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Lecture 3
Learning to Use Regression Analysis
اقتصادسنجيا
計量經濟學
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Steps in AppliedRegression Analysis
• The first step is choosing the dependent variable – this step is determined by the purpose of the research (see Chapter 11 for details)
• After choosing the dependent variable, it’s logical to follow the following sequence:
1. Review the literature and develop the theoretical model
2. Specify the model: Select the independent variables and the functional form
3. Hypothesize the expected signs of the coefficients
4. Collect the data. Inspect and clean the data
5. Estimate and evaluate the equation
6. Document the results© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 1: Review the Literature andDevelop 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 the underlying 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)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 2: Specify the Model: IndependentVariables and Functional Form
• After selecting the dependent variable, the specification of a model involves choosing the following components:1. the independent variables and how they
should be measured,
2. the functional (mathematical) form of the variables, and
3. the properties of the stochastic error term
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 2: Specify the Model: IndependentVariables 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 choices –also denoted imposing their priors
• Example:
• when estimating a demand equation, theory informs us that prices of complements and substitutes of the good in question are important explanatory variables
• But which complements—and which substitutes?
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 2: Specify the Model: IndependentVariables and Functional Form (cont.)
• Once the variables are selected, it’s 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.
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 4: Collect the Data & Inspectand Clean the Data
• A general rule regarding sample size is “the more observations the better”
• as long as the observations are from the same general population!
• The reason for this goes back to notion of degrees of freedom (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 a Precision
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Figure 3.1 Mathematical Fit of aLine to Two Points
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Figure 3.2 Statistical Fit of a Lineto Three Points
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 4: Collect the Data & Inspectand Clean the Data (vcont.)
• Estimate model using the data in Table 2.2 to get:
• Inspecting the data—obtain a printout or plot (graph) of the data
• Reason: to look for outliers– 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?
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 5: Estimate and Evaluatethe Equation
• Once steps 1–4 have been completed, the estimation part is quick
– using Eviews or Stata 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 as expected?
• Afterwards may add sensitivity analysis (see Section 6.4 for details)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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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 error of the estimated coefficient, and the t-value is the one used to test the hypothesis that the true value of the coefficient is different from zero on (more this later!)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Case Study: Using Regression Analysisto Pick Restaurant Locations
• Background:
• You have been hired to determine the best location for the next Woody’s restaurant (a moderately priced, 24-hour, family restaurant chain)
• Objective:
• How to decide location using the six basic steps of applied regression analysis, discussed earlier?
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 1: Review the Literature andDevelop the Theoretical Model
• Background reading about the restaurant industry
• Talking to various experts within the firm
– All the chain’s restaurants are identical and located in suburban, 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)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 2: Specify the Model: IndependentVariables 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
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 2: Specify the Model: IndependentVariables and Functional Form
• Based on this, the exact definitions of the independent variables you decide to include are:
– N = Competition: the number of direct competitors within a two mile radius of the Woody’s location
– P = Population: the number of people living within a three-mile radius of the location
– I = Income: the average household income of the population measured in variable P
• With no reason to suspect anything other than linear functional form and a typical stochastic error term, that’s what you decide to use
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 3: Hypothesize the ExpectedSigns of the Coefficients
• After talking some more with the in-house experts and thinking some more, you come up with the following:
(3.4)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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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 Woody’s restaurants
• Next, you inspect the data
• The data quality is judged as excellent because:
• Each manager measures each variable identically
• All restaurants are included in the sample
• All information is from the same year
• The resulting data is as given in Tables 3.1 and 3.3 in the book ( using Eviews and Stata, respectively)© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 5: Estimate and Evaluatethe Equation
• You take the data set and enter it into the computer
• You then run an OLS regression (after thinking the model over one last time!)
• The resulting model is:
(3.5)
Estimated coefficients are as expected and the fit is reasonable
• Values for N, P, and I for each potential new location are then obtained and plugged into (3.5) to predict Y
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Step 6: Document the Results
• The results summarized in Equation 3.5 meet our documentation requirements
• Hence, you decide that there’s no need to take this step any further
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Table 3.1aData for the Woody’s Restaurants Example
(Using the Eviews Program)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Table 3.1bData for the Woody’s Restaurants Example
(Using the Eviews Program)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Table 3.1aData for the Woody’s Restaurants Example
(Using the Eviews Program)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Table 3.2aData for the Woody’s Restaurants Example
(Using the Eviews Program)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Table 3.2bData for the Woody’s Restaurants Example
(Using the Eviews Program)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Table 3.3Data for the Woody’s Restaurants Example
(Using the Eviews Program)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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Table 3.3bData for the Woody’s Restaurants Example
(Using the Eviews Program)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
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27
Table 3.4aData for the Woody’s Restaurants Example
(Using the Eviews Program)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
Departm
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28
Table 3.4bData for the Woody’s Restaurants Example
(Using the Eviews Program)
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
Departm
en
t of E
con
om
ics a
nd D
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29
Key Terms from Lecture 04
• The six steps in applied regression analysis
• Dummy variable
• Cross-sectional data set
• Specification error
• Degrees of freedom
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
Departm
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con
om
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30
The End of Lecture 3
Practice Makes
Perfect:
Learning to Use Regression Analysis
© Dr. Yoke Muelgini, M.Sc© Dr. Yoke Muelgini, M.Sc.. FE FEBB Unila, 20 Unila, 201212
Departm
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31
