. The results of the socio-economic analysis of the economy in Central Java province when seen from the conditions of employment, which absorbs the most amount of power keraja is in the agricultural sector, which amounted to 31%, followed by the trade sector 22% and industry 19%.</p><p>Keyword: Decentralization, PAD, GRDP</p>

scholarly journals Hubungan antara Morfologi Ambing, Produksi Susu dan Komponen Susu pada Sapi Friesian Holstein

2019 ◽  
Vol 19 (2) ◽  
pp. 91-98
Author(s):  
Dian Wijayanti Solechah ◽  
Dian Wahyu Harjanti ◽  
Rudy Hartanto
Keyword(s):  
Linear Regression ◽  
Dairy Cows ◽  
Milk Production ◽  
Significant Relationship ◽  
Regression Equation ◽  
Coefficient Of Determination ◽  
Simple Linear Regression ◽  
Holstein Friesian ◽  
Livestock Productivity ◽  
The Relationship

ABSTRAK. Ukuran-ukuran ambing merupakan salah satu indikator yang menentukan produksi susu sapi perah. Morfologi ambing dapat digunakan untuk menilai produktivitas ternak. Penelitian ini bertujuan untuk mengetahui hubungan antara ukuran-ukuran ambing, produksi susu dan komponen susu. Materi yang digunakan yaitu 30 ekor sapi (Friesian Holstein) FH periode laktasi III-V dan bulan laktasi 3-4. Analisis yang digunakan adalah regresi linier sederhana dengan SPSS 16. Hasil penelitian menunjukkan ada hubungan yang nyata (P 0,05) antara kedalaman ambing belakang dan panjang ambing terhadap produksi susu secara berturut-turut dengan persamaan regresi Y = -1,142 + 0,435 X (r = 0,494 dan R2 = 0,244),Y = -9,197 + 0,463 X (r = 0,625 dan R2 = 0,390), lebar ambing belakang terhadap produksi susu dan jarak antar puting depan dengan produksi susu dengan persamaan regresi secara berturut-turut Y = 1,236 + 0,28 X (r = 0,397 dan R2 = 0,157) dan Y = 17,203-0,996 X (r = 0,367 dan R2 = 0,134). Kesimpulan yang didapat bahwa ada hubungan antara ukuran-ukuran ambing dengan produksi susu sapi Friesian Holstein, dimana terdapat hubungan yang signifikan antara kedalaman ambing belakang, panjang ambing serta lebar ambing belakang dan jarak antar puting depan dengan produksi susu dengan koefisien korelasi (r) tertinggi sebesar 0,625 dan koefisien determinasi (R2) sebesar 39%.  (Relationship between udder morphology, milk production and milk components of friesian holstein cows) ABSTRACT. The size of the udder is one indicator that determines the production of dairy cows. The udder morphology can be used to assess livestock productivity. This study aimed to determine the relationship between udder measurements, components of milk and milk production. The material used was 30 Holstein Friesian (FH) lactation periods III-V and lactation months 3-4. The analysis used was a simple linear regression with SPSS 16. The results showed a significant relationship (P 0.05) between the depth of the udder and length of the udder to milk production in a row with the regression equation Y = -1,142 + 0,435 X (r = 0,494 and R2 = 0,244), Y = -9,197 + 0,463 X (r = 0,625 and R2 = 0,390), width of the rear udder to milk production and the distance between the front nipple and milk production with consecutive regression equation Y = 1,236 + 0,28 X (r = 0,397 and R2 = 0,157) and Y = 17,203 – 0,996 X (r = 0,367 and R2 = 0,134). The conclusion that there is a relationship between udder measurements with Holstein Friesian milk production, where there is a significant relationship between the depth of the udder, udder length and width of the udder and the distance between the front nipples with milk production with the highest correlation coefficient (r) of 0,625 and the coefficient of determination (R2) of 39%.

DO ENVIRONMENTAL FACTORS AFFECT THE TAXONOMIC RELIABILITY OF LEAF CUTICULAR MICROMORPHOLOGICAL CHARACTERS? A CASE STUDY IN PODOCARPACEAE

2017 ◽  
Vol 74 (3) ◽  
pp. 299-343 ◽  
Author(s):  
J. A. R. Clugston ◽  
C. E. Jeffree ◽  
A. Ahrends ◽  
R. R. Mill
Keyword(s):  
Environmental Factors ◽  
First Record ◽  
Small Sample ◽  
Climate Data ◽  
Sample Sizes ◽  
Small Sample Sizes ◽  
Micromorphological Characters ◽  
Multiple Samples ◽  
The Relationship

Leaf cuticle micromorphology has been cited as an important set of taxonomic characters in gymnosperms, but previous studies have largely been based on small sample sizes. The premise of this study was to understand whether external factors affect cuticular micromorphology of Podocarpaceae. Two example species, Prumnopitys andina and Podocarpus salignus, were studied. Of 21 sampled characters, nine (c.43% of the total) were visually assessed as being moderately reliable or highly reliable for taxonomic discrimination for both species, with an additional six (c.29%) being moderately reliable or highly reliable for only one or other of the example species, and six characters (c.29%) unreliable for both. Seven of the most variable stomatal characters were selected for further analysis to establish whether environmental factors affect them. The relationship between these seven stomatal characters, the environment and climate was analysed using the R ‘vegan’ package and climate data gathered from WorldClim. Our results showed that both species had larger stomata in moist and shady conditions, and a higher density of (smaller) stomata in sunny and drier conditions. An additional novel finding was the presence of stomata on the adaxial leaf surface in 46% of samples of Prumnopitys andina: the first record of adaxial stomata in this species, highlighting the necessity of studying multiple samples of a given species. In conclusion, these results indicate that larger sample sizes than have hitherto been employed in cuticle micromorphological studies are necessary to fully document the amount of phenotypic variation that exists.

