The Error Bound on SLLN
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The document discusses analyzing the error bound on the strong law of large numbers for Bernoulli random variables through a computer simulation experiment. The experiment is conducted for different probability (p) parameters between 0 and 1. The results show that the error relates to the number of experiments (n) in the form of E=an^b, where a and b are real number coefficients that vary with different p values. A table shows the calculated a and b coefficients for different p parameters.
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2. It discusses the importance of dimensional homogeneity in equations and lists several common SI base units like meters, kilograms, and seconds.
3. Errors in measurements are classified as either systematic or random. Precision refers to the spread of measurements while accuracy refers to how close measurements are to the true value.
D041114862
The document describes the application of log-linear modeling on medical data from Akanu Ibiam Federal Polytechnic Medical Centre. Log-linear models were used to study the associations between age, sex, and blood group. Interactions between the variables were observed in the fitted models. Specifically, interactions between age and sex, sex and blood group, and age and blood group were significant at the 5% level based on tests of partial association.
MSc Finance_EF_0853352_Kartik Malla
This document describes using traditional models and the error correction model approach to analyze the forward premium puzzle using US dollar/Japanese yen exchange rate data from 1989 to 2008. It first tests the level specification model and returns model but finds issues with non-stationarity and cointegration. It then introduces an extended model with macroeconomic variables but finds insignificant coefficients. Finally, it specifies an error correction model incorporating lagged differences and the residuals from the level specification, finding this model fits the data well without issues of non-stationarity, heteroskedasticity, autocorrelation or structural breaks.
Looking for cooperation on working paper - Expenditure model
Looking for cooperation on working paper - Expenditure modelMiss. Antónia FICOVÁ, Engineer. (Not yet Dr.)
This document presents the results of a model examining the impact of various factors on government expenditure for Eurozone countries from 2002-2013. It finds that approximately 48.89% of changes in government expenditure can be explained by changes in gross debt, inflation rate, investment, and real GDP growth rate. A positive correlation exists between debt and expenditure, while a negative correlation exists between growth rate and expenditure. Tests for heteroskedasticity show that the model exhibits homoskedasticity.1Linear Regression and Time Studies 2Linear Regres
1
Linear Regression and Time Studies 2
Linear Regression and Time Studies
Linear Regression and Time Studies
In this assignment, we are going to perform linear regression on the COVID tracking data for the state of my residence, i.e., Maryland, for the following variables:
1. “%tested”
2. “%positive” and
3. “deaths”.
In linear regression for the data, we will first be choosing an independent variable x and a dependent variable y and try to find a best possible linear relationship between the two. We will be trying to find coefficients a and b such that y = bx+c. Here b is the slope of the line and c is the y intercept.
1. LINEAR REGRESSION FOR THE VARIABLE “% TESTED”
For the variable % tested we choose the independent variable, x to be the “date” and the dependent variable y to be “% tested”. We formulate the null and alternate hypotheses as follows:
Null Hypothesis: “The slopewhich means that y is independent of x.”
Alternate Hypothesis: “The slope ≠ 0 which means that y is dependent on x.”
Output:
First, we note that the equation of the straight line we obtained is y = 0.0038x - 165.24. Hence the value of slope b = 0.0038 and c =- 165.24.
In the following two tables, we summarise the output data we got by performing the linear regression:
Regression Statistics
Multiple R
0.9624
R Square
0.926214
Adjusted R Square
0.926014
Standard Error
0.114243
Observations
372
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Lower 95.0%
Upper 95.0%
Intercept
-165.242
2.431183
-67.9679
4.1E-211
-170.023
-160.462
-170.023
-160.462
% tested
0.003759
5.52E-05
68.15053
1.6E-211
0.003651
0.003868
0.003651
0.003868
We observe the following from the output data:
1. r-squared value: The r-squared value, 0.926214 is very close to 1. This means that there is a strong positive linear relationship between the two variables x and y.
2. p-value: We find that the p-value is 1.6E-211which is way less than 0.05. Hence we reject the null hypothesis and we conclude that the alternate hypothesis is significant in the 0.05 significance level.
Graph of the data and the linear fit:
Using the p-value, we concluded that this model is significant. Now, we use this model predicted outcomes for the next 7 days after the end of the workshop and put it in the following table:
DATE
% tested
08-03-2021
1.144655
09-03-2021
1.148415
10-03-2021
1.152174
11-03-2021
1.155933
12-03-2021
1.159692
13-03-2021
1.163451
14-03-2021
1.16721
2. LINEAR REGRESSION FOR THE VARIABLE “% POSITIVE”
For the variable % positive, we choose the independent variable, x to be the “date” and the dependent variable y to be “% positive”. We formulate the null and alternate hypotheses as follows:
Null Hypothesis: “The slopewhich means that y is independent of x.”
