Statistics 110, Professor Utts, HW 7, page 1, Due: Nov 19th
Homework 7 Solutions
Assigned Wed, Nov 13: 4.4 and in Part c give Cp for the model you choose
4.4 Use the other variables in the Fertility dataset (but not LowAFC) to consider models for
predicti
Homework #2: Introduction to Probability
Statistics
Instructor: Jonathan Cook
Due on September 15, 2016
Problem 1. There are 13 people in our class. What is the probability that some
people in our class have the same brithday? (Assume that there are 365 d
Statistics 110, Professor Utts, HW 5, page 1, Due: Nov 5th
Homework 5 Solutions
3.19, 3.32, and comment on a plot of residuals vs predicted values for the final model you choose.
(Midterm on Wed, Oct 30 no assignment)
Assigned Mon, Oct 28
3.19 a. Fit a re
Statistics 110, Professor Utts, HW 3, page 1, Due: October 22nd
Homework 3 Solutions
Monday, Oct 14: 2.11a, 2.14a
Wed, Oct 16: 2.4, 2.8, 2.12, 2.41
Assigned Mon, Oct 14
2.11a. Step 1: Hypotheses are H0: 1 = 0 versus Ha: 1 0 (Note that we are not told what
Chapter 1
Probabilities and random variables
Probability theory is a systematic method for describing randomness
and uncertainty. It prescribes a set of mathematical rules for manipulating and calculating probabilities and expectations. It has been applie
Statistics 110, Practice Final Exam KEY
1. The scatterplot below shows the regression fit to predict Y = the typical time of a hike in
the Adirondack Mountains (in New York) using X = length of the hike (in miles).
a. Add three new data points to this plo
Statistics 110
PRACTICE MIDTERM EXAM
Open notes. Calculator required.
1.
The R output below shows a regression analysis of data from 84 medium-sized counties
in the US. For each county, X = percentage of adults in the county having at least a high-school
Chapter 10
Poisson processes
The Binomial distribution and the geometric distribution describe the behavior
of two random variables derived from the random mechanism that I have called
coin tossing. The name coin tossing describes the whole mechanism; the
Statistics 110
PRACTICE MIDTERM EXAM KEY
Note that pages have been condensed on this key to fit on 3 pages, to save paper if you print it.
1.
The R output below shows a regression analysis of data from 84 medium-sized counties in the
US. For each county,
Chapter 9
Poisson approximations
The Bin(n, p) can be thought of as the distribution of a sum of independent
indicator random variables X1 + + Xn , with cfw_Xi = 1 denoting a head on
the ith toss of a coin. The normal approximation to the Binomial works b
Statistics 610 fall 2013
Solutions to sheet 4
Please attempt at least the starred problems or the starred parts of problems. Of course, if you are hoping for an H (or an A) in the course you
should attempt more than the bare minimum of homework problems.
Stats 110, Section 2:
What can we do when regression assumptions are violated?
Michael Thomas Wojnowicz
October 16, 2013
The main topic for this section was using R to answer the questions: What can we do when assumptions for
regression are violated? For
Chapter 1
Probabilities and random variables
Probability theory is a systematic method for describing randomness
and uncertainty. It prescribes a set of mathematical rules for manipulating and calculating probabilities and expectations. It has been applie
Statistics 610 fall 2013
Solutions to sheet 2
Please attempt at least the starred problems or the starred parts of problems. Of course, if you are hoping for an H (or an A) in the course you
should attempt more than the bare minimum of homework problems.
Statistics 110, Practice Final Exam (Note that more space would be provided to write
answers if this were a real exam.)
1. The scatterplot below shows the regression fit to predict Y = the typical time of a hike in
the Adirondack Mountains (in New York) u
Section 6
Source lists
are taken at randombased on a juror id assigned at random to each name
on the master listin response to requests from the courts for jurors. For the
1997-98 master list, JIS will use names from ve sources: town voter lists;
DMV list
Statistics 110 Homework assignment for Mon, November 24th, due WED, Dec 4th
Use the same data set as for the November 20 assignment, linked to the class webpage, called
Student0405.txt (tab separated) or student0405.txt (comma separated), which contains d
Statistics 110 Midterm Review
The midterm exam will cover Chapters 0, 1, 2, and part of 3, including all material covered up to
Monday, October 28. You are expected to know how to read and interpret R commands and
output from R, but you dont need to know
Multicollinearity Example
n = 25 males; height is in inches, Rtfoot and Leftfoot are foot lengths in centimeters
Correlation matrix:
Height LeftFoot
RtFoot
Height
1.0000000 0.5466786 0.5345347
LeftFoot 0.5466786 1.0000000 0.9078141
RtFoot
0.5345347 0.9078
Example illustrating how order matters for the coefficients and anova table
> Full <- lm(HeadCirc~Height+Male+RtArm, data=Caps)
> summary(Full)
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 43.1582
5.2866
8.164 1.07e-10 *
Height
0.2373
0.
Chapter 2
Multivariate normal distribution
2.1
Basic facts
Let Z1 , Z2 , . . . , Zn be independent N (0, 1) random variables. When treated
as the coordinates of a point in Rn they dene a random vector Z, whose
(joint) density function is
f (z) = (2 )n/2 e
STATISTICS 110, FALL 2013
November 18 Homework
Due Tues, November 26
CLARIFICATION ADDED ON SATURDAY, NOVEMBER 23
The file Nov18Hmwk.txt contains a subset of the data for the student and parents height data set
that we have used in numerous examples. The
Chapter 13
Multivariate normal distributions
The multivariate normal is the most useful, and most studied, of the standard
joint distributions. A huge body of statistical theory depends on the properties of
families of random variables whose joint distrib
Homework #6
Use the PhysicalData.txt file (linked to the website) for this assignment. The data set consists of
physical measurements for n=55 college students. Measurements were made by the students
during a class activity. (Source: William Harkness, Pen
Statistics 110 Homework assignment for Wed, November 20th, due Tues, Nov 26th
Do the following exercises from Chapter 5: #6, 10, 12, 20*
*For 20c, you will need the R command to find the p-value for an F statistic. Here it is:
> pf(F,df1,df2,lower.tail=FA
Statistics 610 fall 2013
Solutions to sheet 3
Please attempt at least the starred problems or the starred parts of problems. Of course, if you are hoping for an H (or an A) in the course you
should attempt more than the bare minimum of homework problems.
Statistics 610 fall 2013
Solutions to sheet 1
Please attempt at least the starred problems or the starred parts of problems.
[1.1]
Suppose P is a probability distribution on the real line. A median for P is
any number m for which P (, m] 1/2 and P [m, ) 1
Review
From our class survey (correlation .4)
What does correlation tell us?
rxy > 0 means that when x is bigger, usually y is bigger too.
rxy < 0 means that when x is bigger, usually y is smaller.
Another way to say this is that rxy is a measure of the l
Todays Class
Introduction
Statistics
Discrete Probability Distributions
(Chapter 5)
Binomial Distribution
Random Walks
Normal approximation
Jonathan Cook
Poisson Distribution
Hypergeometric Distribution
September 15, 2016
Practice Problems
2 / 45
Discrete