R Tutorial : Multiple and logistic regression

Key Takeaways

hi my name is Ben Ballmer I'm an assistant professor of statistical and data Sciences at Smith College and I'll be your instructor for this course on multiple and logistic regression in this course we will learn how to extend simple linear regression to an arbitrary number of explanatory variables which can be a mixture of numeric and categorical will also learn about logistic regression which allows us to model a binary response okay let's consider a situation in which simple linear regression might not be sophisticated enough to suit our needs this scatter plot shows the relationship between highway fuel economy and engine size 477 configurations of manual transmission cars popular from 1999 to 2008 it appears as though there is a negative relationship between engine size and fuel economy which should make sense bigger engines tend to go in bigger cars which tend to be heavier and which tend to get worse mileage we could certainly fit a linear regression line through these points but that would only tell us part of the story the truth is that while these cars were popular in each of the 10 years between 1999 and 2008 the observations we have are only from 1999 or 2008 did fuel economy improve over time these side-by-side box plots suggest that it might have but does that represent a feat of Engineering were merely a change in consumer tastes how do we know that the increase in fuel economy was not just due to the cars in 2008 generally having smaller engines which we've already observed to be associated with greater fuel economy what we really want is a model that will assess the effects of engine size in year simultaneously that is we want to understand the effect of time on fuel economy after controlling for engine size here we see a visual depiction of a parallel slopes model these models occur when one of the explanatory variables is numeric and the other is categorical in this case the year variable has two levels and the model accordingly consists of two parallel lines multiple regression allows us to build such models by simply adding another variable and another coefficient to our model as you might suspect telling our about the second variable in our regression model is just as easy we simply add another term to the right side of the formula that we pass to the LM function here we have to be a bit careful to make sure that our interprets year as a categorical variable since it is encoded as a number for our purposes the year should be thought of as a label not a quantity now you'll try it out in the exercises