Alternate Hypothesis: “The slope ≠ 0 which means that y is dependent on x.”
Output:
First, we note that the equation of the straight line we obtained is y = -0.0004x + 19.331. Hence the value of slope b = -0.0004 and c = 19.33 ...
Comparing the methods of Estimation of Three-Parameter Weibull distribution
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Ijetcas14 608
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Regression
Regression is a statistical technique used to model relationships between variables. The key steps are to identify variables, select a dependent variable to predict, examine relationships visually, and find a way to predict the dependent variable using other variables. Correlation coefficients measure the strength of relationships between 0-1. Positive relationships have variables moving in the same direction, while negative relationships have them moving in opposite directions. Non-linear regression can model curvilinear relationships using quadratic terms. Logistic regression is used for categorical dependent variables.
Mva 06 principal_component_analysis_2010_11
Principal component analysis (PCA) is a technique used to reduce the dimensionality of large data sets by transforming correlated variables into a smaller number of uncorrelated variables called principal components. PCA identifies patterns in data and expresses the data in such a way as to highlight their similarities and differences. The main goals of PCA are data reduction and interpretation. It works by identifying the directions (principal components) along which the variation in the data is maximized.
KNN and ARL Based Imputation to Estimate Missing Values
Missing data are the absence of data items for a subject; they hide some information that may be important. In practice, missing data have been one major factor affecting data quality. Thus, Missing value imputation is needed. Methods such as hierarchical clustering and K-means clustering are not robust to missing data and may lose effectiveness even with a few missing values. Therefore, to improve the quality of data method for missing value imputation is needed. In this paper KNN and ARL based Imputation are introduced to impute missing values and accuracy of both the algorithms are measured by using normalized root mean sqare error. The result shows that ARL is more accurate and robust method for missing value estimation.
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Recommender System Based On Statistical Implicative Analysis.docDịch vụ viết đề tài trọn gói 0934.573.149
This document is a summary of a doctoral thesis on recommender systems based on statistical implicative analysis. It was completed at the University of Danang in Vietnam. The thesis proposes several new recommender models that apply measures from statistical implicative analysis, including a model based on implication index, a collaborative filtering model based on implication intensity, and a collaborative filtering model based on statistical implicative similarity measures. It also develops an empirical toolkit for these models in the R language. The thesis aims to address the complex information needs of users in today's data-rich environment through these new recommender approaches.Exploring Support Vector Regression - Signals and Systems Project
Our team competed in a Kaggle competition to predict the bike share use as a part of their capital bike share program in Washington DC using a powerful function approximation technique called support vector regression.
SupportVectorRegression
This document summarizes an analysis of using Support Vector Regression (SVR) to predict bike rental data from a bike sharing program in Washington D.C. It begins with an introduction to SVR and the bike rental prediction competition. It then shows that linear regression performs poorly on this non-linear problem. The document explains how SVR maps data into higher dimensions using kernel functions to allow for non-linear fits. It concludes by outlining the derivation of the SVR method using kernel functions to simplify calculations for the regression.
Approximate ANCOVA
Talk given at ISCB 2016 Birmingham
For indications and treatments where their use is possible, n-of-1 trials represent a promising means of investigating potential treatments for rare diseases. Each patient permits repeated comparison of the treatments being investigated and this both increases the number of observations and reduces their variability compared to conventional parallel group trials.
However, depending on whether the framework for analysis used is randomisation-based or model- based produces puzzling difference in inferences. This can easily be shown by starting on the one hand with the randomisation philosophy associated with the Rothamsted school of inference and building up the analysis through the block + treatment structure approach associated with John Nelder’s theory of general balance (as implemented in GenStat®) or starting on the other hand with a plausible variance component approach through a mixed model. However, it can be shown that these differences are related not so much to modelling approach per se but to the questions one attempts to answer: ranging from testing whether there was a difference between treatments in the patients studied, to predicting the true difference for a future patient, via making inferences about the effect in the average patient.
This in turn yields interesting insight into the long-run debate over the use of fixed or random effect meta-analysis.
Some practical issues of analysis will also be covered in R and SAS®, in which languages some functions and macros to facilitate analysis have been written. It is concluded that n-of-1 hold great promise in investigating chronic rare diseases but that careful consideration of matters of purpose, design and analysis is necessary to make best use of them.
