DSC 211
CLASS NOTES 31
INVESTIGATION OF RELATIONSHIPS
AMONG PROPERTIES (VARIABLES)
OVERVIEW:
In this last module, we will study "possible relationships" among properties of some population.
For example, based on a sample
Issue:
Some business population (all our employees) and two or more properties/variables
for the property we'd like to be able to predict or understand  if we knew values for the x's (independent variables).
Three
(A) Does the sample provide evidence that a relationship exists among y, x1, x2, …?
For Example:
Business
In this question, note that we must hypothesize a specific form, e.g., a linear or quadratic relationship.
Questions:
question.
And often, a final business question is the following:
provide sufficient evidence that
(C ) If yes to (A) and (B), what is an estimate (with margin of error) for mean y, E(y), for given values of x's?
a relationship exists.
Data:
in the sample data accounted
for by the relationship.
Analysis:
REGRESSION ANALYSIS  4 STEPS  Given hypothesized model and sample data
Using the sample data, develop estimates for the intercept and all coefficients of a possible relationship.
How strong is the fit of the sample data to the model?  2 measures.
Statistically, can we say that the sample provides strong, or very strong, evidence that a relationship exists?
 Hypothesis tests
Using the sample data, can we conclude that four required conditions hold?
Answers:
Provide, in business language, the best answers to the questions above.
Class Notes 3 1 will introduce regression analysis for the most basic relationship between two variables.
the 4 steps of analysis  plus examples.
Can weight be predicted by height for (all) 12 year olds?
If we obtained a sample of 12 year olds, how would we
investigate that question?
The general name for the analysis we will study is
REGRESSION ANALYSIS
.
For this course, we will always
use the following BFDA and the 4 steps of regression analysis:
of the members of the population.
We'll use symbols y, x
1
, x
2
, …
The symbol y (dependent variable) is used
Population:
All our sales people
For example, we might hypothesize:
y
= annual sales ($)
y = beta(o) + beta(1) * x
1
+ beta(2) * x
2
+ e.
x
1
= sales aptitude score
where the beta's are constants and e stands for all other random error we cannot predict with x
1
and x
2
.
x
2
= district 1, 2, or 3
(B)
If yes to (A), how "strong" and "significant" is the relationship?
Not always stated but always an implied
Significant
 sample results
Strength
 amount of variation
A sample of size n of values of y, x
1
, x
2
, …
1.
Estimate the model
(the relationship).
such as:
y = 10.25 + 0.55 * x
1
 6.00
* x
2
.
2.
Assess the estimated model
.
3.
Check the required conditions
(of regression analysis) 
FOUR CONDITIONS.
4.
Estimate mean y for given values of the x's
. If 2 and 3 provide good results,
Develop a single estimate
for mean y and a margin of error
 since all this is based on a sample.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '07
 Dunne
 Linear Regression, Regression Analysis, R Square

Click to edit the document details