Assignment 1
There are totally 10 equally weighted questions. Include all necessary R codes and output in
your answers.
Q1.
Consider simple linear regression with one covariate:
𝑌 = 𝛽0 + 𝛽1𝑋 + 𝜀, 𝜀~𝑁(0, 𝜎
2
),
show that 𝛽̂
0, 𝛽̂
1 are unbiased estimators, and calculate their variance.
Q2.
Q
3. Q4.
1
Q
5.
Q
6.
Q
7.
(e) Comment on the results obtained. How accurately can we predict the number of college
applications received? Is there much difference among the test errors resulting from these three
approaches?
Q8.
Q9.
(g) Which of these methods appears to provide the best results on this data?
(h) Experiment with different combinations of predictors, including possible transformations
and interactions, for each of the methods. Report the variables, method, and associated confusion
matrix that appears to provide the best results on the held out data.
Q10.
