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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

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 "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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