# Statistics Symbols

The entries in the "Palm" column are taken from William J. Palm III's Introduction to Matlab 7 for Engineers, 2/e[1] book, while those in the "Chapra" column are taken from Steven C. Chapra's Applied Numerical Methods with MATLAB for Engineers and Scientists, 2/e[2] book. Entries in the "EGR 103" column, when not taken from Chapra or Palm, have been developed over the course of several years' of EGR 103 lectures. $\begin{array}{|c|c|c|c|}\hline \mbox{Quantity} & \mbox{Palm} & \mbox{Chapra} & \mbox{EGR 103}\\ \hline \mbox{Independent Data} & x & x & x \\ \hline \mbox{Dependent Data} & y & y & y \\ \hline \mbox{Individual Elements} & y_i & y_i & y_i \\ \hline \mbox{Mean Value} & \bar{y}=\frac{1}{n}\sum_{i=1}^ny_i & \bar{y}=\frac{\sum y_i}{n} & \bar{y}=\frac{\sum y_i}{n} \\ \hline \mbox{Sum of Squares of Data Residuals} & S=\sum_{i=1}^m\left(y_i-\bar{y}\right)^2 & S_t=\sum\left(y_i-\bar{y}\right)^2 & S_t = \sum\left(y_i-\bar{y}\right)^2 \\ \hline \mbox{(Sample) Standard Deviation} & \sigma=\sqrt{\frac{\sum_{i=1}^n(y_i-\bar{y})^2}{n-1}} & s_y=\sqrt{\frac{S_t}{n-1}} & s_y=\sqrt{\frac{S_t}{n-1}} \\ \hline \mbox{Coefficient of Variation} & \mbox{Not Used} & \mbox{c.v.}=\frac{s_y}{\bar{y}}*100\% & \mbox{c.v.}=\frac{s_y}{\bar{y}}*100\% \\ \hline \mbox{Estimates (Linear)} & f(x_i) & a_0+a_1x_i& \hat{y}_i=P(1)x_i+P(2) \\ \hline \mbox{Estimates (General)} & f(x_i) & \hat{y}_i=\sum_{j=0}^ma_jz_{ji} & \hat{y}_i=\sum_{k=1}^Na_k\phi_k(x_i) \\ \hline \mbox{Sum of Squares of Estimate Residuals (linear fit)} & J=\sum_{i=1}^m\left[f(x_i)-y_i\right]^2 & S_r=\sum\left(y_i-a_0-a_1x_i\right)^2 & S_r=\sum\left(y_i-\hat{y}_i\right)^2 \\ \hline \mbox{Standard Error of the Estimate (linear fit)} & \mbox{Not Used} & s_{y/x} = \sqrt{\frac{S_r}{n-2}}& s_{y/x} = \sqrt{\frac{S_r}{n-2}} \\ \hline \mbox{Sum of Squares of Estimate Residuals (general fit)} & \mbox{Not Used} & S_r=\sum_{i=1}^{n} \left(y_i-\hat{y}\right)^2 & S_r=\sum\left(y_i-\hat{y}_i\right)^2 \\ \hline \mbox{Standard Error of the Estimate (general fit)} & \mbox{Not Used} & s_{y/x} = \sqrt{\frac{S_r}{n-(m+1)}}& s_{y/x} = \sqrt{\frac{S_r}{n-N}} \\ \hline \mbox{Coefficient of Determination} & r^2=1-\frac{J}{S} & r^2=\frac{S_t-S_r}{S_t} & r^2=\frac{S_t-S_r}{S_t} \\ \hline \end{array}$