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3-1 2011 Pearson Addison-Wesley. All rights reserved.
Steps in Applied
Regression Analysis
The first step is choosing the dependent variable this step isdetermined by the purpose of the research (see Chapter 11 fordetails)
After choosing the dependent variable, its logical to follow thefollowing sequence:
1. Review the literature and develop the theoretical model
2. Specify the model: Select the independent variables and thefunctional form
3. Hypothesize the expected signs of the coefficients4. Collect the data. Inspect and clean the data
5. Estimate and evaluate the equation
6. Document the results
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3-2 2011 Pearson Addison-Wesley. All rights reserved.
Step 1: Review the Literature and
Develop the Theoretical Model
Perhaps counter intuitively, a strong theoretical foundation
is the best start for any empirical project
Reason: main econometric decisions are determined by theunderlying theoretical model
Useful starting points:
Journal of Economic Literature or a business oriented publication of
abstracts
Internet search, including Google Scholar
EconLit, an electronic bibliography of economics literature (for more
details, go to www.EconLit.org)
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Step 2: Specify the Model: Independent
Variables and Functional Form
After selecting the dependent variable, thespecification of a model involves choosing thefollowing components:
1. the independent variables and how they should bemeasured,
2. the functional (mathematical) form of the variables,and
3. the properties of the stochastic error term
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Step 2: Specify the Model:
Independent Variables and
Functional Form (cont.)
A mistake in any of the three elements results in a specification error
For example, only theoretically relevant explanatory variables should
be included
Even so, researchers frequently have to make choicesalso denoted
imposing theirpriors
Example:
when estimating a demand equation, theory informs us that prices of
complements and substitutes of the good in question are importantexplanatory variables
But which complementsand which substitutes?
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3-5 2011 Pearson Addison-Wesley. All rights reserved.
Step 3: Hypothesize the Expected
Signs of the Coefficients
Once the variables are selected, its important to
hypothesize the expected signs of the regression
coefficients
Example: demand equation for a final consumption good
First, state the demand equation as a general function:
(3.2)
The signs above the variables indicate the hypothesized
sign of the respective regression coefficient in a linear
model
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7/303-6 2011 Pearson Addison-Wesley. All rights reserved.
Step 4: Collect the Data & Inspect
and Clean the Data
A general rule regarding sample size is the moreobservations the better
as long as the observations are from the same general
population!
The reason for this goes back to notion ofdegrees offreedom (mentioned first in Section 2.4)
When there are more degrees of freedom:
Every positive error is likely to be balanced by a negative error(see Figure 3.2)
The estimated regression coefficients are estimated with agreater deal ofprecision
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8/303-7 2011 Pearson Addison-Wesley. All rights reserved.
Figure 3.1 Mathematical Fit of a
Line to Two Points
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9/303-8 2011 Pearson Addison-Wesley. All rights reserved.
Figure 3.2 Statistical Fit of a Line
to Three Points
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10/303-9 2011 Pearson Addison-Wesley. All rights reserved.
Step 4: Collect the Data & Inspect
and Clean the Data (cont.)
Estimate model using the data in Table 2.2 to get:
Inspecting the dataobtain a printout or plot (graph)
of the data
Reason: to look foroutliers
An outlier is an observation that lies outside the range of the rest of
the observations
Examples:
Does a student have a 7.0 GPA on a 4.0 scale?
Is consumption negative?
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11/303-10 2011 Pearson Addison-Wesley. All rights reserved.
Step 5: Estimate and Evaluate
the Equation
Once steps 14 have been completed, the estimation part
is quick
using Eviews orStata to estimate an OLS regression takes less
than a second!
The evaluation part is more tricky, however, involving
answering the following questions:
How well did the equation fit the data?
Were the signs and magnitudes of the estimated coefficients asexpected?
Afterwards may add sensitivity analysis (see Section 6.4
for details)
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3-11 2011 Pearson Addison-Wesley. All rights reserved.
Step 6: Document the Results
A standard format usually is used to present estimated
regression results:
(3.3)
The number in parentheses under the estimated coefficient
is the estimated standard errorof the estimatedcoefficient, and the t-value is the one used to test the
hypothesis that the true value of the coefficient is different
from zero (more on this later!)
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Case Study: Using Regression Analysis
to Pick Restaurant Locations
Background:
You have been hired to determine the best location
for the next Woodys restaurant (a moderately priced,24-hour, family restaurant chain)
Objective:
How to decide location using the six basic steps ofapplied regression analysis, discussed earlier?
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3-13 2011 Pearson Addison-Wesley. All rights reserved.
Step 1: Review the Literature and
Develop the Theoretical Model
Background reading about the restaurant industry
Talking to various experts within the firm
All the chains restaurants are identical and located insuburban, retail, or residential environments
So, lack of variation in potential explanatory variables to help
determine location
Number of customers most important for locational decision
Dependent variable: number of customers (measured by
the number of checks or bills)
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3-14 2011 Pearson Addison-Wesley. All rights reserved.
Step 2: Specify the Model: Independent
Variables and Functional Form
More discussions with in-house experts
reveal three major determinants of sales:
Number of people living near the location
General income level of the location
Number of direct competitors near the location
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3-15 2011 Pearson Addison-Wesley. All rights reserved.
Step 2: Specify the Model: Independent
Variables and Functional Form (cont.)
Based on this, the exact definitions of the independentvariables you decide to include are:
N = Competition: the number of direct competitors within a two-mile radius of the Woodys location
P = Population: the number of people living within a three-mileradius of the location
I = Income: the average household income of the populationmeasured in variable P
With no reason to suspect anything other than linearfunctional form and a typical stochastic error term,thats what you decide to use
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Step 3: Hypothesize the Expected
Signs of the Coefficients
After talking some more with the in-house
experts and thinking some more, you
come up with the following:
(3.4)
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Step 4: Collect the Data &
Inspect and Clean the Data
You manage to obtain data on the dependent and
independent variables for all 33 Woodys restaurants
Next, you inspect the data
The data quality is judged as excellent because:
Each managermeasures each variable identically
Allrestaurants are included in the sample
All information is from the sameyear
The resulting data is as given in Tables 3.1 and 3.3 in the
book (using Eviews and Stata, respectively)
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Step 6: Document the Results
The results summarized in Equation 3.5
meet our documentation requirements
Hence, you decide that theres no need to
take this step any further
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Table 3.1a
Data for the Woodys Restaurants Example
(Using the Eviews Program)
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Table 3.1b
Data for the Woodys Restaurants Example
(Using the Eviews Program)
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Table 3.1c
Data for the Woodys Restaurants Example
(Using the Eviews Program)
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Table 3.2a
Actual Computer Output
(Using the Eviews Program)
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Table 3.2b
Actual Computer Output
(Using the Eviews Program)
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Table 3.3
Data for the Woodys Restaurants Example
(Using the Stata Program)
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Table 3.3b
Data for the Woodys Restaurants Example
(Using the Stata Program)
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Table 3.4a
Actual Computer Output
(Using the Stata Program)
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Table 3.4b
Actual Computer Output
(Using the Stata Program)
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3 29
Key Terms from Chapter 3
The six steps in applied regression analysis
Dummy variable
Cross-sectional data set
Specification error
Degrees of freedom