Econ 203 Lab Session

# Econ 203 Lab Session
## Research Project
### Marcelino Guerra
### April 28, 2020

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# Announcements

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# Step 1
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# Scatter Plots
.font90[You need to create scatter plots for each pair `$(Y,X_{1})$`, `$(Y, X_{2})$`, etc. of your data. In this very first step, you can spot outliers - points very far from the line, such as Qatar and Vietnam, in my case. Then, decide if you will get rid of them.
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# Scatter Plots
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# Descriptive Statistics
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# Creating dummy variables
.font90[I need to transform continents (names) into numbers. Since I have five categories (Africa, Asia, Europe, South America, and North America), I am creating four dummy variables. I took out Europe, the most common case in my sample. Therefore, Europe is my baseline.  
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# Step 2
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# Run the Full Model
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__Run the Full Model__
+ Check significance: individual (t-test) and global (F-test)<br>

+ What is the `$R^{2}$`? Can you explain what does that value mean?<br>
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# Run the Full Model
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# Step 3
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# Full Model Assumptions
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__Check the Full Model assumptions__
+ Normality of Errors <br>
Create a histogram using __standardized residuals__ and bin values.
+ Homoskedasticity x Heteroskedasticity <br> 
Create a scatter plot of __residuals__ vs predicted values. In case you find that the model violates heteroskedasticity, transform the dependent variable using `$ln$`.
+ Independence of Errors x Autocorrelation <br>
If you are working with time series, run the Durbin-Watson test. In case you have autocorrelation, add a trend variable in your model.
+ Outliers <br>
You already did it in step #1.
+ Multicolinearity<br>
Construct the correlation matrix. Check if there is high correlation between your independend variables.

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# Normality
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# Homoskedasticity
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# Multicolinearity
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# Step 4
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# Run the Reduced Model
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.font120[
__Run the Reduced Model__
+ Drop the variables that are not statistically significant in your full model (check for `$\hat{\beta}s$` with p-value>.05 or p-value>.1, you decide!)<br>

+ Check significance: individual (t-test) and global (F-test)<br>

+ What is the `$R^{2}$`? Can you explain what does that value mean?<br>
]
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# Run the Reduced Model
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# Step 5
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# Reduced Model Assumptions

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.font120[
__Check the Reduced Model assumptions__
+ Normality of Errors <br>

+ Homoskedasticity x Heteroskedasticity <br>

+ Independence of Errors x Autocorrelation (if you are working with time series)<br>
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Yes, you have to do it again.
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# Step 6
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# Partial F-test
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Reject `$H_{0}$` if:

`$$\dfrac{\frac{SSR_{f} - SSR_{r}}{k_{d}}}{MSE_{f}}>F_{\alpha, k_{d}, (n-k-1)_{f}}$$`

where `$SSR_{f}$` is the Sum of Squares Regression from the full model, `$SSR_{r}$` is the Sum of Squares Regression from the reduced model, `$k_{d}$` is the number of variables that you eliminated and `$MSE_{f}$` is the Mean Square for Error from the full model.

__If you are rejecting `$H_{0}$`, use the Full Model for the section "Empirical Results". Otherwise, use the Reduced Model.__
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# Partial F-test
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<video width=890px height=460px>
    <source src="media/partial.mp4" type="video/mp4">
</video>
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# Writing a report
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# Writing a report
1. __Introduction__<br>
Start with the motivation: why your topic is important/interesting? State your research question and briefly discuss your results
2. __Data__<br>
Describe the sources of your data. If you transformed your variables, explain what you did. Also, comment the descriptive statistics and the correlation matrix.
3. __Regression Analysis__<br>
First and foremost: we want to see equations! Also, state every step that you did, from outliers to the partial F-test. What is your final model? Is it robust? Does it satisfy the model assumptions?
4. __Empirical Results__<br>
Time to interpret your results: `$\hat{\beta}$`'s and `$R^{2}$`. Does the result match your prior beliefs? Explain statistically significant results and mention those coefficients not statistically different from zero. Which one is your final model? Full or reduced?
5. __Summary and Discussion__<br>
Restate your research question and highlight your main findings. Suggest improvements for future studies, etc.