Due at the beginning of class on Wednesday February 7, 2018
A nice short homework assignment since you have a midterm this week.
Except for calculating one p-value, there is no R programming needed for this assignment.
IMPORTANT INSTRUCTIONS
All homework pages (except the top sheet) must be stapled (before you come to class).
The rst page (‘top sheet’) should contain ONLY your name, student ID, discussion section,
and homework number. Use the format shown below. Do NOT staple to the rest of your
homework.
The second page (which means a new sheet of paper, so not the back side of the rst page)
should ALSO contain your name, student ID, discussion section, and homework number.
Use the format shown below.
After I collect homeworks I put all of the top sheets into a folder before passing the home-
works to the grader. If at any point during the quarter there is a homework that you know
you turned in, but it does not show on Canvas, contact me. I will look to see if I have your
top sheet from the homework. If I have your top sheet then I will give you credit for the
homework.
It is your responsibility to make sure every homework assignment you submit has a top sheet
with your correct discussion section number. If you tell me you turned in a homework, but
there is no Canvas grade and no top sheet in my folder then you will get a 0.
You will not loose any point for not making a top sheet. But if your homework goes missing
you will have no way to prove you turned it in.
On both the rst page (‘top sheet’) and second page write your name and student ID on the
top left, homework number on the top center, and section on the top right. For example,
for homework 3 if your name is John Smith, your student ID is 123456789, and you are in
section A01, then the top of your rst page should look like this
John Smith Homework 3 A01
123456789
Points lost if you
don’t follow the rule
correct format for name, ID, homework and section number 1
Staple all pages EXCEPT the top sheet 1
If your homework is on paper pulled out of a notebook,
cut o all of the fringes (from the torn horizontal threads
that attached the paper to the notebook). 1
Be kind to the grader.
make sure you write your name clearly (so it is easy to read)
write neatly
2
Suppose we have run a regression model with n = 30 (x;y) pairs. The sample variance
of y1;:::;y30 is 946 and the MSE is 822.
1. Find the SSR (sum of squares regression).
2. Calculate the ANOVA approach F statistic for the null hypothesis H0 : 1 = 0.
F = MSRMSE
3. What is the numerator degrees of freedom for the F statistic you calculated in the
previous question?
4. What is the denominator degrees of freedom for the F statistic you calculated in the
previous question?
5. What is the distribution of the test statistic F if the null hypothesis is true? Be sure
to give all necessary degrees of freedom.
6. Find the p-value for the hypothesis test of H0 : 1 = 0. (You will need to use R for
this question.)
7. If = 0:05, does the data provide evidence for the alternative hypothesis H1 : 16= 0?
How did you make your decision?
8. Assuming b1 < 0, use your answer from question 2 to nd t = b1=s(b1).
9. Check that your p-value using t as the test statistic is exactly the same as using F
as the test statistic.
No answer is required for this question.