## STOR 455 Homework 6: Due Wednesday, March 17

Note: Questions 1 and 2 are to be done directly from the formulas in the text, not using the $l m$ function. For Question 3, you may use $R$ functions in any form that you like, and I do recommend using $\mathrm{lm}$ and other functions that go with it as discussed in class.

1. This is Question 3.7.1 of the course text (do all parts – data on sakai)
2. This is Question 3.8.1 of the course text (do all parts – same data as 3.7.1)
3. Return to the Exam2004.txt dataset that you saw in the midterm exam.
(a) Using $l \mathrm{~m}$, fit the linear regression directly in the form $\mu_{Y}(x)=\beta_{0}+\beta_{1} x$.
(b) Draw a scatterplot of the data (midterm scores on the $x$ axis, final scores in the $y$ axis) and draw the fitted straight line on the plot. Then show, on the same plot, the simultaneous $95 \%$ confidence bounds computed from the Working-Hotelling procedure.
(c) Compute a 95\% prediction interval for the final exam score of a student who scored (i) 40 , (ii) 60, (iii) 80 points on the midterm exam. For the student who scored 60, what is the probability that she or he scores more than 80 on the final? (Note that in this question, unlike what you were asked to do on the midterm exam, you are supposed to take into account the uncertainty in estimating $\widehat{\beta}{0}, \widehat{\beta}{1}$ and $\hat{\sigma}$. The final answer involves a $t$ distribution.)

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# 概率论代考

## Materials and Websites for the Class:

Textbook: Graybill and Iyer, REGRESSION ANALYSIS: Concepts and Applications. Available for
free at http://www.stat.colostate.edu/%7Ehari/regression_book/index.html
There is be a tab for the textbook on Sakai, and other materials will also be provided during the course.
Gradescope: All homework will be handed in on Gradescope, which you can access through the
Piazza: Piazza is a forum where students can ask questions of me and each other and get responses in a
timely fashion. I have not previously used it myself, but several colleagues (including Dr. Cunningham,
who is teaching the parallel STOR 455.2) have used it and highly recommend it. However, Piazza is
moving to a for-payment model with a more limited free option. I need to find out what other people are
doing before making a firm decision myself. I will get back to you once I have a recommendation how to
proceed.
Programming Requirement: Throughout the course, we will be taking advantage of the R
programming language. Before the course, you should download R, R-studio and R-markdown, all of
which are free. If needed, I will provide further references for use of R.
Prerequisites: STOR 155 or equivalent. Some familiarity with matrix algebra is recommended, but
not required.
Final Grade: 30% HW, including Case Studies and Projects; 25% midterm 1, 25% midterm 2; 20%
final exam at noon on Saturday, May 8.
Pass-Fail Option: Similar to Fall 2020. Students have the option of switching to P/F grading if you
file the registrar’s office form by Wednesday, May 5.
HW Assignments:
Homework due dates will be made clear throughout the course. In general, there will always be some
problems to be working on although the due dates will vary. Please watch for class announcements for
more details of the homework schedule. Every assignment will be posted on Gradescope at least one
week before the assignment is due.
• On homework, it is ok to work with others, but the work you turn in should be yours alone. Do
not copy-paste code from other students, this is easily detected and defeats the purpose of the homework.

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