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Linear Regression

Topic Review on "Title":
  • 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


Rapid Study Kit for "Title":
Flash Movie Flash Game Flash Card
Core Concept Tutorial Problem Solving Drill Review Cheat Sheet

"Title" Tutorial Summary :

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.

Tutorial Features:

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.

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

See all 24 lessons in Introductory Statistics, including concept tutorials, problem drills and cheat sheets:
Teach Yourself Introductory Statistics Visually in 24 Hours

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