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Regression Models. Professor William Greene Stern School of Business IOMS Department Department of Economics. Regression and Forecasting Models. Part 1 – Simple Linear Model. Theory. Demand Theory: Q = f(Price) “The Law of Demand” Demand curves slope downward

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regression models

Regression Models

Professor William Greene

Stern School of Business

IOMS Department

Department of Economics

regression and forecasting models

Regression and Forecasting Models

Part 1 – Simple Linear Model

theory
Theory
  • Demand Theory: Q = f(Price)
  • “The Law of Demand” Demand curves slope downward
  • What does “ceteris paribus” mean here?
data on the u s gasoline market
Data on the U.S. Gasoline Market

Quantity = G = Expenditure / Price

is there a theory for this
Is There a Theory for This?

Scatter plot of box office revenues vs. number of “Can’t Wait To See It” votes on Fandango for 62 movies.

deterministic relationship not a theory
Deterministic Relationship: Not a Theory

Expected High Temperatures, August 11-20, 2013, ZIP 10012, NY

probabilistic relationship what explains the noise
Probabilistic RelationshipWhat Explains the Noise?

Fuel Bill = Function of Rooms + Random Variation

the regression model
The Regression Model

y = 0 + 1x + 

y = dependent variable

x = independent variable

The ‘regression’ is the deterministic part,

0 + 1x

The ‘disturbance’ (noise) is .

The regression model is E[y|x] = 0 + 1x

slide14

y

E[y|x] = 0 + 1x

1 = slope

0 = y intercept

x

Linear Regression Model

the model
The Model
  • Constructed to provide a framework for interpreting the observed data
    • What is the meaning of the observed relationship (assuming there is one)
  • How it’s used
    • Prediction: What reason is there to assume that we can use sample observations to predict outcomes?
    • Testing relationships
slide16

The slope is the interesting quantity.Each additional year of education is associated with an increase of 3.611 in disability adjusted life expectancy.

a cost model
A Cost Model

Electricity.mpj

Total cost in $Million

Output in Million KWH

N = 123 American electric utilities

Model: Cost = 0 + 1KWH + ε

interpreting the model
Interpreting the Model
  • Cost = 2.44 + 0.00529 Output + e
  • Cost is $Million, Output is Million KWH.
  • Fixed Cost = Cost when output = 0 Fixed Cost = $2.44Million
  • Marginal cost = Change in cost/change in output= .00529 * $Million/Million KWH= .00529 $/KWH = 0.529 cents/KWH.
covariation and causality
Covariation and Causality

Does more education make you live longer (on average)?

causality
Causality?

Estimated Income = -451 + 50.2 Height

Height (inches) and Income

($/mo.) in first post-MBA

Job (men). WSJ, 12/30/86.

Ht. Inc. Ht. Inc. Ht. Inc.

70 2990 68 2910 75 3150

67 2870 66 2840 68 2860

69 2950 71 3180 69 2930

70 3140 68 3020 76 3210

65 2790 73 3220 71 3180

73 3230 73 3370 66 2670

64 2880 70 3180 69 3050

70 3140 71 3340 65 2750

69 3000 69 2970 67 2960

73 3170 73 3240 70 3050

fitting a line to a set of points
Fitting a Line to a Set of Points

Yi

Gauss’s methodof least squares.

Residuals

Predictionsb0+ b1xi

Choose b0and b1tominimize the sum of squared residuals

Xi

slide27

b1= 72.718

b0=-14.36

summary
Summary
  • Theory vs. practice
  • Linear Relationship
    • Deterministic
    • Random, stochastic, ‘probabilistic’
    • Mean is a function of x
  • Regression Relationship
    • Causality vs. correlation
    • Least squares