lec37v3_1up

lec37v3_1up - Stat 104 Quantitative Methods for Economists...

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Stat 104: Quantitative Methods for Economists Class 37: Course Review 1
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So I sat there for the entire semester thinking “what a horrible Introduction to Spanish Class”. 2
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General Course Concepts s Visualize Organizing and displaying data (descriptive statistics) s Conceptualize Methods for data collection (observational studies, mple surveys and controlled experiments) 3 sample surveys and controlled experiments) s Analyze Probability theory and sampling distributions Using samples to make inferences about populations Inference for means and proportions Linear regression and logistic regression
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Visualize- Displaying Data s Population and Samples s s Measures of center and spread s Empirical Rule, Chebysev’s Rule 4 s Relationships between 2 variables s Scatterplots and correlation ( r ) s Least-squares regression
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Dotplot and Histogram 60 80 100 rzen_age .08 5 20 40 par 0 10 20 30 Frequency 0 .02 .04 .06 Density 20 40 60 80 100 parzen_age
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Summarizing Data 1 1 n i i X X n = = n ( ) 2 1 1 n i i X X s n = - = - 6 1 Q 2 Q 3 Q The median ( ) 1 1 2 2 - - = = n X X s n i i
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Can also summarize by group 7
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Box and Whisker Plot s A Graphical display of data using a 5-number summary: Minimum -- Q1 -- Median -- Q3 Maximum IQR = Q3-Q1 Outlier if point < Q1-1.5IRQ or point > Q3+1.5IQR Minimum 1st Median 3rd Maximum Quartile Quartile 25% 25% 25% 25% 8
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In Stata 80 100 0 1 9 20 40 60 Graphs by male [I’m now going to remove that extreme age observation from the data. Harrumph!]
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Empirical and Chebysev’s Rule s If data is “mound shaped”, approximately 95% of the data is in the interval ( , ) x s x s x s x x x - + = ± 2 2 2 s Without any assumptions, the proportion of the data that lies within k standard deviations of the mean is at least: 10 2 k 1 1 -
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Correlation and Covariance s Measures of association between two variables. s Correlation also gives a measure of strength of the relationship (covariance does not). hese ideas also work for random variables s These ideas also work for random variables . s Note that Cov(X,X)=Var(X). 11 r s s s xy xy x y = s n x x y y xy i i i n = - - - = 1 1 1 ( )( )
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Correlation and Covariance in Stata 12
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Basic Probability Concepts s Some notation Idea Phrase Concept Notation Intersection A and B Both A and B A B 13 Union A or B Either A or B or both Complement Not A Opposite of A Conditional A given B Given B has occurred, the chance A occurs A | A B A B
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Rule Name Definition Complement Rule Addition Rule Multiplication Rule ( ) 1 ( ) P A P A = - ( ) ( ) ( ) ( ) P A or B P A P B P Aand B = + - ( ) ( ) ( ), , P A and B P A P B if A Bindependent = 14 Conditional Probability Total Probability Independence
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This note was uploaded on 03/27/2012 for the course STATS 104 taught by Professor Michaelparzen during the Fall '11 term at Harvard.

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lec37v3_1up - Stat 104 Quantitative Methods for Economists...

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