Ec 331 01 02 econometrics i fall 2011 lecture notes chapters 1 2 3
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EC 331. 01&02 ECONOMETRICS I Fall 2011 Lecture notes Chapters 1-2-3. Brief Overview of the Course. This course is about using data to measure causal effects. In this course you will:. Review of Probability and Statistics (SW Chapters 2, 3). The California Test Score Data Set.

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Ec 331 01 02 econometrics i fall 2011 lecture notes chapters 1 2 3
EC 331. 01&02ECONOMETRICS IFall 2011 Lecture notesChapters 1-2-3



This course is about using data to measure causal effects
This course is about using data to measure causal effects.





Initial look at the data you should already know how to interpret this table
Initial look at the data:(You should already know how to interpret this table)

  • This table doesn’t tell us anything about the relationshipbetween test scores and the STR.


Ec 331 01 02 econometrics i fall 2011 lecture notes chapters 1 2 3
Question: Do districts with smaller classes have higher test scores? Scatterplot of test score v. student-teacher ratio

What does this figure show?


Ec 331 01 02 econometrics i fall 2011 lecture notes chapters 1 2 3
We need to get some numerical evidence on whether districts with low STRs have higher test scores – but how?


Initial data analysis compare districts with small str 20 and large str 20 class sizes
Initial data analysis: Compare districts with “small” (STR < 20) and “large” (STR ≥ 20) class sizes:

1.Estimation of  = difference between group means

2.Test the hypothesis that  = 0

3.Construct a confidence interval for 










B moments of a population distribution mean variance standard deviation covariance correlation
(b) Moments of a population distribution: mean, variance, standard deviation, covariance, correlation


Moments ctd
Moments, ctd. standard deviation, covariance, correlation


R andom variables joint distributions and covariance
R standard deviation, covariance, correlationandom variables: joint distributions and covariance


The covariance between test score and str is negative
The standard deviation, covariance, correlationcovariance between Test Score and STR is negative:

so is the correlation…


The correlation coefficient is defined in terms of the covariance
The standard deviation, covariance, correlationcorrelation coefficientis defined in terms of the covariance:


The correlation coefficient measures linear association
The correlation coefficient measures standard deviation, covariance, correlationlinear association


C conditional distributions and conditional means
(c) Conditional distributions and conditional means standard deviation, covariance, correlation


Conditional mean ctd
Conditional mean, ctd. standard deviation, covariance, correlation



Distribution of y 1 y n under simple random sampling
Distribution of Y population: 1,…, Ynunder simple random sampling




The sampling distribution of when y is bernoulli p 78
The sampling distribution of when population: Yis Bernoulli (p = .78):





The sampling distribution of when n is large
The sampling distribution of when population: n is large


The law of large numbers
The population: Law of Large Numbers:


The central limit theorem clt
The population: Central Limit Theorem (CLT):



Same example sampling distribution of
Same example population: : sampling distribution of :



B why use to estimate y
(b) Why Use To Estimate population: Y?


Why use to estimate y ctd
Why Use To Estimate population: Y?, ctd.



Calculating the p value with y known
Calculating the p-value with population: Y known:




What is the link between the p value and the significance level
What is the link between the population: p-value and the significance level?



Comments on this recipe and the student t distribution
Comments on this recipe and the Student population: t-distribution







Summary
Summary: population:


Let s go back to the original policy question
Let population: ’s go back to the original policy question:


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