This is not the document you are looking for? Use the search form below to find more!

Report

# Regression Analysis

Document Description
Regression Analysis with S-Plus Robert A. Yaffee, Ph.D. Statistics, Social Science, and Mapping Group Academic Computing Services Information Technology Services Office: 75 Third Avenue Level C-3 Phone: 212-998-3402 E-mail: yaffee@nyu.edu
File Details
Submitter
Embed Code:

Related Documents

## An Introduction to Regression Analysis

by: bizmana, 33 pages

Regression analysis is a statistical tool for the investigation of relationships between variables. Usually, the investigator seeks to ascertain the causal eVect of one variable upon ...

## Regression Analysis Tutorial (excel & matlab)

by: bizmana, 15 pages

Regression analysis can be used to identify the line or curve which provides the best fit through a set of data points. This curve can be useful to identify a trend in the data, whether it is linear, ...

## Regression Analysis and the Philosophy of Social Sciences: a Critical Realist View

by: bizmana, 44 pages

This paper challenges the connection conventionally made between regression analysis and the empiricist philosophy of science and offers an alternative explication for the way regression analysis is ...

## LOGISTIC REGRESSION ANALYSIS

by: bizmana, 9 pages

Logistic regression analysis (LRA) extends the techniques of multiple regression analysis to research situations in which the outcome variable is categorical. In practice, situations involving ...

## Robust Regression Analysis: Some Popular Statistical Package Options

by: bizmana, 12 pages

Robust regression analysis provides an alternative to a least squares regression model when fundamental assumptions are unfulfilled by the nature of the data. When the analyst estimates his ...

## Introduction to Regression Analysis

by: bizmana, 8 pages

This course provides an introduction to the theory, methods, and practice of regression analysis. The goals are to provide students with the skills that are necessary to: (1) read, understand, and ...

## A Second Course in Statistics: Regression Analysis, 7th Edition, William Mendenhall, Terry Sincich, PEARSON, ISM+STUDENT SOL MANUAL

by: mysmandtb, 9 pages

Solution Manuals and Test Banks I have huge collection of solution manuals and test banks. I strive to provide you unbeatable prices with excellent support. So, I assure you that you won’t be ...

## Understanding Regression Analysis - Quantitative Application In The Social Sciences

by: edmee, 96 pages

Understanding Regression Analysis - Quantitative Application In The Social Sciences

## 13. Poisson Regression Analysis

by: lakesha, 8 pages

We have so far considered situations where the outcome variable is numeric and Normally distributed, or binary. In clinical work one often encounters situations where the outcome variable is numeric, ...

## Regression Analysis: Basic Concepts

by: frej, 4 pages

This model represents the dependent variable, yi , as a linear function of one independent variable, xi , subject to a random ‘disturbance’ or ‘error’, ui . yi = β0 + β1xi + ui The ...

Content Preview
Regression Analysis
with S-Plus
Robert A. Yaffee, Ph.D.
Statistics, Social Science, and Mapping Group
Information Technology Services
Office: 75 Third Avenue
Level C-3
Phone: 212-998-3402
E-mail: yaffee@nyu.edu
1

Outline of Lecture
1.
Graphical Examination of the Model
1.
Suppose we have a group of variables.
2.
We are in the exploratory mode.
3.
Scatterplot matrix with splom
4.
Loess: A test for linearity of functional form
5.
Bivariate loess plots can be done
6.
Do this with the dependent and
each of the independent variables
7.
Run the anova.loess
8.
Run the plot.loess
2.
Linear Regression
1.
Analysis of MPG on cars
2.
Analysis of Employee discrimination
3.
Residual Analysis plot(regression object)
4.
Normality of residuals plotting and testing
5.
Heteroskedasticity of residuals plotting and testing
(Use White’s test)
6.
Outlier analysis:
1.
Saving the residuals
2.
Computing Standardized residuals
3.
Assessing Leverage or Cook’s distance
2

Outline-cont’d
1.
Weighted Least Squares Regression
1.
When to apply it
2.
Caveats
3.
Perform the regression analysis
4.
Compute and save the residuals
5.
Compute and save the standardized residuals
6.
Rerun the regression analysis with the weight =
1/stdev(resid)^2
2.
Robust Regression
1.
When to apply it: when there are outliers that
can’t be deleted
2.
Preliminary: Load Robust Library at beginning
3.
4.
LMS Estimation with lmsreg Used when
the residuals are nonnormal
5.
LTS Estimation with ltsreg Used with
outliers
6.
M estimation rlm Used with outliers
7.
MM estimation lmRob
3

Graphical Data Mining
• Exploring potential regression
models
– Plotting multivariate relationships
– Plotting functional forms
4

Linear Regression with
Ordinary Least Squares
estimation
• Decomposition of sums of
squares
• Derivation of intercept
• Derivation of slope
• Multivariate case
5

Hence our ANOVA table for the
whole regression model is
constructed:
6

Decomposition of Sums
of Squares
SS total = SS regression + SS error
If we divide both sides of the equation by the
Respective df, we obtain the MS
SS total/n -1 = SS regression/k + SS error/n- k - 1
Where n = sample size and k = # independent vars in
model
MS total = MS regression + MS error
Since MS = variance
Variance total = Regression Variance + error variance
We divide both sides by the total variance to obtain
1 = R square regression + R square error
F = Regression Variance
---------------------------
Error Variance
7

Derivation of the Intercept
y = a + bx + e
e = y ? a ? bx
n
n
n
n
e
? = y
? ? a
? ? b x
?
i
i
i
i
i=1
i=1
i=1
i=1
n
Because by definition
e
? =0
i
i=1
n
n
n
0 =
y
? ? a
? ? b x
?
i
i
i
i=1
i=1
i=1
n
n
n
a =
y ? b
x
? ?
?
i
i
i
i =1
i=1
i=1
n
n
na =
y
? ? b x
?
i
i
i=1
i=1
a = y ? bx
8

Derivation of the
Regression Coefficient
Given : y = a + b x + e
i
i
i
e = y ? a ? b x
i
i
i
n
n
e
? = (y
? ? a ? bx )
i
i
i
i=1
i=1
n
n
e
? 2 = (y
? ? a ? bx )2
i
i
i
i=1
i=1
n
? e
? 2i
n
n
i=1
= 2x
( y )
?
? 2b
x x
?
i
i
i
i
b
?
i=1
i=1
n
n
0
= 2x
( y )
?
? 2b
x x
?
i
i
i
i
i=1
i=1
n
x y
? i i
i
b
=
=
1
n
x
? 2i
9
i=1

The Multiple
Regression Formula
• If we recall that the formula for
the correlation coefficient can
be expressed as follows:
10

Regression Analysis

Share Regression Analysis to:

example:

http://myblog.wordpress.com/
or
http://myblog.com/

Share Regression Analysis as:

From:

To:

Share Regression Analysis.

Enter two words as shown below. If you cannot read the words, click the refresh icon.

Share Regression Analysis as:

Copy html code above and paste to your web page.