Statistics 600 Problem Set 1
Due in lab on Tuesday, September 23rd
1. Suppose that X1 , . . . , Xn are uniformly spaced from 0 to 1, and Yi = Xi2 . We use
ordinary least squares to t the model Yi = + Xi . Derive approximate values for
and by approximat
Author(s): Kerby Shedden, Ph.D., 2010
License: Unless otherwise noted, this material is made available under the
terms of the Creative Commons Attribution Share Alike 3.0 License:
http:/creativecommons.org/licenses/by-sa/3.0/
We have reviewed this materia
Author(s): Kerby Shedden, Ph.D., 2010
License: Unless otherwise noted, this material is made available under the
terms of the Creative Commons Attribution Share Alike 3.0 License:
http:/creativecommons.org/licenses/by-sa/3.0/
We have reviewed this materia
Author(s): Kerby Shedden, Ph.D., 2010
License: Unless otherwise noted, this material is made available under the
terms of the Creative Commons Attribution Share Alike 3.0 License:
http:/creativecommons.org/licenses/by-sa/3.0/
We have reviewed this materia
Author(s): Kerby Shedden, Ph.D., 2010
License: Unless otherwise noted, this material is made available under the
terms of the Creative Commons Attribution Share Alike 3.0 License:
http:/creativecommons.org/licenses/by-sa/3.0/
We have reviewed this materia
Author(s): Kerby Shedden, Ph.D., 2010
License: Unless otherwise noted, this material is made available under the
terms of the Creative Commons Attribution Share Alike 3.0 License:
http:/creativecommons.org/licenses/by-sa/3.0/
We have reviewed this materia
Overview of R
Kerby Shedden
October, 2007
R
R is a programming language for statistical computing, data analysis,
and graphics. It is a re-implementation of the S language, which was
developed in the 1980s.
R is a high level language. The core language
Author(s): Kerby Shedden, Ph.D., 2010
License: Unless otherwise noted, this material is made available under the
terms of the Creative Commons Attribution Share Alike 3.0 License:
http:/creativecommons.org/licenses/by-sa/3.0/
We have reviewed this materia
Author(s): Kerby Shedden, Ph.D., 2010
License: Unless otherwise noted, this material is made available under the
terms of the Creative Commons Attribution Share Alike 3.0 License:
http:/creativecommons.org/licenses/by-sa/3.0/
We have reviewed this materia
Author(s): Kerby Shedden, Ph.D., 2010
License: Unless otherwise noted, this material is made available under the
terms of the Creative Commons Attribution Share Alike 3.0 License:
http:/creativecommons.org/licenses/by-sa/3.0/
We have reviewed this materia
1. A certain medical study utilizes standard hospital patient records at time of admittance, as shown below.
Patient ID
Blood Type
(O, A, B, AB)
Rh Factor
(+, )
Body Temp
(F)
Pulse
(beats/min)
(systolic mm/Hg / diastolic mm/Hg)
00001
00002
00003
00004
000
1. (b)
X = # Days is a discrete random variable; the average is given by the formula =
x f ( x) =
2.5 days.
(1)(.30) + (2)(.25) + (3)(.20) + (4)(.15) + (5)(.10) = Exercise: What would the variance 2 be?
2. (c)
$0.70
4/9
x
WIN
LOSE
f ( x)
$0.65
5/9
There
1. (d)
While Income ($) itself is a numerical variable, Income Level (for example, 1 = Low,
2 = Middle, 3 = High) is a classification into ordered categories, not measurements.
2. (c)
The mode is simply
Statistics 600 Midterm Exam
October 25, 2011
1. Suppose we plan to t a linear model in which the design matrix satises
X X/n =
1
0
0
0
0
0
1
r
0
0
0
r
1
0
0
0
0
0
1
r
0
0
0
r
1
.
The usual linear model properties E[Yi |Xi ] = Xi and cov(Y |X) = 2 I ho
From the Central Limit Theorem, we know that if X ~ N(, ), then X ~ N ,
. Therefore,
n
1. (b)
9.1 9.0
0.24
X ~ N 9,
= 3.09, and
, so the X -score = 9.1 transforms to a Z-score =
0.24 55
55
likewise, the symmetric X -score = 8.9 transforms to a Z-sc
Statistics 600 Problem Set 3
Due in class on Monday, October 27th
1. (a) Suppose we are applying the Bonferroni procedure in a setting where the endpoints
of each interval are independent of the endpoints of each other interval. Derive an
expression for t
Statistics 600 Exam 1
October 22, 2014
1. Suppose we have a 4n 4 design matrix X in which the rst n rows of X are (1, 0, 0, 0),
the next n rows of X are (0, 1, 0, 0), the next n rows of X are (0, 0, 1, 0), and the nal
n rows of X are (0, 0, 0, 1). We obse
Statistics 600 Problem Set 2
Due in lab on Tuesday, October 7th
1. Suppose we plan to collect data on two predictor variables X1 and X2 , and a response
variable Y , then t a linear model of the form Y = 0 + 1 X1 + 2 X2 + X1 X2 using
OLS. The sample corre
Statistics 600 Exam 1
October 16, 2013
1. Prove that the horizontal residuals in a simple linear regression sum to zero. The
horizontal residuals are the horizontal dierences obtained by following the line segments
connecting each data point (Xi , Yi ) to
1. (b)
With events A = Al goes and B = Bob goes, we have P ( A B ) = 0.95 , P ( A) = 0.80 , and
P ( B ) = 0.75 from the given. Via the addition rule P ( A B ) = P ( A) + P ( B ) P ( A B ) , we obtain
0.95 = 0.80 + 0.75 P ( A B ) , so that P ( A B ) = 0.60
1. A worker bee inspects a hexagonal honeycomb cell, starting at corner A. When done, she proceeds
to an adjacent corner (always facing inward as shown), either by randomly moving along the lefthand edge with probability 0.35, or independently, along the
1. According to astronomers, many of the stars that are visible with the naked eye are
actually binary systems, i.e., two stars that orbit each other around a common center
of mass. Generally, the variable X = Luminosity relative to the sun of a single st
Statistics 600 Exam 2
December 9, 2008
1. (a) Suppose we have covariates X1 and X2 that are standardized to have sample mean
zero and sample variance 1, and have sample correlation r between them. We observe
data from the linear model Y = X1 + X2 + , wher