Understanding Categorical Variables in Multiple Regression Analysis
Learn how to interpret and calculate residuals for categorical variables using indicator variables in multiple regression analysis.
Understanding Categorical Variables in Multiple Regression Analysis
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Multiple Regression Using Indicator Variables
Try this … 1. What is the formula for residual? 2. A variable can be either _________ or __________. 3. What is being interpreting with each phrase?
Categorical Variables • So far, we have been working with numerical data. • If a variable in a regression is categorical, it is called an _________ / ________ variable. • The dummy variable can be on (__) or off (__).
Ex: Winter Olympics (Vancouver) Using y = number of medals won in 2010 x1 = number of medals won in 2006 x2 = whether or not a country was at home ŷ = 0.1283 + 0.9569x1 + 7.9270x2 s = 1.53 1. Does this regression model suggest that there was a home field advantage?
Ex: Winter Olympics (Vancouver) Using y = number of medals won in 2010 x1 = number of medals won in 2006 x2 = whether or not a country was at home ŷ = 0.1283 + 0.9569x1 + 7.9270x2 s = 1.53 2. Calculate and interpret the residual for Iceland who did not win a single medal.
Ex: Winter Olympics (Vancouver) Using y = number of medals won in 2010 x1 = number of medals won in 2006 x2 = whether or not a country was at home ŷ = 0.1283 + 0.9569x1 + 7.9270x2 s = 1.53 Calculate and interpret the residual for the U.S. which won 25 medals in 2006 and 37 medals in 2010. 3.
Sum it Up • An indicator variableis a _________ explanatory variable with two possible outcomes. These outcomes are coded numerically so they can be included in regression calculations. Typically, a success is reported as a ‘__’ and a failure is recorded as a ‘__’.