1. Variables
   1. Explanatory or Predictor
      1. x-axis
   2. Response
      1. y-axis
2. Predictions
   1. Line of Best Fit
      1. Least Square Regression
         1. Line of which the sum of the least squared residuals is smallest
   2. Predicted Value
      1. y-hat
   3. Regression to the Mean
      1. property of the linear model, the line is the linear model
   4. Residuals
      1. Difference between observed and predicted value
      2. Chart of residuals used to predict linearity
3. Correlation
   1. Explains Strength and Direction
      1. Close to 1 or -1 is strong
      2. Sign determines positive or negative
   2. Measured in r
      1. r= sum of z scores of x times y divided by n minus 1
   3. Warnings
      1. Doesn't prove linearity
      2. Only quantitative Variables
      3. Outliers can distort
      4. Not Prove Causation
         1. Preschoolers have correlation between shoe size and reading level
   4. r squared
      1. measures how successful the regression line is in linearity relating x to y
4. Models
   1. Scatter Plots
      1. A graph to display relationships between 2 quantitative variables measured on same cases
   2. Linear Model
      1. y-hat=Bsub0 + Bsub1 times x
         1. Y-hat is prediction
         2. Bsub0 is y-intercept
         3. Bsub1 is slope
            1. y-units per x-units
      2. Don't assume linearity, test it out
5. Assessment
   1. Direction
      1. Positive
         1. Slope is positive
         2. bottom-left to upper-right
      2. Negative
         1. Slope is negative
         2. upper-left to bottom-right
   2. Form
      1. Decision if Linear
         1. if it follows a line
   3. Scatter
      1. Is there a pattern?
      2. Look for outliers
         1. y-outlier
         2. x-outlier
         3. model outlier
         4. Influential Observations
            1. Change slope of regression line
            2. If x-value is extraordinary than can use leverage to change slope
6. Influence
   1. Use Residuals to check for linearity
   2. Subsets
      1. Look for two separate sets of data
         1. i.e. boys and girls, age, demographics
   3. Bends
      1. If it bends, it is not linear
   4. Extrapolation
      1. Venturing into x territory not covered by data
   5. Outliers
   6. Lurking Variables
      1. Variables may be linked by these