XX.—On the Theory of Statistical Regression

1934 ◽  
Vol 53 ◽  
pp. 260-283 ◽  
Author(s):  
M. S. Bartlett
Keyword(s):  
Correlation Coefficient ◽  
Partial Correlation ◽  
Regression Coefficient ◽  
Multiple Correlation Coefficient ◽  
Statistical Regression ◽  
Multiple Correlation ◽  
Partial Regression ◽  
Partial Regression Coefficient ◽  
Moment Distribution ◽  
A Chain

1. The product moment distribution in the general case of p normal variates, obtained in 1928 (1), and again in 1933 (2), has been awaiting further analysis. Some indication has already been given (Wishart, 1928) that new results might be expected from it; in the particular case of two variates obtained previously by Fisher (3), it has been used to deduce the distributions of the correlation coefficient (3), co-variance (4), and regression coefficient (5). In the general case, it has been used by Wilks (6) to furnish a proof of Fisher's distribution of the multiple correlation coefficient (7), and also in connection with his idea of a generalized variance (8). Further analysis appears to be most fruitful in studying statistical regression in general. It is shown in Part I of this paper that the product moment distribution can be split up into a chain of independent factors. Most of the known distributions related to regression or partial correlation are simply obtained, in a manner which clearly indicates the relations they bear to one another; the distribution of a partial regression coefficient of any order is also readily derived.

IMBALAN DAN GAYA KEPEMIMPINAN PENGARUHNYA TERHADAP KEPUASAN KERJA KARYAWAN DI BALAI BESAR INDUSTRI HASIL PERTANIAN BOGOR

2018 ◽  
Vol 1 (01) ◽  
pp. 17
Author(s):  
Ramlan Ruvendi
Keyword(s):  
Job Satisfaction ◽  
Multiple Regression ◽  
Correlation Coefficient ◽  
Analysis Of Variance ◽  
Partial Correlation ◽  
Multiple Correlation Coefficient ◽  
Multiple Correlation ◽  
Average Value ◽  
Partial Correlation Coefficient

The study was carried out to find out whether there were influence and correlation bet-ween : a) Reward received by the IRDABI’s employees on their job satisfaction. b) style of the leader-ship on the job satisfaction. c) Reward together with style of leadership on the job satisfaction of IR-DABI’s employees.The result of the study showed that there was significant correlation and influence between the reward on the job satisfaction with was shown by the value of partial correlation coefficient of 0.6185 and coefficient of multiple regression for reward variable (β1) of 0.412. The influence of variable for style of leadership on the job satisfaction was also significant with the partial correlation coefficient of 0.5495 and coefficient of multiple regression (β2) of 0.355.In the test of Analysis of Variance (ANOVA) on the equation of multiple regression show that F-value was bigger that F-table (F = 58.97 > F-table = 3.098) or the Probability Value smaller than 0.05. At showed that there was significant correlation and influence between reward variables all together with style of leadership on the job satisfaction of employees. The value of multiple correlation coefficient (R) was 0.751 and R Square (R2) was 0.564. Value of R Square (0.564) meant that 56.5% of variation pro-portion total of job satisfaction can be eliminated of equation of multiple regression was used as the es-timator rather than using average value of job satisfaction as the estimator.

scholarly journals On the partial correlation ratio

1915 ◽  
Vol 91 (632) ◽  
pp. 492-498 ◽  
Keyword(s):  
Linear Regression ◽  
Correlation Coefficient ◽  
Partial Correlation ◽  
Regression Line ◽  
Multiple Correlation Coefficient ◽  
Correlation Ratio ◽  
Multiple Correlation ◽  
Non Linear ◽  
Single Number ◽  
Gaussian Surface