Maintaining Customer Loyalty by Intensifying Service Quality and Customer Satisfaction in Commuter Line Jabodetabek

2019 ◽  
Vol 10 (9) ◽  
pp. 902-909
Author(s):  
Umbas Krisnanto ◽  
◽  
Conny Marpaung ◽  
Keyword(s):  
Data Analysis ◽  
Linear Regression ◽  
Customer Satisfaction ◽  
Service Quality ◽  
Hypothesis Testing ◽  
Customer Loyalty ◽  
T Test ◽  
Coefficient Of Determination ◽  
Simple Linear Regression ◽  
Significance Level

This study aims to determine and analyze the influence of Service Quality and Customer Satisfaction on Customer Loyalty in Jabodetabek Commuter Line. The sample of this study was 50 people. Methods of collecting data by distributing questionnaires. Data analysis using the analysis used is simple linear regression, t test and coefficient of determination. The results showed 1) Service Quality has a positive and significant effect on Customer Loyalty in Jabodetabek Commuter Line, with a significance level of 0.048; and supported by the results of hypothesis testing with a t-count value of 4.433 > t-table value of 1.95, with a significance of 0.048 or < 0.05; 2) Customer Satisfaction positive and significant effect on Customer Loyalty in Jabodetabek Commuter Line, with a level significance of 0,000; and supported by the results of hypothesis testing with a t-count value of 4,969 > t-table value of 1.95, with a significance of 0,000 or < 0.05, 3) Service quality and Customer Satisfaction have a positive and significant effect on Customer Loyalty in Jabodetabek Commuter Line, with a significance level of 0,000. This means that the hypothesis H0 is rejected and Ha is accepted so that it can be concluded that service quality and customer satisfaction together have a positive and significant effect on customer loyalty in Jabodetabek Commuter Line.

PENGARUH HARGA DAN BRAND TRUST TERHADAP KEPUTUSAN PEMBELIAN OPPO SMARTPHONE (Studi kasus pada OPPO Store, Sinergy Celular Medan)

2019 ◽  
Vol 14 (1) ◽  
pp. 17
Author(s):  
Andi S Tarigan ◽  
Zulkarnaian Siregar
Keyword(s):  
Data Analysis ◽  
Linear Regression ◽  
Multiple Linear Regression ◽  
Coefficient Of Determination ◽  
Purchase Decision ◽  
Brand Trust ◽  
Significance Level ◽  
Research Hypothesis ◽  
Analysis Technique ◽  
The Relationship

AbstrakPenelitian ini bertujuan untuk mengetahui Pengaruh Harga dan Brand Trust Terhadap Keputusan Pembelian pada Sinergy Celular Medan.Sampel dalam penelitian ini adalah seluruh pengunjung Sinergy Celular Medan sebanyak 77 orang.Teknik pengumpulan data yang digunakan adalah melalui kuesioner (angket) yaitu dengan cara menyebarkan kuesioner kepada sampel (responden) dan mengumpulkannya kembali. Teknik analisis data yang digunakan adalah Regresi Linear Berganda.Sebelum data diregresikan maka terlebih dahulu di uji keterkaitannya antara variabel, datanya diuji menggunakan uji normalitas data, multikolinearitas, dan heterokedastisitas.Serta untuk mengetahui kontribusi faktor Harga dan Brand TrustTerhadap Keputusan Pembelian digunakan rumus Koefisien Determinasi (R2). Hipotesis penelitian diterima apabila t hitung >  t tabel dengan tingkat signifikansi 0,1. Nilai t tabel dalam penelitian ini 1,993. Nilai t hitung variabel X1 sebesar 2,107 t hitung lebih besar dari t tabel maka hipotesis di terima, nilai t hitung variabel X2   sebesar 3,405 t hitung lebih besar dari t tabel maka hipotesis di terima. Kata kunci: Harga, Brand Trust, Keputusan Pembelian AbstractThis study aims to determine the Influence of Price and Brand Trust on Purchasing Decision at Sinergy Celular Medan. The sample in this study is all visitors Sinergy Celular Medan as many as 77 people.Data collection technique used is through questionnaire (questionnaire) that is by distributing questionnaires to the sample (respondent) and collect it back. Data analysis technique used is Multiple Linear Regression. Before the data is diregresikan then first in the test the relationship between variables, the data tested using the test of data normality, multicollinearity, and heterokedastisitas. And to know the contribution of price factors and Brand Trust Against Purchase Decision is used the formula Coefficient of Determination (R2). Research hypothesis accepted if t arithmetic> t table with significance level 0,1. The value of t table in this study is 1,993. Value t arithmetic variable X1 of 2.107 t arithmetic greater than t table then the hypothesis received, the value of t arithmetic variable X2 of 3.405 t arithmetic greater than t table then the hypothesis received. Keywords: Price, Brand Trust, Purchase Decision

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