R Tutorial : Visualizing parallel slopes models

Key Takeaways

in this video you'll learn more about visualizing parallel slopes models in this scatterplot we use color to differentiate the cars from 2008 from those from 1999 do you notice anything about the green points relative to the red points in this manner we have depicted three variables two numeric and one categorical on the same scatterplot thus this plot will enable us to visualize our parallel slopes model in the data space we're going to make use of a little high school algebra to inform our understanding of the geometry of our model first since our categorical explanatory variable year only has two levels we're going to define a binary variable called newer that takes on the value 1 for cars from 2008 and is zero otherwise then we can express our model mathematically using this equation we compute the fitted coefficients using LM so what happens when the cars are newer plugging in and simplifying reveals the equation for a line note that since displacement is our numeric explanatory variable the slope of this line is negative three point six one one miles per gallon per liter and the intercept is 36 point six seven eight miles per gallon the sum of the other two coefficients what about the older cars from 1999 in their case the value of newer is zero and plugging that into our equation also results in the equation for our line this line also has a slope of negative three point six one one miles per gallon per liter but now the intercept is just thirty five point two seven six miles per gallon thus our model consists of two parallel lines one for newer cars from 2008 and one for older cars from 1999 the two lines are parallel because they have the same slope but they're not the same line because they have different intercepts this is why models with one numeric explanatory variable and one categorical explanatory variable are called parallel slopes models notice how the geometry was informed by the mathematics in order to visualize our model we need to extract the necessary information about our model that was created la conceptually the 330 coefficients will give us that information however it's easier in ggplot to simply plot the fitted values and connect them with a line this process is streamlined by the augment function from the Broom package applying augment to our model will return a data frame with the fitted values attached like the one you see here note that the name for the variable that contains the fitted values is dot fitted and the name of the categorical variable is factor dot year dot finally we can use the Geo mind function to put the two lines on the scatter plot that we created previously we need to tell genome line to plot the fitted values rather than the observed values and those values only exist in the Augmented model object that we created previously now it's your turn to build some visualizations