Multiple Linear Regression with Interaction in R (R Tutorial 5.9) Video Lecture | Mastering R Programming: For Data Science and Analytics - Database Management

hi I'm Mike Marin and in this video
we'll discuss the concept of interaction
or effect modification in linear
regression as well as how to include
this in a linear regression model in R
we will actually discuss the concept of
interaction in a few different videos
using a few different examples putting
it generically if x1 and x2 interact
this means that the effect of x1 on Y
depends on the values of x2 and
vice-versa we will be working with the
lung capacity data I've already imported
this data into R and attached it we will
examine the interaction or effect
modification between smoking and age
first let's make a plot of the lung
capacity versus the age and smoking and
discuss the concept of interaction I've
written a script to produce this plot
you can find a link to download a copy
of this script in the video description
below and you can check out some of our
earlier videos for a more detailed
discussion of the commands that will be
used to produce this plot now let's go
ahead and produce this plot first for
the non-smokers and let's add in the
points for the smokers and let's also
add in a legend to this plot we can
think of the regression model that we
will fit using the explanatory variables
of age and smoke as fitting two
regression lines to this plot one for
smokers and one for non-smokers recall
that in an earlier video we fit a model
to this data that did not include
interaction this model had two parallel
lines one for smokers and one for
non-smokers this model that did not
include interaction assume that the
effect of age was the same for smokers
and non-smokers this also assumed that
the effect of being a smoker was the
same for all ages let's begin a
discussion of interaction or effect
modification such a model would result
in non parallel lines for the sake of
our discussion suppose that the model
looked as presented here this model
suggests that the
effect of age on the mean lung capacity
depends on whether someone smokes or not
as can be seen by lines with differing
slopes this can also be stated as the
effect of age is modified by smoking or
specific to whether or not someone
smokes this model can also be
interpreted as suggesting that the
effect of smoking on the mean lung
capacity is dependent on the age this is
also stated as the smoking effect is
modified by age in this example the
effect of age and the effect of smoking
interact this can also be stated as the
effect of age and the effect of smoking
are dependent on one another they do not
act independently on the mean lung
capacity now let's take a look at how to
fit a model that includes interaction in
our I'll use this script that I've
already prepared we can see that we can
fit this model that includes interaction
or effect modification by using the age
star smoke doing this will include the
main effects of age as well as smoke in
the model and also their interaction age
time smoke we can also produce the same
model using the colon which I prefer to
do myself here we will enter age plus
smoke plus h : smoke which is their
interaction term now let's ask for a
summary of the model we can see that the
fitted regression equation is the mean
lung capacity being equal to one point
zero five two plus zero point five five
eight times age plus zero point two two
six times the indicator for smoking
minus 0.06 times age times the indicator
for smoking recall that the indicator
for smoking equals one if the individual
smokes and zero if they do not we can
then calculate the regression line for
the non-smokers as being one point zero
five two plus zero point five five eight
times age plus zero point two two six
times zero minus 0.06 times age times
zero which results in an equation of 1.0
five two plus zero point five five eight
times eight calculating the regression
line for smokers the smoking indicator
will equal one and the regression line
is then one point zero five two plus
zero point five five eight times age
plus zero point two two six times one
minus zero point zero six times
age times one which results in an
equation of one point two seven eight
plus zero point four nine eight times H
here we can see that the interaction
term of negative zero point zero six
acts as a sort of adjustment to the age
effect or the slope of the line for a
smoker relative to a nonsmoker now let's
add these two lines to the plot using
the script I've prepared to do so we
will use the AV line command first
adding the line for non-smokers and then
adding the line for smokers there are
some questions we want to ask ourselves
about this interaction term and whether
or not we should include it in our model
the first question we want to ask
ourselves is does this interaction make
sense conceptually in other words does
it make sense that the effect of smoking
should depend on the age for example
should the smoking effect on a 19 year
old be different than the smoking effect
on a 15 year old probably not the second
question we want to ask ourselves is the
interaction term statistically
significant essentially this is asking
the question of whether or not we
believe the slopes of the two regression
lines to really be significantly
different let's ask for that model
summary again taking a look at the
p-value here for the interaction term
zero point three seven seven we can see
that it is not statistically significant
in order to include an interaction term
in our model the answer to both of those
questions should be yes that is it
should make sense conceptually and it
should be statistically significant
since our interaction term does not make
sense conceptually and it's not
statistically significant we should not
include it in our model a more
appropriate model to fit would be one
that does not include the interaction
term we can see that model here
for a detailed discussion of this model
you can check out one of our earlier
videos where we fit and discuss this
model that does not include the
interaction later in this series of
videos will introduce the partial left
test which is one more option for
comparing nested models and deciding
which model is more appropriate for
modeling our data we will also explore
the concept of interaction or effect
modification further in following videos
thanks for watching this video and make
sure to check out my other instructional
videos