Categorical Variables in Linear Regression in R; Example #2 (R Tutorial 5.8) Video Lecture | Mastering R Programming: For Data Science and Analytics - Database Management

hi I'm Mike Marin and in this video
we'll take a look at another example of
including a categorical variable into a
regression model we'll be working with
the lung capacity data that was
introduced earlier in this series of
videos I've already imported the data
into R and attached it I've also already
created a categorical representation of
the height variable to learn how to
create a categorical variable from a
numeric variable you can check out our
video on how to do this we will fit a
model using age and categorical height
as our independent or explanatory
variables you can see here taking a look
at the levels of categorical height they
are a b c d e f 6 categories or level
which are going to require five dummy
variables or indicator variables i've
prepared a script that we're going to
work through in this video so let's go
ahead and use that to fit this
regression model here we're going to
submit the command to fit the model
using age and categorical height to
estimate the mean lung capacity let's
also ask for a summary of this model we
can see that the fitted regression
equation to estimate the mean lung
capacity is 0.98 plus 0.2 times age plus
one point four eight times the indicator
for category B plus two point six nine
for the indicator for height category C
and so on all the way up to six point
five for the indicator for height
category F the height category B
indicator will equal one if the
individuals in height category B and
zero otherwise
same with category C the indicator for
category C will equal one if they're in
height category C zero otherwise to
calculate the regression line for height
category a all of the other height
category indicators will equal zero we
can see that the regression line will
then be 0.98 plus zero point two times H
calculating the regression line for
height category B all of the height
category indicators will equal zero
except for the category B indicator
which will equal one the regression line
will then be
2.46 plus 0.2 times h following a
similar process we can calculate the
regression line for each of the height
categories now let's take a look at
these visually I've prepared a script to
produce a plot of these lung capacities
verse age for each of the height
categories represented using a different
color you can take a look at our video
on modifying plots as well as our video
on adding legends to plots for more on
the commands that are going to be used
to produce this plot first we're going
to go ahead and plot the age verses lung
capacity only for those in height
category a we're going to use color two
and again we're going to set Y limits as
well as label the x and y axes and
include a title now we're going to add
in the points for category B using color
3 and add in the points for height
category C using color for the points
for height category D using color five
the points for hate category e using
color six and finally the points for
height category F using color seven
we're also going to add a legend to this
plot and now let's add in the regression
lines using the AV line command
recall that to use this command a
specifies the intercept for the line B
specifies the slope so let's add in the
line for height category a an intercept
of zero point nine eight slope of point
two again we're going to use color too
now we're going to use a line width of
three to have these lines nice and fat
and easily visible again let's add in
the line for category B the line for
category C the line for category D line
for category E and finally the line for
category F now let's take a closer look
at this plot and discuss the model and
its interpretations we can see that as
the age increases the lung capacity
increases that is the mean lung capacity
increases by zero point two for each
additional year independent of the
height category the age effect is
assumed
to be the same for all height categories
as mentioned in earlier videos this
model assumes no interaction or no
effect modification we will get to
discussing interaction or effect
modification in later videos for now
let's recall the regression equation and
relate this to what we see in this plot
the intercept of 0.98 is the estimated
mean lung capacity for someone in height
category a our reference category of age
zero the age effect of zero point two
tells us that for each additional unit
increase in age we expect an increase of
zero point two in the mean lung capacity
the coefficient for height category B of
one point four eight tells us the change
in the mean lung capacity for someone in
height category B relative to height
category a the reference in other words
the regression line for height category
B should increase by one point four
eight relative to category A the height
category C coefficient of two point six
nine tells us the expected change in
mean lung capacity for someone in height
category C relative to height category a
the reference in other words the
regression line for height category C
should increase by two point six nine
relative to category a this
interpretation is the same for all eight
categories so for height category F the
effect or coefficient of six point five
four tells us the change in mean lung
capacity for someone in height category
F relative to height category a again
the regression line for height category
F will increase six point five for
relative to category A in following
videos we'll discuss including multiple
numeric as well as multiple categorical
variables in the model and interpreting
these as well as fitting and
interpreting models that include
interaction or effect modification
thanks for watching this video and make
sure to check out my other instructional
videos