# ECON 2613 Study Guide - Final Guide: Billy Bishop, Reverse Engineering, Neurology

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9 Aug 2016
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Empirical Analysis ECON 2613
HISTOGRAMS
Steps to make a Histogram:
1) sort data into ascending order (smallest to biggest)
2)find the range of the data
3) choose how many bins you want in your histogram
4)divide the range by the number of bins this gives you the width of your bins
5)set the limits of the bins and use the COUNTIF function to find results
6)divide the COUNTIF results by the total number of observations and multiply by 100 to get frequency %
7) highlight %s and the bin lits, then put into graph
****NOTE: COUNTIF results should add up to the number of observations****
CENTRAL TENDENCY
how the data values group around a typical or central value
Masures:
>Arithmetic Mean(average) add all values/# of values
>Median n+1/2 gives position of median
>Mode most common value
>Geometric Mean {(1+R)* (1+R2) …}^1/n
VARIATION
dispersion or scattering of values
Measures:
>Range --- Largest to Smallest
>Interquartile range --- Q3-Q1 (eliminates
problems with range)
>variance(average of squared deviations from the mean) --- S^2=(value*-mean)^2/n-1
>Standard Deviation(variation about the mean)--- s=SQRT[(value-mean)^2/n-1]
>Coefficient of Variation (shows variation to mean, can compare two
or more sets of data with diff. units) --- (stdev/mean)*100
*All values in the observations not just 1 specific value. Add the differences then divide
QUARTILE MEASURES
splits the ranked data into 4 segments (each take 25% of the whole)
Q1=25% observations are smaller and 75% are greater (n+1)/4
Q2= 50% also the median (n+1)/2
Q3=75% observations are smaller and 25% are greater 3(n+1)/4
***NOTE: gives position of the value not the actual value***
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Z-Score/Z-stat
(value-mean)/stdev
Shape of a Distribution
Mean<Median=left skewed
Mean=Median = symmetric
Mean>Medain=right skewed
EMPIRICAL RULE
approx. the variation in a bell shape distribution
states that:
68% of data is within 1 stdev
95% of data is within 2 stdev
99.7% of data is within 3 stdev
Sample Covariance: ***Shows independence*****
measures strangth of the linear relationship between 2 numerical variables
SC=(xvalue-xmean)(yalue-ymean)/n-1
>0 move in same direction
<0 move in opposite directions
if =0 X and Y are independent
Correlation Coefficient
measures the relative strength of the linear relationship between 2 variables
closer to -1 negative relationship
closer to 1 positive relationship
closer to 0 weak any relationship
BINOMIAL DISTRIBUTION
Syntax: BINOMDIST(success, trials, Psuccess, total)
sucesses=#of trials which turn out positive
trials=# of trials
Psuccess= probability any given trial is a success
Total= false/true
When to use: when looking for a probability of success in a set amount of trials
ie: lottery tickets
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Empirical Analysis ECON 2613
EX: A lottery ticket pays out some winnings 22% of the time. If I buy 5, with what probability do I lose on all five?
successes = 0 trials = 5 P(success) = 0.22 total? = false
P(lose all five) = BINOMDIST(0, 5, 0.22, false) = 28.9%
A lottery ticket pays out some winnings 22% of the time. If I buy 5, with what probability do I win on two or more?
successes ≥ 2 trials = 5 P(success) = 0.22 total? = true
P(win two or more) = 1 − BINOMDIST(1, 5, 0.22,true) = 30.4%
POISSON DISTRIBUTION
Syntax=POISSON(events,average, total)
events=#of times event occurs
average=# of events we expect
total= false/true
When do we use: expected arrivals but need the probability of arrivals in a given minute or
area of opportunity. How may times it occurs in an area of opportunity.
BEWARE!!: do not confuse with Exponential
ie: production lines
EX: We are working a polling station. Based on last year’s election, we expect three arrivals per
minute. What is the probability a given minute sees nobody arrive?
events = 0 average = 3 total = false
P(events = 0) = POISSON(0, 3, false) = 4.98%
EX2: Based on JD Power quality measures, the average new Ford has 1.18 problems when it
rolls off the assembly line. What is the probability that a new Ford has at least 3 problems?
events ≥ 3 average = 1 total =
true
P(events ≥ 3) = 1−P(events < 3) = 1−POISSON(2, 1.18,true) = 11.6%
NORMAL DISTRIBUTION
Syntax: NORMDIST(point,mean,stdev,total)
point=the value you're interested in
mean=mean of the variable
stdev= standard deviation
total=false/true
When to use: when looking for a probability of hitting an exact number or outcome
ie: consuming a certain point or more/less
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