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Statistics 652Material Covered on Test 1
Chapter 11Simple Linear Regression
Model for simple linear regression and its implications
Scatterplots
1 , 2
Inference concerning 1
ANOVA table, SS , r 2 , test for linearity
Estimating 0 ,
Confidence interv
Statistics 652
Chapter 8One-Way Analysis of Variance
Basic terms from experimental design
Completely randomized design with a single factor
Model for one-way ANOVA
ANOVA table, SS , df
F test for equality of means
Testing equality of variances
Check
Statistics 652
17
Models with One or More Random Effects
We have been studying experiments with fixed effects where the experimenter is interested
in the specific treatments or the specific levels of factors in the experiment.
In other experiments, the
Plain without any ordering with Hot Dogs Data (exclude Poultry and Scrumptious):
OR=(3/6)/(16/8)=1/4=0.25
SE=sqrt(1/3)+(1/6)+(1/16)+(1/8)= 0.829156
Lower bound=0.25/exp(1.96*0.829156)=0.049221
Upper bound=0.25*exp(1.96*0.829156)=1.26979
Value ordering use
Statistics 652
Chapter 10Categorical Data
Binomial experiment
Confidence interval for a binomial proportion
Hypothesis tests for a binomial proportion
Poisson distribution, tests and confidence intervals for the Poisson
mean
Inference concerning the
Statistics 652
16
The Analysis of Covariance
We have been studying methods for comparing treatment means. Often there are other factors
that also affect the mean responses. We used blocking as one approach to take into account
extraneous factors. Another
Statistics 652
9
Multiple Comparisons in ANOVA
Recall the model for one-way ANOVA:
Yij = i + ij , i = 1, . . . , t, j = 1, . . . , ni .
Rejecting the null hypothesis of equal means just tells us that some means differ.
Specific comparisons of interest ca
Statistics 652
15
Analysis of Variance for Blocked Designs
We studied the completely randomized design (CRD) which is most useful for comparing treatment
means when the experimental units are homogeneous. When a source of extraneous variation
can be ident
Statistics 652
12
Multiple Linear Regression
12.1
Examples
Distance to Pulmonary Artery: Heart catheterization is sometimes performed on children
with congenital heart defects. A catheter (Teflon tube) 3mm in diameter is passed into a major
vein or arter
Statistics 652
10.15.5
Models with Two Qualitative Predictors
Suppose that there are two qualitative predictors, X and Z , each with two levels. We then have a
2 2 2 table. The data are
(Xi , yi , zi ), i = 1, . . . , n
Yi = 1 if yes,
= 0 if no
xi = 1 i
Statistics 652
8
Design and Analysis of Single Factor Experiments
Regression Analysis The study of the effects of numerical factors called predictors on a
response. This results in a predictive model relating the mean response to the predictors.
Analysis
Hotdogs data in Help-Sample Data-Food and Nutrition, JMP
Purpose: To see if we can predict the $/oz by the sodium and see if this prediction
changes from Beef to Poultry. Notice that sodium is the covariate and type
(beef/meat/poultry) is the fixed factor
Statistics 652
14
Analysis of Variance for the Completely Randomized
Design
Analysis of Variance The study of the effects of one or more qualitative factors on the response.
This results in a determination of the differences in the effects due to the leve
Statistics 652
1
Introduction
Statistics - body of concepts and methods used to collect and interpret data and to draw
conclusions when uncertainty and variation are present
Steps in a Scientific Study
1. Planning the Experiment
What questions do we want
Statistics 652
13
More on Multiple Regression
13.1
Selecting Variables for the Model
1. Use scientific knowledge of problem. Often the researcher will know that certain predictors
need to be included in the model, whereas other predictors are only of pote
I will use the Membrane data that is located in JMP
The data is under help-sample data-analysis of variance-membrane
There are 7 different brands and the count1 or count2 are the dependent variables. For the
demonstrations, I will use count1.
Model: Count