final_review_session

STAT 151A Final Review Session December 6, 2023 3 Categorical regression Let’s imagine that 80 students took a particular course at sophomores, 20 were juniors and 20 were seniors. In R, I have saved the final scores (out of 100) for the 20 freshmen in the vector g1 , for the 20 sophomores in g2 , juniors in g3 and seniors in g4 . Also, for i = 1 , · · · 80, let - y i : Final score of the i th student in the class - x i 1 : Takes the value of 1 if the i th student is a freshman and 0 otherwise - x i 2 : Takes the value of 1 if the i th student is a sophomore and 0 otherwise - x i 3 : Takes the value of 1 if the i th student is a junior and 0 otherwise - x i 4 : Takes the value of 1 if the i th student is a senior and 0 otherwise I fit the linear model: y i = β 0 + β 1 x i 1 + β 2 x i 2 + β 3 x i 3 + β 4 x i 4 + ϵ i to this data via R to obtain the following output: a) Why does the R output above say ”1 not defined because of singularities”? How would you fix the problem? b) Fill in the 3 missing values in the R output with proper reasoning. c) Explain why the standard error estimates for the coefficients of x 1, x 2, x 3 are all the same. 5