(1) In a paper communicated to the Royal Society in 1903 I gave very briefly in a footnote the properties of the correlation ratio . These properties were discussed more at length in my memoir, “On the General Theory of Skew Correlation and Non-linear Regression,” published in 1905. The two papers dealt only with the total correlation ratio , or the relation between two variates without consideration of any other correlated variates. The introduction of the correlation ratio enabled the measure of the relationship between two variates to be expressed by a single number, measuring its total intensity, in cases where the regression line was of any form. The ratio passed into the usual correlation coefficient when the regression line became straight. This correlation ratio has been generally accepted by statisticians as a useful measure of relationship in cases of skew correlation and non-linear regression. Shortly after the appearance of the above memoirs I generalised this coefficient in a manner comparable with the generalisation of the coefficient of correlation, namely, by the definitions of the multiple correlation ratio and of the partial correlation ratio . These ratios correspond to the multiple correlation coefficient and the partial correlation coefficient in multiple linear regression. Their importance is very considerable, as they enable us to measure the intensity of association between two variates when other correlated variates are considered as constant without any assumption that the regression is linear, still less that the frequencies follow the normal (or Laplace-Gaussian) surface. I had not intended to discuss the results of the present paper before the probable errors had been provided, but the recent revival of interest in skew regression, and its fundamental importance in all higher statistical inquiry, justifies, at least, the publication of those formulæ which are fundamental to the subject. (2) I deal first with the problem of three variates, although the extension to any number is not hard to make.

scholarly journals Pengaruh Laba Bersih dan Debt to Equity Ratio terhadap Dividen pada PT. Adaro Energy Tbk 2010 - 2017

2019 ◽  
Vol 3 (2) ◽  
pp. 80-84
Author(s):  
Septi Utami ◽  
Nor Norisanti ◽  
Faizal Mulya Z
Keyword(s):  
Correlation Coefficient ◽  
Financial Statements ◽  
Multiple Correlation Coefficient ◽  
Debt Ratio ◽  
Net Income ◽  
Multiple Correlation ◽  
Net Profit ◽  
Equity Ratio ◽  
R Value ◽  
Moderate Relationship

The purpose of this study was to study the effect of net income and the Debt Ratio on Equity to Dividends at PT. Adaro Energy Tbk 2010-2017. The technique used in this study was purposive sampling. The population used in this study is the financial statements of PT. Adaro Energy Tbk, which is listed on the IDX. And the sample from financial statements is available for 32 periods (quarterly). The results of the determination coefficient test (R2) of 0.253 can be interpreted that the effect of Net Profit and Debt To Equity Ratio to Dividend is 25.3%. The remaining 74.4% is influenced by other factors not explained in this study. Based on the multiple correlation coefficient test seen from the R value of 0.503, indicating that there is a moderate relationship between Net Profit and Debt To Equity Ratio with Dividends. Based on the F test the probability value sig. 0.015 <0.05 which means that together the value of Net Profit (X1) and Debt To Equity Ratio (X2) have a significant effect on dividends (Y). Based on the t test shows that Net Profit (X1) does not significantly influence dividend (Y), Debt To Equity Ratio (X2) does not significantly influence dividend (Y).

scholarly journals Analisis Kualitas Makanan dan Perceived Value terhadap Kepuasan Konsumen pada Industri Rumah Makan

2019 ◽  
Vol 3 (2) ◽  
pp. 58-64
Author(s):  
Clara Candra Komala ◽  
Nor Norisanti ◽  
Asep M. Ramdan
Keyword(s):  
Customer Satisfaction ◽  
Correlation Coefficient ◽  
Food Quality ◽  
Consumer Satisfaction ◽  
Perceived Value ◽  
Multiple Correlation Coefficient ◽  
Coefficient Of Determination ◽  
Multiple Correlation ◽  
F Test ◽  
Effect Of Food

The purpose of this study was to analysis the effect of food quality and perceived value on consumer satisfaction in the restaurant industry. The sample used in this research was 98 respondents and data collection methods using a questionnaire. The method used in this study is the use the type of probability sampling includes in the simple random sampling. The analysis technique using validity test, reliability test, multiple linear regression analysis, including test coefficient of determination, multiple correlation coefficient, and simultaneous test (F test).The results of the test coefficient of determination seen from value (Adjusted R2) of 0,473 can be interpreted that the effect of Food Quality and Perceived Value on consumer satisfaction is 4,73%. The remaining 52,7% is influenced by other factors not explained in this study. Based on the multiple correlation coefficient test seen from the R value of 0.696, it shows that there is a strong relationship between food quality and perceived value with customer satisfaction. Based on the F test the probability value sig. 0,000 <0,05, which means that together Food Quality (X1) and Perceived Value (X2) significantly influence customer satisfaction (Y).

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