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Stat 118 Introductory Business Statistics, Section 01 (7664) Sp
Homework: Chapter 4 Homew
CH 15. Multiple Logistic Regression
Multiple logistic regression
Logistic regression is a method for fitting a regression curve, y = f(x), when y is a categorical
variable. The typical use of this model is predicting y given a set of predictors x. The pre
STAT 520
SUARAY
Mathematical Statistics Ch4,5 Review
PROBLEM: Let X1,.X n ~ Unif (! , 0), ! > 0.
A. Find an unbiased estimator for based on Yn = min(X1,.X n ) . Call this estimator !1 .
B. Find a consistent estimator for based on the weak law of large num
STAT 410/510 HW 3 Due by 10/24 Monday
1. Consider the least squares estimator b ( XX) 1 XY . Using matrix method, show that b
is an unbiased estimator. This is problem 5.29 on page 212.
2. Obtain an expression for the variance-covariance matrix of the fit
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 10
General Linear Model
Special Cases
Interaction Effect
Qualitative Predictor Variables
Example: Predict length of hospital stay (Y) based on age (X1) and gender
(X2) of the patient.
Polynomia
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 1: Overview of Regression Analysis
Regression analysis is a statistical tool for investigating relationships among variables.
Examples:
Home sale prices may depend on the location, size and yea
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 6
Using the Model for Estimation and Prediction
We will learn:
A confidence interval for estimating the mean response for a given value of the
predictor x
A prediction interval for predicting a
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 7
Diagnostics and Remedial Measures
What can go wrong with the model?
1)
2)
3)
4)
5)
6)
The regression model is not linear
The error variance is not constant
i are not independent
i are not dis
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 2
Simple Linear Regression
Suppose we have observations on subjects consisting of a dependent variable and an
explanatory variable .
Table 1: Data
Given the data set, n pairs of observations,
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 6
Measure the strength of linear association
Coefficient of determination
2 =
=1-
0 2 1
2 *100 percent of the variation in is explained by the variation in predictor
r is called the correlat
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 3
Simple Linear Regression
Maximum Likelihood Approach
Assume
then
Probability density function for :
Likelihood function for n observations, 1 , 2 , , :
Maximizing log likelihood function wi
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 4
Inference concerning
Hypothesis Test for 1
Test whether there is a linear association between x and y
Decision Rule
The confidence interval at the (1-)100% level for 1 is
.
Inference concer
STAT 410/510 Regression Analysis
Spring 2016
Dr. Zhou
Lecture 8
Diagnostics and Remedial Measures (Continued)
Normality of Error Terms
Residuals that are normally distributed
Normal Probability Plot
Right Skew - If the plotted points appear to bend up and
STAT 108
Lecture 17
Tu, Nov 1, 2016
9.4 Hypotheses Tests About a
Population Proportion: Large
Samples
A sample of size n ( n 30) is drawn, and the
sample proportion p is observed. Suppose
p0
we want to test H 0 : p p0against H1 : p
p0 or H1 : p p0where p
STAT 108
Lecture 2
Th, Aug 25, 2016
1.5 Cross-Sectional Data
Versus Time Series Data
Depending on how data are collected
over time, they can be classified as
either cross-sectional or time series.
1
Definition. Cross-sectional data are
collected by taking
STAT 108
Lecture 15
Tu, Oct 25, 2016
8.2 Estimation of a Population Mean
When is Assumed Known
Recall that a critical value z / 2 for a
100 (1 )% CI is defined as satisfying
P ( z / 2 z z / 2 ) 1 where z is a
standard normal random variable.
1
To deri
STAT 108
2016
Lecture 21
Tu, Nov 29,
13.1 Simple Linear Regression
Model
Example. Is there a relation between
students scores on exam 2 and exam3?
If we plot the scores on exam 3 against
the scores on exam 2, we get a scatter
diagram.
1
Scatter Diagram
ex
You will need eight (8) scantron
forms 882-E
1
STAT 108
Lecture 1
Tu, Aug 23, 2016
1.1 What is Statistics?
Definition. Statistics is a branch of
mathematics that deals with the
collection, organization, analysis, and
interpretation of numerical observatio
STAT 108
Lecture 8
Th, Sep 22, 2016
5.1 Discrete Random Variable
Definition. A random variable is a
variable which values are determined by
the outcome of a random experiment.
Notation. Capital Latin letters at the
end of the alphabet X, Y, Z, T, W, V.
1
STAT 108
Lecture 12
Th, Oct 6, 2016
6.2 Standardizing a Normal
Distribution
Rule. If x is a normallydistributed random
variable with
mean and standard
deviation , then x
z
is a standard normal random variable.
1
Note that
x z ,
that is, z tells us how m
STAT 108
Lecture 9
Tu, Sep 27, 2016
4.6 Factorials, Combinations, and
Permutations
Definition. The factorial of a number n,
denoted by n! (read n factorial) is the
product of all integers from n to 1,
that is, n!(n)(n 1)(n 2) . (2)(1)
By definition, 0! =1
STAT 108
Lecture 7
Tu, Sep 13, 2016
Venn Diagram
Definition. A Venn diagram depicts the
sample space S as a rectangle and any
event as a circle within this rectangle.
Example. In general, the Venn diagram
for any two events A and B looks like
this:
1
S
A
STAT 108
2016
Lecture 13
Tu, Oct 11,
7.1 Sampling Distributions
Definition. Let x denote the sample
mean. For different samples, the values of
x are different, but there exists a
probability distribution of those values,
called the sampling distribution o
STAT 108
Lecture 10
Th, Sep 29, 2016
5.4 The Binomial Probability
Distribution
Definition. A binomial experiment is a random
experiment that satisfies the following four
conditions:
There are n identical trials.
The trials are independent, that is, the
STAT 108
Lecture 11
Tu, Oct 4, 2016
6.1 Continuous Probability
Distribution
Definition. A continuous random variable
assumes values in an interval.
Examples. Height, weight, age, commute
time, distance to school, length of line in
cafeteria, length of son
STAT 108
Lecture 4
Th, Sep 1, 2016
3.2 Measures of Dispersion
Definition. A measure of dispersion for
a data set determines how spread the
data are.
Three measures of dispersion are
defined: range, sample variance, and
sample standard deviation.
1
Definit
STAT 108
Lecture 16
Th, Oct 27, 2016
9.1 Hypothesis Tests: An Introduction
Suppose a sample of size 100 produced
the sample mean x 12.5. We are
Interested in finding out whether the
true population mean 12, say.
To answer this question, we perform
a hypot
STAT 108
Lecture 3
Tu, Aug 30, 2016
2.2 Organizing and Graphing Quantitative Data
Recall that a quantitative variable is measured
numerically, and arithmetic operations on these
numbers make sense.
Examples. Height, weight, income, age, blood
pressure, ch
STAT 108
2016
Lecture 20
Th, Nov 17,
10.3 Hypothesis Test for Two
Means When
Suppose we want to test H 0 : 1 2
against H1 : 1 2or H1 : 1 or
2
H1 : 1 2 .
We studied the test when we assumed
that 1 2 .Now we study the case
when 1 2 .
1
We are given n1 , x