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I am. Mike marin and in this video. Well introduce the idea of a a dummy variable or indicator variable and their use in regression models.
We can include or qualitative variables. Also known as factors in a regression model using dummy or indicator variables. Well be working with the lung capacity data that was introduced earlier in these series of videos.
I have already gone ahead and imported the data into r and attached it you can also notice here that i have created a categorical representation of the height variable individuals are placed into height categories where category a is less than 50 inches category b. 50 to 55 category c. 55 to 60 and so on all the way up to the category f.
70. Or greater. A categorical variable.
That has k levels or categories. Requires k. 1.
Dummy. Or indicator variables to represent it. For example.
The variable smoke has two levels. No and yes these two levels will require 1 indicator variable in order to represent smoking status we can create a dummy or indicator variable well call it xsmoke and well set this equal to 1. If the individual smokes or smoking is yes and zero otherwise then for a non smoker.
The xsmoke indicator will equal 0. Its worth noting that conversely. We could instead create an indicator for non smoking.
Instead of an indicator for smoking. Now. Lets go over the same idea.
But this time using the categorical height variable. Youll notice that categorical height has 6 levels therefore. Well need.
5. Dummies or indicators to represent this we can create an indicator or dummy. Well call it xb and well set this equal to 1 if the individual is in height category b.
And 0 otherwise we can create another dummy or indicator well call this xc and well set this equal to 1 if the individual is in height category c. And 0 otherwise we could also create indicators xd xe and xf indicating categories. D.
E or f. You can notice. That height category.
A. Is serving as a reference or baseline. Group.
An individual in height category a will have xb equal to 0 xc equal to 0 xd xe xf all equal to 0 an individual in height category b. Will have xb equal to 1 and xc xd xe and xf all equal to 0. An individual in height category c.
Will have xc equal to 1 and all other x indicators equal to 0. Same. For category.
D category. E. And category f.
These. 5. Dummy or indicator variables allow us to identify.
Which of the 6 height categories. An individual falls into in a moment. We will look at the use of these in a regression model.
But first lets take a look at the mean lung capacity for each of the groups formed by categorical height. Ive already written some code to do this so ill go ahead and submit that up here. Well go ahead and calculate the mean lung capacity for each of the height categories here.
We are asking r to calculate the mean lung capacity only for those in height category a and then the mean lung capacity only for those in height category b. And so on now lets keep an eye on those means so that we can compare these with the regression model that were gonna fit lets go ahead and fit a linear regression model. We will relate lung capacity to this variable categorical height.
We can ask for summary of this model and here we can see the r output as well as the fitted. Model the intercept or constant term bnot b0 of 215. Is the estimated mean y value for all xs equal.
0. That is our reference or baseline group in this particular model. It is the mean lung capacity for someone in height category a the coefficient for category b of 151.
Is the change in mean lung capacity. We would expect for someone in category b relative to category. A for someone in category b we would have their.
Estimated mean lung capacity equal to. 215 plus 151. Times 1.
Here we have the xb. Indicator equal to. 1 because the individual is in category.
B. Plus. 325 times.
0. The xc indicator is equal to 0. As this individual is not in category c.
And so on all other x indicators equal to 0 the mean lung capacity for. Someone. In category b.
Is 215 plus. 151 which is equal to 366. This is the mean lung capacity for someone in category b.
The slight difference you see is due to rounding error the coefficient for category. C of 325. Is the change in mean lung capacity.
We would expect for someone in category c. Relative to someone in category. A for someone in category.
C. The xc indicator will equal 1. All other indicators will equal 0 in.
This case their estimated mean lung capacity will. Be 215 plus. 325 which equals to 54.
You can repeat this process to calculate the mean lung capacity for all other height categories. And if you do this youll see the mean. For.
Category d. Is. 717 the mean for.
Category e. Is. 869 and the mean for category.
F is 108. Using dummy or indicator variables is how we can include categorical or qualitative variables into a regression model. When including a categorical variable into a regression model r will create the dummy or indicator variables automatically the category that r chooses as the reference or baseline category will be.
The category. That. Comes first alphabetically.
Or numerically if categories are coded using. 012. And so on in a separate video.
Ill show how you can change. Which category serves as the reference also in a later video. Ill show how to fit.
And interpret. A regression model that uses both categorical and numeric variables. Thanks for watching this video and make sure to check out my other instructional videos.
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