stats 212

• Linear Regression formula 


  y=B0 + B1x
• y=(B0) + B1x


  intercept
• y=B0+(B1)x


  slope
• y=B0+B1(X)


  Explanatory variable
• $R^2$


  1-$SSres/SStot$
• conditions for the least squares line

  1. Linearity
  2. Nearly Normal residuals
• conditions for the least squares line

  1. Linearity
  2. Nearly Normal residuals
  3. Constant Variability
• nearly normal residuals

  the residuals should be nearly normal

  this condition may not be satisfied when there are unusual observations that don't follow the trend of the rest of the data

  check using histogram
• constant variability

  the variability of points around the least squares line should be roughly constant --> this implies that the variability of residuals around the 0 line should be roughly constant as well (also called homoscedasticity)

  check using residuals plot
• linearity


  the relationship between the explanatory and the response variable should be linear

  check using a scatterplot of the data, residuals plot