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 = +
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:/creativecommon
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:/creativecommon
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:/creativecommon
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:/creativecommon
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:/creativecommon
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
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:/creativecommon
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:/creativecommon
Statistics 600
Applied statistics and data analysis I
Instructor:
GSI:
Oce:
E-mail:
Oce hours:
GSI oce hours:
Course web page:
Kerby Shedden
Tianxi Li
461 West Hall
[email protected]
Tuesday 3-4, Fri
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:/creativecommon
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)
(systol
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
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
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
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
like
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 endpo
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
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
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
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
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 e
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 var
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