Acknowledgement
This work is partly supported by the European Union’s 7th Framework Programme for research, technological development and demonstration under grant agreement no. 602552. “IDEAL”
ML Module 3.pdf
Regression
Use Case
Simple Linear, Multi, Polynomial
Gradient Descent
Evaluation Metric
Regularization
Data Trend Analysis by Assigning Polynomial Function For Given Data Set
This paper aims at explaining the method of creating a polynomial equation out of the given data set which can be used as a representation of the data itself and can be used to run aggregation against itself to find the results. This approach uses least-squares technique to construct a model of data and fit to a polynomial. Differential calculus technique is used on this equation to generate the aggregated results that represents the original data set.
Prediction of house price using multiple regression
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- SAS was used for Variable profiling, data transformations, data preparation, regression modeling, fitting data, model diagnostics, and outlier detection.
Artificial intelligence.pptx
Artificial intelligence is the simulation of human intelligence processes by machines, especially computer systems. Specific applications of AI include expert systems, natural language processing, speech recognition and machine vision.
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The Error Bound on SLLN
- 1. The Error Bound on Strong Law of Large Numbers of Bernoulli Random Variables
- 2. Adviser Prof. Dr. Kritsana Neammanee , Chulalongkorn University Mr. Suwat sriyotee , Mahidol Wittayanusorn School Research Fund NSTDA JSTP YSC
- 3. Introduction From Strong Law of Large Numbers almost surely convergence to E(X i )
- 4. Problem We can estimate by E(X i ) which is equal to p when n converges to infinity. Therefore; the problem is to know the error between those two values when n is known.
- 5. Objective - To implement a computer program to do the random experiment which different p parameters. - To know the error bound on Strong Law of Large Numbers for Bernoulli random variables by analyzing the data from experiment.
- 6. Method Picture showing the program implementation
- 7. Picture showing random experiment with p=1/2 Method
- 8. The data from the experiment is a maximum error of random variable values summation from expectation value Therefore; we should divide the data by n to change them into the error bound on Strong Law of Large Numbers Method
- 9. Analyzing the changed data to obtain the equations and graphs Graph Examples p=0.5 , p=0.25 Method
- 10. Let The trend line of data is tend to be the power graph, E=an b , so we use the properties of logarithm to simply it into linear equation as follows we can draw the graph between log E and log n as a linear graph Analysis
- 11. Graph Examples p=0.5 , p=0.25 Analysis
- 12. Picture showing data analysis Analysis
- 13. The error bound on strong law of large numbers of Bernoulli random variables do relate to the number of times doing the random experiment in form of when a and b are the real numbers as the table. Conclusion
- 14. Conclusion Table showing notaion (b) and coefficient (a) in different p 1.8605 -0.4811 0.6 1.8628 -0.4779 0.4 1.9903 -0.4984 0.3 1.5455 -0.4983 0.2 1.4359 -0.5102 0.1 0.7037 -0.6714 0.000977 0.7509 -0.6466 0.001953 0.7173 -0.6006 0.003906 0.9052 -0.5958 0.007813 1.046 -0.5752 0.015625 1.0159 -0.5232 0.03125 1.828942 -0.568 0.0625 1.5959 -0.5189 0.125 1.7936 -0.4977 0.25 2.3093 -0.5034 0.5 a(coefficient) b(notation) p a(coefficient) b(notation) p 2.2552 -0.5274 0.7 0.869161 -0.5898 0.99 0.994031 -0.5582 0.98 1.240224 -0.5624 0.97 1.223207 -0.5417 0.96 1.477406 -0.5542 0.95 1.631549 -0.5084 0.85 1.915579 -0.5024 0.75 1.812174 -0.4832 0.65 1.988841 -0.4869 0.55 1.997101 -0.4959 0.45 1.899328 -0.4918 0.35 1.712379 -0.5141 0.15 1.583434 -0.5201 0.9 1.882 -0.5057 0.8
- 15. K. Neammanee, “ ทฤษฎีความน่าจะเป็นขึ้นสูงและขอบเขตการประมาณค่า ” , พิทักษ์การพิมพ์ , 2005. R.G. Laha , V.K. Rohatfi, “ Probability Theory ”, Bowling Green State University,1979. Feller,W , “ An Introduction to Probability Theory and Its Application vol 1 ” , Newyork: Wiley,1968. Feller,W , “ An Introduction to Probability Theory and Its Application vol 2 ” , Newyork: Wiley,1971. Abdi, H , “ Encyclopedia for research methods for the social sciences ” , Thousand Oaks(CA),2003 Reference