Sampling
Textbook section 1.1
Population
All potential observations of interest.
Finite Population: the number of members of the
population is limited. (e.g. The undergraduate students
at Northwestern.)
A census is when the entire population is
observed.
Multiple Regression
Our Model
yi ~ N ( , )
yi ~ N ( 0 1 xi , ) and indep. for all i.
Model : yi 0 1 xi i
i ~ N (0, ) i.i.d . for all i.
What about W/C Ratio?
Matrix Plot
New Regression with 2 Predictors
1 Predictor
Model Summary
S
Rsq
455.592 88.00%
Rs
The Scientific Process of Learning
Data
Deduction
Induction
Deduction
Hypothesis
Induction
Deduction
Car Talk
Induction and Deduction
Induction  Knowing how a particular instance
works and arguing to a general principle
Deduction  Knowing a general pr
Numerical Populations
A population where all possible values are
numerical  like the height of all Northwestern
undergraduates
Size of population is N.
Notation for numerical data: (x1, x2, . xN)
Probability Distribution
A representation of the prob
Hypothesis Testing
General steps for Hypothesis testing
1. From the problem context, identify the parameter of interest.
2. State the null hypothesis, H0 involving an equality for the
parameter of interest.
3. Specify an appropriate alternative hypothesis
Confidence Interval for a
Proportion
How would we find a rigged coin?
Our Theory: p=P(Heads)=0.5.
The Scientific Process of Learning
n 50
p 30 / 50
0.6
Deduction
Hypothesis (p=0.5)
Induction
Data
Deduction
Induction
Need a CI to decide
whether we have eno
Process and Statistical Thinking
Almost any activity can be thought of
as a process
Inputs
Process
Outputs
Statistics I
Copyright 2004 by Bruce Ankenman. All rights reserved.
1.1
Variation in the Process
There will almost always be variation
in any proce
Properties of Estimators
Parameter is (example: for Pop. Mean.)
Characteristic of the Population (unknown)
Estimator is (example: X for Sample Mean.)
Function of the data in the sample, it is a
random variable since the data is random.
Properties of Estim
Regression
Concrete
Cement, Water, Sand, Aggregate (Rocks)
_
+
Permeability is measured by total charge transferred in 6 hours.
Predict the Permeability of the
Next Cylinder
Assume
yi ~ N ( , ) i.i.d . for all i.
1
3374 2.061288 1
25
746 C yn 1 6001 C
Pl
Central Limit Theorem
How do we find out about the
properties of an estimator?
We need to know about
SAMPLING DISTRIBUTION: the actual
probability distribution that you would get if
you collected a similar sample an infinite
number of times from the same
Design of Experiments
Classical Approach
OneFactor at a Time Approach to
Experiments with Multiple Factors
Vary only one factor at a time, hold everything else
constant
Replicate the points to get an estimate of noise
Run
Number
1
2
3
4
5
6
7
8
Tempera
Comparison Tests
The Windowlift Motor
The Windings
The Weld Attachment

Electricity
+
The Motor Protector
The Circuit (Switch Open)
Switch
Battery
Motor
Protector
+

Motor Windings
The Circuit (Switch Closed)
Switch
Battery
Motor
Protector
+

Motor Win