Dedication To my father and mother who always picked me up on time and encouraged me to go on every adventure especially this one To my brothers and sister
Pola
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Acknowledgements First I would like to thank the Almighty God for helping me to accomplish my work, and I am grateful to my supervisor, Dr. Akhterkhan Sabir Hamad, whose expertise generous guidance and support made it possible for me to work on a topic.
I would like to thank the dean of the college of administration and economics Asst. Professor Dr. Kawa Mohammad Jamal Rashid and best thanks go to the head of Department of Statistics, Asst. Professor Dr. Mhammad Mahmod Faqe.
I extend my gratitude to the Asst. Professor Dr. Nawzad Mohammad, Professor Dr. Monem Aziz, Asst. Professor Dr. Shawnim Abdulkader, and Asst. Professor Dr. Mhammad Mahmod Faqe for the many courses that they have taught me during my years of study as an undergraduate and graduate student. My sincere thanks go to librarians in Administration and Economics College.
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Abstract The purpose of this study is to represent one of the most important problems that affect the accuracy of standard error of the parameters estimates of the linear regression models. This problem named heteroscedasticity.
According to the ordinary least square, estimation of the parameter of the linear model does not possess the best linear unbiased estimator. To treat this problem, weighted least square and transformation methods were used, on the other hand wavelet shrinkage was proposed also to treat this problem.
In wavelet shrinkage, the sure thresholding method has been used to obtain the level of thresholding parameter, so as applying soft thresholding rules to treat the wavelet coefficient, as well as two wavelet filters Daubechies and Biorthogonal was used to filter the data.
The application part included the data set which consisted of (132) families from Sulaimani city in Iraqi, Kurdistan Region, then the results obtained between different methods were compared by using {MSE, ๐น, R2} criteria. The wavelet shrinkage method especially (bior6.8) has been possessed the lowest (MSE) and largest (R2), with more significant (๐น) and lowest standard error of parameters compared to other.
Finally the most appropriate model was obtained to predict as follow: ๐ฆ๐ = 0.156 + 0.001๐ฅ2 + 0.001๐ฅ3 + 0.0000899๐ฅ5
Data Used in Multiple Regression Analysis Test of Normality Test of Multicollinearity Test the Auto Correlation of Residual Regression Parameter and Standard Error for the Model 3-2 Test of Normality Test of Homoscedasticity Test of Multicollinearity Test of Auto Correlation Regression Parameter and Standard Error for the Model 3-3 ANOVA Table for the Model 3-3 Regression Parameter and Standard Error for the Model 3-4 ANOVA Table for the Model 3-4 Regression Parameter and Standard Error for the Model 3-5 ANOVA Table for the Model 3-5 Regression Parameter and Standard Error for the Model 3-6 ANOVA Table for the Model 3-6 Regression Parameter and Standard Error for the Model 3-7 ANOVA Table for the Model 3-7 Regression Parameter and Standard Error for the Model 3-8 ANOVA Table for the Model 3-8 Regression Parameter and Standard Error for the Model 3-9 ANOVA Table for the Model 3-9 Regression Parameter and Standard Error for the Model 3-10 ANOVA Table for the Model 3-10 Regression Parameter and Standard Error for the Model 3-11 ANOVA Table for the Model 3-11 Regression Parameter and Standard Error for the Model 3-12 ANOVA Table for the Model 3-12 Regression Parameter and Standard Error for the Model 3-13 ANOVA Table for the Model 3-13 Comparison between Methods Comparison between the Standard Error of Parameters for all Methods
Heteroscedasticity A Wave and Wavelet Scaling Function and Wavelet Vector Space Discrete Wavelet Transform for Three Levels The Hierarchical Process for DWT Coefficients The Haar Wavelet ๐(๐ฅ) The Haar Scaling Function ๐(๐ฅ) The Daubechies Scaling and Wavelet Functions Wavelet Function and Scaling Function for ๐ถ๐๐๐3 and ๐ถ๐๐๐5 Biorthogonal Wavelet Wavelet Shrinkage Steps Hard and Soft Thresholding Normal Q-Q plot for Standard Residual Scatter Plot for Standardized Residual vs. Prediction Normal Q-Q plot for Standard Residual Scatter Plot for Standardized Residual vs. Prediction db5/ First Iteration db5/ Second Iteration db5/ Third Iteration bior2.4/ First Iteration bior2.4 / Sixth Iteration bior2.6 / First Iteration bior2.6 / Tenth Iteration bior2.8/ First Iteration bior2.8/ Twelfth Iteration bior4.4 / First Iteration bior4.4 / Eighth Iteration bior5.5 / First Iteration bior6.8 / First Iteration bior6.8 / Sixth Iteration
Comparing Some Methods to Treat Heterogeneity of.pdf
I would like to thank the dean of the college of administration and. economics Asst. Professor Dr. Kawa Mohammad Jamal Rashid and. best thanks go to theย ...
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