• Table of Contents
  • Foreword
  • Chapter 1. Introduction to Structural Equation Modeling
  • Chapter 2. Center and Spread
  • Chapter 3. Type of Data, Distributions, Graphs
  • Chapter 4. Covariance and Correlation
  • Chapter 5. Directionality and Causality
  • Chapter 6. Standard Errors and p-values
  • Chapter 7. Linear Regression
  • Appendix A. Introduction to SPSS
  • Appendix B. Introduction to AMOS
  • Appendix C. Common Formulas
  • Translations
  • Appendix C

    Common Formulas

    R-Squared

    $$ R^{2}=\frac{N\sum xy-\sum x \sum y}{\sqrt{\left[N\sum x^{2}-\left(\sum x\right)^{2}\right]\left[N\sum y^{2}-\left(\sum y\right)^{2}\right]}} $$

    F Test

    $$ F=\frac{Variance\ of\ set\ 1}{Variance \ of \ set \ 2} = \frac{\sigma _{1}^{2}}{\sigma _{2}^{2}} $$

    See Variance.

    Chi-Square

    $$ \chi ^2 = \sum{\frac{(O-E)^2}{E}} $$

    Population Mean

    $$ \mu = \frac{\sum{X_i}}{N} $$

    Mean

    $$ \overline{x} = \frac{\sum{x}}{n} $$

    Variance

    $$ \sigma ^2 = \frac{\sum{(x-\overline{x})^2}}{n} $$

    Standard Deviation

    $$ S=\sigma=\sqrt{\frac{\sum{(x-\overline{x})^2}}{n}} $$

    Linear Regression

    $$ y=a+bx $$

    Where a (or the intercept) is:

    $$ a =\frac{\sum y \sum x^{2} – \sum x \sum xy} {(\sum x^{2}) – (\sum x)^{2}} $$

    And b (or the slope) is:

    $$ b=\frac{n\sum xy-\left(\sum x\right)\left(\sum y\right)}{n\sum x^{2}-\left(\sum x\right)^{2}} $$

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