What’s the plan? First, we are going to look at the correlation between two variables: studying for calculus and the final percentage grade a student gets in the class. We want to know several things: Is there an association between the two variables? What is its direction? How strong is the relationship (e.g., is studying always, usually, sometimes, or not at all associated with a change in the class grade)? What is the slope of the regression line? How much more does each hour of studying impact the expected grade? Is the association we see statistically significant? (Is there at least a 5% chance the slope is actually zero?) Do we need to control for another variable? Is the relationship between studying and a better grade linear such that any one unit increase in studying has the same impact on the grade? What do we do if our variable is not continuous, but instead is dichotomous? We use logistic regression

Intercept = Value Y when X = 0: 55

What happens when we “control” for the effect of already having taken calc in high school?

What if we want to know the how more hours of study impacts the “odds” or “probability” of getting a C grade or better?

HOW DOES LOGISTIC REGRESSION WORK? Because of the nature of logistic curve, interpreting logistic regression is modestly more complex than interpreting a slope statistic. One option is to report how a one-unit increase in a dependent variable increases or decreases the odds of an outcome. Here, we would find that as students increase the number of hours studied each week, they increase their odds of getting a C in the class. A second option is to report the specific probability that the outcome will occur if the independent variables are set at certain values. Thus, if we control for the effect of whether a student has previously taken calculus in high school, we can compare the probability that a student will pass calculus with different time commitments. This is complex so let’s look at some actual data…