The Professor's Response
I don't know if I don't understand it or its just that I've been all day doing problems, but I don't know how to do D. Can you help me please?? :)
I plugged an entire class of 200 into SPSS in order to calculate the least squares line for the entire data set. The results were as follows: y^ = 0.512 x + 70.196 .
a) What does x = 0 represent here?
b) What is the expected grade for students who do not earn any clicker points?
c) What is the average grade for a student who has 20 clicker points?
d) I pulled the grade and clicker points for a randomly chosen student from a different class of statistics from the spring term 2010. That student had 35 clicker points and a 94% in the class. Plug 35 points into our model, and determine the prediction error for this case.
See the professor's answer below.
We have to compare, by subtraction, what the actual grade for the student who had 35 points was and what the model predicts for students with x = 35 points.
First plug 35 into the model: 0.512*35 +70.196 = 88.116 This means the model says students on average will have an 88.116% when they earn 35 points. In reality, the student we pulled from the grade book had a 94%, so the prediction error is y - y-hat = 94 -88.116 = 5.884