Chapter 4 Formulas and Vocabulary

• Correlation coefficient, $r$ (p. 192).
  Definition formula:
  

  $r={\displaystyle \frac{\Sigma \left(x-\overline{x}\right)\left(y-\overline{y}\right)}{\left(n-1\right)s_x{s}_y}}$

  
  Computational formula:
  

  $r={\displaystyle \frac{\Sigma xy-\left(\Sigma x\Sigma y\right)/n}{\sqrt{\left[\Sigma x^2-{\left(\Sigma x\right)}^2/n\right]\left[\Sigma y^2-{\left(\Sigma y\right)}^2/n\right]}}}$

• Positive and negative correlation (p. 196).
• Scatterplot (p. 188)

• Extrapolation (p. 215)
• Prediction error, or residual (p. 214).
  

  $\left(y-\hat{y}\right)$

• Regression equation (regression line) (p. 210).
  

  $\hat{y}=b_{1}x+b_0$

• Slope of the regression line (p. 210).
  Definition formula:
  

  $b_1={\displaystyle \frac{\Sigma \left(x-\overline{x}\right)\left(y-\overline{y}\right)}{\Sigma {\left(x-\overline{x}\right)}^2}}$

  
  Computational formula:
  

  $b_1={\displaystyle \frac{\Sigma xy-\left(\Sigma x\Sigma y\right)/n}{\Sigma x^2-{\left(\Sigma x\right)}^2/n}}$

• $y$ Intercept of the regression line (p. 210).
  

  $b_0=\overline{y}-\left(b_1\cdot \overline{x}\right)$

• Coefficient of determination, $r^2$ (p. 230).
  

  $r^2=\text{SSR}/\text{SST}$

• Least-squares criterion (p. 226)
• SSE, sum of squares error (p. 226).
  

  $\text{SSE}=\Sigma {\left(y-\hat{y}\right)}^2$

• Standard error of the estimate, $y$ (p. 228).
  

  $s=\sqrt{{\displaystyle \frac{\text{SSE}}{n-2}}}$

• SSR, sum of squares regression (p. 230).
  Definition formula:
  

  $\text{SSR}=\Sigma {\left(\hat{y}-\overline{y}\right)}^2$

  
  Computational formula:
  

  $\text{SSR}={\displaystyle \frac{{\left[\Sigma xy-\left(\Sigma x\right)\left(\Sigma y\right)/n\right]}^2}{\Sigma x^2-{\left(\Sigma x\right)}^2/n}}$

• SST, total sum of squares (p. 229).
  Definition formula:
  

  $\text{SST}=\Sigma {\left(y-\overline{y}\right)}^2$

  
  Computational formula:
  

  $\text{SST}=\Sigma y^2-{\left(\Sigma y\right)}^2/n$