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<br />. <br /> <br />CONTENTS <br /> <br />Preface____________________________________ <br />Abstractn _ _ _ _ _ _ _ _ __ _ _ _ - -- _ - - - - - - - -- - - - - - -- <br />1ntroduction_ _ __ _ ____ __ ---- ----- ------ ----- <br />Distributionsn_ _ _ _ n _ _ _ _ _ _ _ _ n _ _ _ _ _ _ _ _ __ - -- <br />Cumulative distributiollS_ - - -- - - --- - ----- <br />Statistical inference___ __ ____ - --- - ------ -- --- <br />Correlation and regression_ _ _ _ _ _ _ _ _ _ _ - - _ _ - - -- <br />Serial correlation_ _ _ _ ___n___n_n_n_n <br />Regression methods__ _ _ _ --- - --- - ------ - -- - -- <br />Regression models_ _ _ __ ____ _ ---- - - - ----- <br />Tra,nsformationB_ __ ___ _ __ _ _ _____ - - --- --- <br />Simple linear regression______n__nnnn <br />Multiple linear regression_ _ _ _ - - - - - - - - - - -- <br />Regression computation using 'Ie" multi- <br />pliers___ ____________________________ <br />Regressions h~ving various numbers of inde- <br />pendent variables___ ____ ----- - - ---- --- <br />Use of digital computers___u nnnn_n_ <br />Application of the regression method_nu_ <br /> <br />. <br /> <br />Page <br />III <br />1 <br />1 <br />1 <br />3 <br />4 <br />6 <br />9 <br />9 <br />9 <br />10 <br />11 <br />12 <br /> <br />Regression methods-Continued <br />Graphical regression____ ______ ---- <br />Graphical multiple regression_____________ <br />Graphical multiple regression when the <br />independent variables are highly corre- <br />lated between themselves _ _ _ _ _ _ - - - - - - -- <br />Choice of graphical or analytical method for <br />multiple regression_ _____ _____ - ---- - --- <br />Determining equations of graphical relations__ <br />General methods_n__ _unn_n__n_____ <br />Definition of equations_ ___________n____ <br />Other toolsnn___ _ u __ _ _ __ _ _ n ___ _ n _ _ _ n__ <br />Analysis of variance___n__nn_n_nn__ <br />Anal;ysis of covariance__ _ __ ___ -- -- - - --- -- <br />Multivariate analysisn___ --- -- -- - --- - --- <br />Characteristics of hydrologic data_n____nn__ <br />Effects of data characteristics on analysis_ <br />Outliers_ _ _ _ ___ _ ____ _ _ ___ ___ __ _ -___ - --- <br />Selected references_ _ _ __ - _ _ ---- - - --- - -- -- - --- <br /> <br />15 <br /> <br />18 <br />18 <br />18 <br /> <br />FIGURES <br /> <br />Histogram, or frequency distribution, of 1,000 tree-ring indicesn_ _ _ -- -- <br />Probability density curve of 1,000 tree-ring indices__nnnnnn_n_nn_ <br />.Probability density curve and its cumulative formnnn__n_nn_nn____ <br />Diagrams showing- <br />4. Normal distributionn__n_________n____ _____n____ _______n___ <br />5. Distribution of means of samples from a normal distribution________ <br />6. Distribution of variances of samplesnn __ _ _ n _ _ __ _ n _ _ _ n _ n n n_ <br />7. Hypothetical sampling distribution of means__n__n_____nn__n <br />8. Normal distribution of plotted points about the regression line - .' - - -- <br />Graph showing plot used in demonstrating the effect of sample rangG on <br />computed correlation coefficient_ _ __ ____ _ n _ _ n _ _ _ _ _ __ _ __ _ _ _ _ n _ _ _ n_ <br />Equations and graphs of some common regression models_________________ <br />Data plotted on natural and log scales showing the achievement of equal <br />variance about the regression line by use of the log transformation_______ <br />Plot of data from table 2 showing computed regression line_ - - - - - - - - - - - - - -- <br />Equations and graphs of three models based on the plotted data__ __ _ n _ _ n <br />Graphs showing four possible outcomes of plotting Y against X - - - - - - - - - - -- <br />Plot showing the two regression lines and the structural line_ - - - - - - - - - - - - -- <br />Graph showing method of estimating the standard error of a graphical re- <br />gression______________________~_______________________------------- <br />Example of graphical multiple regression___n_____________n____n_ _n__ <br />Example of graphical multiple regression using arithmetic scales______ _ _ n -- <br />Graphical regression using highly correlated independent variablesn___u___ <br />Graphical regression in which one variable is used twice_ _ _ - - - - - - - - - - - - - -- <br />Graph showing multiple linear regression by the method of residuals___ <br />Graph showing coaxial graphical multiple regressionuunu________n_u_ <br /> <br /> 9. <br /> 10. <br /> 11. <br /> 12. <br /> 13. <br /> 14. <br /> 15. <br /> 16. <br /> 17. <br /> 18. <br /> 19. <br /> 20. <br /> 21. <br />. 22. <br /> <br />1. <br />2. <br />3. <br />4-8. <br /> <br />Page <br />2 <br />2 <br />3 <br />4 <br />4 <br />5 <br />6 <br />7 <br />8 <br />10 <br />11 <br />12 <br />20 <br />21 <br />21 <br />22 <br />23 <br />25 <br />25 <br />28 <br />30 <br />31 <br />v <br /> <br />Page <br /> <br />21 <br />22 <br /> <br />24 <br /> <br />26 <br />27 <br />28 <br />29 <br />31 <br />31 <br />33 <br />35 <br />36 <br />36 <br />:37 <br />38 <br />