Start with review, some new definitions, and pictures on the white board.
Assumptions in the Normal Linear Regression Model
A1: There is a linear relationship between X and Y.
A2: The error terms (and thus the Ys at each X) have constant variance.
A3: The
Announcements
Dont forget to put your Homework Code on
your homework. Codes linked to course website.
A few of you might receive an email from me
changing your code.
Today:
Additional explanation of normal probability plots
(AKA q-q plots), on white bo
#3 b)
DF=(3-1)*(3-1)=4
pchisq(73.4,4,lower.tail = F)
[1] 4.34244e-15
The p-value is smaller than a, 0.005. We reject the null hypothesis, and conclude happiness and family are not
independent.
c) Assume the data we collect follow normal distribution, cove
Probability and Sampling Distributions
NOTE: All cumulative probabilities are defined as: F(x) = P(X<=x)
Binomial Distribution
Enter the parameters below:
Probability and Cumulative Probability
n
p
x
f(x) = P(X=5)
F(x) = P(X<=5)
20
0.5
5
0.0147857666
0.02
STATS 120B, W. Shen, Winter 2016
Hypothesis testing: what is it about?
Statistical inference: use data (sample) to study/describe the
population characteristics
Estimation: estimate the value of unknown parameters.
Point estimate, interval estimate
Wh
STATS 120B, W. Shen, Winter 2016
Several common mistakes from the midterm
(1) WLLN, CLT, use
p
d
Should be using and
(2) Zero covariance implies independence
Need to say bivariate normal distribution
(3) Likelihood. Write
Should write n
Q
Qn
i=1 f
STATS 120B, W. Shen, Winter 2016
HW4 Problem 3
Suppose that X1 , . . . , Xn form a random sample from a
uniform distribution with the following pdf
f (x|) =
1
I( x 2)
(f) Whats the mode of f (x|)?
Find x that maximizes f .
Any x between and 2 will do.
Chapter 12
Testing
Hypotheses
About
Proportions
Review: Sampling Distribution of a
Sample Proportion, p
Standard deviation =
For large samples,
approximately normal
p(1 p)
n
x-axis = all
possible sample
proportions
Mean = p
p
Sample Proportion ( p )
Revie
Chapter 2
Sections 2.4 2.7
Turning
Data Into
Information:
Summarizing
quantitative
variables
1
h"ps:/www.youtube.com/watch?v=QFrqTFRy-LU
Published on Mar 14, 2016
If the populaBon of the world was only 100 people, what
would society look like?
Prod
Chapter 6
Gathering Useful
Data for
Examining
Relationships
1
Principle Idea:
The way in which a study is
conducted affects our ability
to infer that a cause-and-effect
relationship exists.
2
6.1 Speaking the Language
of Research Studies
Observational Stu
Chapter 1
Statistics Success
Stories and
Cautionary Tales
1
1.1 What is Statistics?
Statistics is a collection of
procedures and principles for
gathering data and analyzing
information in order to help
people make decisions when
faced with uncertainty.
2
Installing
and Using
R-commander
Installing and Using R-commander
R is a sophisticated and free statistical
programming language.
R-Commander is an add-on, also free, that is
menu-driven. It doesnt do everything R does.
You can use R-Commander in the I
Chapter 4
Relationships
Between
Categorical
Variables
1
4.1 Quantitative vs. Categorical
Last chapter we looked at two quantitative
(or numeric) variables. This chapter we
look at two categorical variables.
Categorical data consists of category
names that
Chapter 8
Random
Variables
1
Midterm 1 next Tuesday
Check Course Information ModuleExam
Information for info on midterm topics and
practice free response and MC questions
Discussion Section on Friday will include
help preparing for the midterm.
I need
Chapter 7
Probability
Unregistered
iClicker: 84338631
Midterm 1 next Tuesday
Check Course Information ModuleExam
Information for info on midterm topics and
practice free response and multiple choice
questions
Discussion Section on Friday will include
he
Sample Final Multiple Choice Questions
1. The expected value of a random variable is the
a. value that has the highest probability of occurring.
b. mean value over an infinite number of observations of the variable.
c. largest value that will ever occur.
Sample Midterm 2 Free Response Questions: SOLUTIONS
PDF
1. Suppose that the amounts that students at a college spend on textbooks this semester have a
normal curve with mean = $360 and standard deviation = $120.
a. Draw a picture of this normal distributi
1) A mail-order company claims to ship 95% of its orders on time. 4000 orders were received
last week. You take a sample of 120 of these orders, and find that 108 were shipped on time.
What is the sample proportion of orders shipped on time?
(a) 3800
(b)
Sample Final Free Response Questions
1. Suppose that the amounts that students at a college spend on textbooks this quarter have a normal
distribution with mean = $360 and standard deviation = $120.
a. Draw a picture of this normal distribution, including
Alex Peterson
1) (d) 0.90
2) (c) contains the population parameter value in 95% of all possible samples.
3) (a) 10.04 years
4) (c) Use the sample SD and the t distribution.
5) (d) The probability of rejecting the null hypothesis when it is true.
6) (d) be
Sample Final Multiple Choice Questions: SOLUTIONS
1. The expected value of a random variable is the
a. value that has the highest probability of occurring.
b. mean value over an infinite number of observations of the variable.
c. largest value that will e
Note to me: Clicker notes
Chapter 2
Sections 2.4 2.7
Remind students to register iClickers through
Canvas
Turning
Data Into
Information:
Summarizing
quantitative
variables
2
2.4 Pictures for Quantitative Data
Look at shape, outliers, center (locatio
4.1 Quantitative vs. Categorical
Chapter 4
Last chapter we looked at two quantitative
(or numeric) variables. This chapter we
look at two categorical variables.
Relationships
Between
Categorical
Variables
1
Categorical data consists of category
names that
1.1 What is Statistics?
Chapter 1
Statistics Success
Stories and
Cautionary Tales
Statistics is a collection of
procedures and principles for
gathering data and analyzing
information in order to help
people make decisions when
faced with uncertainty.
1
Ca
Installing and Using R-commander
Installing
and Using
R-commander
Installing R and R-commander
(Rcmdr)
(You need to be connected to the Internet):
R and R-Commander are two separate packages.
You will need to install R first.
INSTALLING R:
Go to http:/
Midterm 1 next Tuesday
Check Course Information ModuleExam
Information for info on midterm topics and
practice free response and multiple choice
questions
Chapter 7
Probability
Discussion Section on Wednesday will
include help preparing for the midterm.