pre-regression basics
DESCRIPTION
Pre-regression Basics. Random Vs. Non-random variables Stochastic Vs. Deterministic Relations Correlation Vs. Causation Regression Vs. Causation Types of Data Types of Variables The Scientific Method Necessary & Sufficient Conditions. Random Vs. Non-random Variables. - PowerPoint PPT PresentationTRANSCRIPT
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Pre-regression Basics
• Random Vs. Non-random variables• Stochastic Vs. Deterministic Relations• Correlation Vs. Causation• Regression Vs. Causation• Types of Data• Types of Variables• The Scientific Method• Necessary & Sufficient Conditions
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Random Vs. Non-random Variables
• A random (stochastic, non-deterministic) variable is one whose value is not known ahead of time.
• EX: Your final grade, tomorrow’s temperature, Wednesday’s lecture topics
• What’s random to Jill may not be random to Joe.
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Non-random Variables
• A non-random (deterministic, non-stochastic variable) is one whose value is known ahead of time or one whose past value is known.
• EX: Tomorrow’s date, yesterday’s temperature.
• Randomness & Time are linked
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Probability
• Probability is the likelihood that a random variable will take on a certain value.
• EX: There is an 85% chance of snow tomorrow. Variable: Weather, Possible values: Snow, No snow.
• Probability Distribution: The set of all possible values of a random variable with the associated probabilities of each.
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Probability Distribution
Event Prob
SNOW 85%
NO SNOW 15%
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Continuous VS. Discrete Distributions
• A continuous distribution shows the probability of the different outcomes for a variable that can take one of several different values along a continuous scale.
• EX: Future inflation may be 3.001%, 3.002 % …50% etc. (The different possible values are close to each other along a smooth continuous scale)
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Continuous Distribution
Inflation Rate Prob
3.001 0.005
3.002 0.0025
3.003 0.34
3.004 0.45
3.004 .
. .
. .
. .
50 0.002
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Discrete Distribution
• A discrete distribution shows the probability of the different outcomes for a variable that can take one of several different values along a discrete scale.
• EX: The number of students in class next time may be 1, 2, 3 etc.
• In reality most distributions (in Econ) are discrete but we sometimes assume continuity for theoretical & analytical ease.
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Discrete Distribution
STUDENTS PROB.
1 0.005
2 0.05
3 0.5
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Subjective & Objective Distributions
• A subjective distribution is when a person has some idea of what the probabilities of the different outcomes (for a RV) are but does not have the exact numbers.
• EX: I have a pretty good guess that I will do well in this class.
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Objective Distributions
• An objective distribution is when the probabilities of each outcome are based on the number of times the outcome occurs divided by the total number of outcomes.
• EX: The probability of drawing a red ball from a jar with 5 red balls and a total of 50 balls is 5/50 or 1 chance in 10.
• Should all probabilities of an event sum to one?
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Intellectual Doubletalk
• A non-random variable is a random variable with a degenerate distribution.
• Translation: Any certain event can be expressed as random event that happens with probability one.
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Stochastic Vs. Deterministic Relations
• Deterministic relationships are exact formulas where the dependent and independent variables are non-random.
• EX: Ohm’s Law Current = k*Voltage• Stochastic relationships are not exact formulas that
relate dependent and independent variables.• EX: Quantity demanded = f(Price, Random Term)• Sources of Randomness: Measurement error,
unobservable variables etc.
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Correlation Vs. Causation• Loosely speaking correlation is the phenomenon of two
(or more) given variables exhibiting a roughly systematic pattern of movement.– Ex: Most of the time when stock prices fall the bond market
rallies.
• Causation is when one of the variables actually causes the other variable to change.
• Correlation does not imply correlation.• Causation implies correlation.• Causation that is not supported by correlation needs to
be examined carefully.
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Regression Vs. Causation
• A significant sign on a regression coefficient does not imply causation.
• However if you suspect causation between X & Y and the regression does not support this you must proceed with caution. What is causing the lack of significance? Experimental design flaw, unobservable variables or poor theory?
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Types of Data• Time Series Data: The data are gathered over the
same set of variables in different time periods.– EX: Price and Quantity of Summit Pale Ale Beer for a
ten year period.
• Cross Sectional Data: The data are gathered over the same set of variables at a point in time over different cross-sections.– Ex: Quantity & Price of beer in ’02 across the fifty
states.– EX2: Advertising and sales data across different firms
in MN in ‘02
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Types of Data
• Pooled Data: The dataset is essentially a cross-sectional dataset collected over the same variables in each of several different time periods.
• EX: Cigarette Price & Quantity data in each of 50 states from 1955 – 1994.
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Types of Variables
• Dependent (Endogenous)
• Independent(Exogenous)
• Discrete
• Continuous
• Categorical
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Dependent Vs. Independent
• The determination of a dependent variable is explained by the theory.
• Independent variables come from outside the theory. We do not know what causes these variables but use the independent variables to study the dependent variable.
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Simultaneity
• Simultaneity: A theory may have more than one dependent variable such that two or more dependent variables influence each other. Such a situation is referred to as a simultaneous relationship.
• EX: Equilibrium price and equilibrium quantity influence each other. Both are endogenous variables explained by price theory.
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Discrete Vs. Continuous
• A discrete variable is one that takes on finitely many values. They do not have to be integers such as 1, 2, 3 etc.
• A continuous variable can take on infinitely many values.
• Dependent & Independent variables can be either discrete or continuous.
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Categorical
• Some variables may be either discrete or continuous but may be grouped into categories for ease of analysis.
• EX: Age 0 – 10 yrs, 11 – 20 yrs etc.
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Historical Origin of Regression
• Regression is the process of finding the line or curve that ‘best’ fit a given set of data points.
• Francis Galton “Family Likeness in Stature”, Proceedings of Royal Society London, vol. 40, 1886.
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The Scientific Method Carefully study it.
Systematic Observation & Measurement
Confirm / Re-examine Not Prove or Disprove
Observe a Phenomenon
Develop a theory to explain the data
Check the implications of your theory against new data from similar circumstances
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Necessary & Sufficient Conditions
• A is said to be a sufficient condition for B. If A happens B will be guaranteed to occur.
• EX: Ceteris Paribus, if it rains then the football field will be wet. Necessary & Sufficient Conditions.
BA
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Testing Causality
• If A is observed and ceteris paribus B does not occur then the idea that A causes B is called into question.
• EX: Theory: C.P. Price is negatively related to quantity demanded. – We observe price falling and ceteris paribus
quantity demanded also falls. Does the data support the theory?
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Testing Causality
• Econometrically we can estimate an equation for demand.
• Q = f(Price, Income, Other Variables)
• What is the predicted sign on the coefficient of price? (Is it significant?)
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Fallacies
• Denying the antecedent:It did not rain therefore the football field cannot
be wet (How about a sprinkler system?)
• Affirming the consequent: The field is wet therefore it must have rained.
(Sprinklers may have been on)
BA ~~
AB
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Contrapositive• The only logical equivalent to A=> B is the
contrapositive statement ~B => ~A.
• EX1: If it rains then the field will be wet.(Contrapositive) The field is dry therefore it did not rain.
• EX2: If cigarettes are addictive then past consumption influences present consumption. (Contrapositive) If past consumption does not influence
present consumption then cigarettes are not addictive.