A large class of students just sat an exam consisting of 20

A large class of students just sat an exam consisting of 20 True-False Questions. The TA recorded the number of correct answers Y and the number of incorrect answers X for each student. Suppose we then regressed Y on X:

a) Write the population regression function

b) What will be the value of the R^2? Explain

c) What will be the value of the standard error of the regression? Explain

Solution

sol)

a) The regression function is

y= -x +20

b) since it is perfectly negative the multiple regression is r=1

Hence Coefficient of determination R² =1

C) Since Coefficient of determination R² =1 we can say that Standard error is 0