Our team has gathered data on students' grades, demographics, and caffeine intake. We looked at 119 colleges in the nation and want to see the impact of coffee intake on grades. Let's call the main consumption variable is coffee. This variable represents the answers to the question asked to the students: In the past month, when you drank coffee, how many coffee cups did you have?"

Suppose that our team wants to measure coffee intake by putting students into the following categories: coffee free, light coffee intake, moderate coffee intaker and heavy coffee intaker. Write a model that allows us to estimate the effects of coffee intake on grades, controlling for other variables in the survey listed below and assuming no interaction between variable. Using this model, explain how to test the null hypothesis that coffee intake has no effect on grades (include the null and alternative hypotheses, and number of restrictions).

Variables in the survey:

Age

Caffeine Consumption Level (none, light, moderate, heavy)

Gender

Class year

Fraternity

Orange Juice

Grades

Work