36-401 HOMEWORK 6 SOLUTIONS
October 28, 2011
1. Textbook problems
6.15(c) Fit the regression model with three predictor variables to the data and state the estimated regression function.
The estimated regression function is
\
Satisfaction
= 158.491 1.142

36-401/607 HOMEWORK 1 SOLUTIONS
September 6, 2016
To receive full credit, you must show all steps in your work.
1. Suppose that X1 , X2 , . . . , Xm and Y1 , Y2 , . . . , Yn are sequences of random variables. Show
that the following identities hold:
(a)
P

36-401A HOMEWORK 1 SOLUTIONS
The below problems are on material from Appendix A and do not require answers in context or descriptions.
To receive full credit, you must show all steps in your work.
1. Show that the following identities hold.
(a)
n
X
i=1
n

36-401 Homework 2
Due: Thursday 9/15/16 at 3pm
(10 min grace period; 15 point penalty after 3:10pm; not accepted after 4:30pm)
When asked to explain, comment, or discuss, use complete sentences and answer thoroughly
for full credit. Use R when appropriate

36-401 HOMEWORK 3
Due: Thursday 9/22/16 at 3pm
When asked to explain, comment, or discuss, use complete sentences and answer thoroughly
in the context of the problem for full credit. Use R when appropriate for the homework
problems, you do not need to han

36-401/607 Section B (Schafer), Fall 2016, HOMEWORK 3
Due Thursday, September 22 at noon
This homework is, in part, an effort to get you prepared for writing full reports on the results of statistical
analyses. Hence, when asked to explain, comment, or di

36-401 Homework #2 Due Thursday Sept 20
1. (10 pts) The data set Prestige.dat (available from the data section of the 401 website;
see also Prestige.cbk) is extracted from the 1971 Census of Canada, and reports various
attributes (average income, educatio

9
10
8
7
20
In particular, the education variable appears to have a positive association with the occ.prestige variable (i.e. when education increases, so does occupational prestige). The scatterplot between the percent female an

36-752 Advanced Probability Overview
Spring 2015
6. Almost Sure Convergence and Strong Law of Large Numbers
Instructor: Jing Lei
Associated reading: Sec 6.1 and 6.2 of Ash and Dolans-Dade; Sec 2.32.5 of Durrett.
e
Overview
Let cfw_Xi : i 1 be i.i.d random

36-752 Advanced Probability Overview
Spring 2015
10. Martingales
Instructor: Jing Lei
Associated reading: Chapter 6 of Ash and Dolans-Dade; Sec 5.2, 5.3, 5.4 of Durrett.
e
Overview
Martingales are elegant and powerful tools to study sequences of dependent

36-401 Homework #3 Due September 27, 2001
1. If A and B are both 8 X 3 matrices, are the following operations possible? If so, what are the
dimensions of the result? Assume that all square matrices are nonsingular.
2. Given the matrix
HHlll
OOOH
OOlO
OHOO

Homework 2 Solutions
401 Fall 2001
Brian Junker and Kimberly Sellers
Thursday, September 20, 2001
1. Learn about variables in the Prestige.dat data set.
In 1971, the Census of Canada collected information regarding the occupational prestige of various
occ

36-401/607 HOMEWORK 3 SOLUTIONS
September 21, 2016
When asked to explain, comment, or discuss, use complete sentences and answer thoroughly in the
context of the problem for full credit. Use R when appropriate for the homework problems, you do not
need to

Midterm 1 Solutions
When asked to explain, comment, or discuss, use complete sentences and answer thoroughly
for full credit. Remember to answer the questions in the framework of the problem (units,
etc); include what your answers mean, not just the numbe

36-401 Homework 3
Benjamin LeRoy
September 22, 2016
1. Old Faithful
a) First do uni-variate exploratory data analysis (numerical, graphical) on the two variables.
Describe their relationship. Also do bi-variate EDA by plotting the variables against each
o

36-401 HOMEWORK 4 SOLUTIONS
September 28, 2011
1. Problem 3.2
[Note: Only the graphs are required for full credit.]
(1) Error variance decreases with X
If the error variance decreases with X, then larger values of X will be easier to estimate and have
sma

Midterm 2 Practice Problem Solutions
When asked to explain, comment, or discuss, use complete sentences and answer thoroughly
for full credit. Remember to answer the questions in the framework of the problem (units,
etc); include what your answers mean, n

36-401 HOMEWORK 5 SOLUTIONS
October 23, 2011
1. Problem 2.31
iid
(a) Consider the regression model yi = 0 + 1 xi + i , i N (0, 2 ), where yi is the crime rate in
the ith city and xi is the diploma possession rate in the ith city.
The ANOVA table for the f

36-401 HOMEWORK 3 SOLUTIONS
September 21, 2011
1. Crime Rate Dataset
This data set is described in Problem 1.28 in the textbook.
(a) Univariate exploratory data analysis.
First, we load the data at look at the first 5 rows:
CrimeData = read.table(file = "

Midterm 1 Solutions
When asked to explain, comment, or discuss, use complete sentences and answer thoroughly
for full credit. Remember to answer the questions in the framework of the problem (units,
etc); include what your answers mean, not just the numbe

36-401 HOMEWORK 2 SOLUTIONS
September 14, 2011
1) Textbook Problems
Problem 1.5 When asked to state the simple linear regression model, a student wrote it as follows:
E[Yi ] = 0 + 1 Xi + i . Do you agree?
Solution No, the proper way to write the model is

36-401 HOMEWORK 1 SOLUTIONS
September 7, 2011
The problems below are on material from Appendix A and do not require answers in context or descriptions.
To receive full credit, you must show all steps in your work.
1. Show that the following identities hol

36-401 - Solutions HW 8
1
Introduction
Health insurance companies must balance their revenues from premiums with their expenses in claims
reimbursement. To do so, these companies attempt to predict accurately the total amount of claims for each
subscriber