• Model: an equation used to characterize the relationship between variables and predict future outcomes.
  
• Models: we can specifically model the relationship of variables with a line and its equation.
  
• Models use parameters are numbers, or numbers that are derived from the data.
  
• Recall that the Normal model was specified with mean µ and standard deviation σ.
  
• A linear model is the equation of a straight line through the data. 
  
• Similar to the slope-intercept form of a line, y = mx + b.
  
• Predicted Value: is the estimate made from a model, known as  (y-hat).
  
• Residual: the difference between the observed value and the predicted value of an observation, otherwise known as error.
  
• Residual =
  
• Line of Best Fit: The line for which the sum of the squared residuals is minimized, known as the least squares regression line.
  
• Residual Plot:  plots residuals on the vertical axis and the explanatory variable on the horizontal axis.
  
• Influential Observations: Are those observations that markedly change the position of the regression line.
  
• R2, coefficient of determination:  the proportion of variability of y accounted for by the least squares regression on x.
  
• Extrapolation: the use of a regression line for prediction outside the domain of values of the explanatory variable we used to obtain the line.
  
• Least Squares Regression Equation,
  
• Slope,
  
• Y-intercept,
  
• Least Squares Regression Line: Also called the best line of fit.
  
• This line minimizes residuals between the line and the observed values.
  
• The y-intercept is the value of y when x = 0
  
• The slope says that a change of one standard deviation of x corresponds to a change of r standard deviations in y along the regression line
  
• In other words, the y units per every x unit

This tutorial shows the definitions of linear regression. Basically, a model is an equation used to characterize the relationship between variables and predict future outcomes. A linear model is the equation of a straight line through the data, similar to the slope-intercept form of a line, y = mx + b.

Therefore by completing this tutorial, you will be able to find a linear regression model that best fit the data (minimized the residuals) and thus able to predict future response values or outcomes.

Specific Tutorial Features:

• Residuals can be used to work out and illustrate the linear regression example problems, step by step.
  
• Examples showing how to build a model and find the line of fit are provided.

Series Features:

• Concept map showing inter-connections of new concepts in this tutorial and those previously introduced.
  
• Definition slides introduce terms as they are needed.
  
• Visual representation of concepts
  
• Animated examples—worked out step by step
  
• A concise summary is given at the conclusion of the tutorial.

• Model
  
• Predicted Value
  
• Residual
  
• Residual Plot
  
• Influential Observations
  
• Verify the fit of a regression line
  
• Identify, calculate and interpret r2, the coefficient of determination