General Linear
Test Approach
We will explain the general test approach in terms of the simple linear
regression model and testing Ho: 1 = 0 vs Ha: 1 0.
The general linear test approach involves three
Homework 2
Due Sept 16
1) You want to know whether adults in your country think the ideal number of children
is 2 or if adults in your country think the ideal number of children is either higher or
lo
Homework 1
Due Sept. 9th
1. If fish lengths have a normal distribution with mean 20 and standard deviation of 10,
what is the sampling distribution of the sample mean for samples of size 400?
2. If th
Homework 1
Due Sept. 9th
1. If fish lengths have a normal distribution with mean 20 and standard deviation of 10,
what is the sampling distribution of the sample mean for samples of size 400?
The samp
Homework 3
Due Sept 26
For any problem that requires using SAS, turn in your code and output. You must
also indicate what your answers are, not just turn in SAS output. For all hypothesis
tests, assum
Homework 2
Due Sept 16
1) You want to know whether adults in your country think the ideal number of children
is 2 or if adults in your country think the ideal number of children is either higher or
lo
Generalized Linear Models
Generalized linear models, GLMs, describe patterns of association
and interaction.
The models help us evaluate which explanatory variables affect the
response, while controll
Logistic Regression Models
The odds of success is the probability of success divided by the
probability of failure:
1
And
log
x
1
1
X
exp( x) exp( ) exp( )
Logistic Regression Models
An odds
Weighted Least
Squares
If the error terms are normally distributed but the variance of the
error term is not constant, a standard remedial measure is to use
weighted least squares.
When using weighted
Polynomial
Regression Models
Polynomial regression models have two basic types of uses:
1)
When the true curvilinear response function is really a polynomial
function.
2)
When the true curvilinear res
Model Selection
For a set of p-1 predictors, there are 2p-1 possible regression
models that can be constructed, based on the fact that each
predictor can be either included or excluded from a particul
Multiple Regression
There are many situations were a single predictor variable in the model
would provide an inadequate description since a number of key
variables affect the response variable.
Furthe
Homework 4
Due Oct. 12th
For any problem that requires using SAS, turn in your code and output. You must
also indicate what your answers are, not just turn in SAS output. For all hypothesis
tests, ass
Homework 5
Due Oct. 19th
For any problem that requires using SAS, turn in your code and output. You must
also indicate what your answers are, not just turn in SAS output. For all hypothesis
tests, ass
Homework 6
Due Oct. 24th
For any problem that requires using SAS, turn in your code and output. You must
also indicate what your answers are, not just turn in SAS output. For all hypothesis
tests, ass
Homework 7
Due Nov. 9th
1)
For the homework6 data (the same SAS file as for last homework)
Calculate the adjusted coefficient of multiple determination for the linear model and the
quadratic model. Yo
Homework 8
Due Nov. 23rd
For any problem that requires using SAS, turn in your code and output. You must
also indicate what your answers are, not just turn in SAS output. For all hypothesis
tests, ass
Homework 8
Due Nov. 23rd
For any problem that requires using SAS, turn in your code and output. You must
also indicate what your answers are, not just turn in SAS output. For all hypothesis
tests, ass
Homework 5
Due Oct. 19th
For any problem that requires using SAS, turn in your code and output. You must
also indicate what your answers are, not just turn in SAS output. For all hypothesis
tests, ass
Homework 4
Due Oct. 12th
For any problem that requires using SAS, turn in your code and output. You must
also indicate what your answers are, not just turn in SAS output. For all hypothesis
tests, ass
Homework 3
Due Sept 26
For any problem that requires using SAS, turn in your code and output. You must
also indicate what your answers are, not just turn in SAS output. For all hypothesis
tests, assum
Homework 7
Due Nov. 9h
1)
For the homework6 data (the same SAS file as for last homework)
Calculate the adjusted coefficient of multiple determination for the linear model and the
quadratic model. You
Standardized
Multiple Regression
Given a fitted multiple regression model, a user typically wants to
compare predictors in terms of the magnitudes of their effects on the
response variable.
For exampl
Multiple Regression
Recall our model for multiple regression is
Yi 0 1 X i1 2 X i 2 p 1 X i , p 1 i
And assuming that Ecfw_i = 0, the regression function is
Ecfw_Y = 0 + 1X1 + 2X2 + .+ p-1Xp-1.
To fit
Inferences on 1
We are assuming the normal error regression model
Yi 0 1 X i i
where
0 and 1 are parameters
Xi are known constants
i are independent N(0,2)
Frequently, we are interested in drawing inf
How different is our sample from the
true population due to chance?
Population
Sample
Sampling variability
Sampling variability: The variability among random samples
from the same population
Populatio
Inferences on 1
Recall that
t*
b1 1
~ t (n 2)
scfw_b1
We use this t distribution of our statistic to do hypothesis tests.
What value do we use for 1 in this statistic and why?
If we want to show the
Simple Linear Regression
Yi 0 1 X i i
The response Yi is the sum of two parts: (1) the constant term 0 +
1Xi and (2) the random term i.
Thus Yi is a random variable.
Since Ecfw_i = 0 and 0 + 1Xi is a
Estimation of
regression function
The Gauss-Markov theorem states that the least squares estimators
b0 and b1 are unbiased an have minimum variance among all
unbiased linear estimators.
Thus Ecfw_b0=