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 fPrice ID: 279558
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Slide1
Regression Models
Professor William GreeneStern School of BusinessIOMS DepartmentDepartment of EconomicsSlide2
Regression and Forecasting Models
Part
1
–
Simple Linear ModelSlide3
Theory
Demand Theory: Q = f(Price)“The Law of Demand” Demand curves slope downwardWhat does “ceteris paribus” mean here?Slide4
Data on the U.S. Gasoline Market
Quantity = G = Expenditure / PriceSlide5
Shouldn’t Demand Curves Slope Downward?Slide6
Data on 62 Movies in 2010Slide7
Average Box Office Revenue is about $20.7 MillionSlide8
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.Slide9
Average Box Office by Internet Buzz Index = Average Box Office for Buzz in IntervalSlide10
Deterministic Relationship: Not a Theory
Expected High Temperatures, August 11-20, 2013, ZIP 10012, NYSlide11
Probabilistic Relationship
What Explains the Noise?
Fuel Bill = Function of Rooms + Random Variation Slide12
Movie Buzz Data
Probabilistic Relationship?Slide13
The Regression Model
y = 0 +
1
x +
y = dependent variable
x = independent variableThe ‘regression’ is the deterministic part, 0 + 1 xThe ‘disturbance’ (noise) is .The regression model is E[y|x] = 0 + 1xSlide14
0
= y intercept
1
= slope
E[y|x] =
0
+
1
x
y
x
Linear Regression ModelSlide15
The Model
Constructed to provide a framework for interpreting the observed dataWhat 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 relationshipsSlide16
The slope is the interesting quantity.
Each additional year of education is associated with an increase of 3.611 in disability adjusted life expectancy.Slide17
A Cost Model
Electricity.mpj
Total cost in $Million
Output in Million KWH
N = 123 American electric utilities
Model: Cost = 0 + 1 KWH +
εSlide18
Cost RelationshipSlide19
Sample RegressionSlide20
Interpreting the Model
Cost = 2.44 + 0.00529 Output + eCost 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 $/KWH = 0.529 cents/KWH.Slide21
Covariation and Causality
Does more education make you live longer (on average)?Slide22
Causality?
Height (inches) and Income
($/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
Estimated Income = -451 + 50.2 HeightSlide23
b
0
b
1
How to compute the y intercept, b
0, and the slope, b1, in y = b
0
+ b
1
x.Slide24
Least
Squares RegressionSlide25
Fitting a Line to a Set of Points
Choose
b
0
and
b
1
to
minimize the sum of squared residuals
Gauss’s method
of
least squares.
Residuals
Y
i
X
i
Predictions
b
0
+
b
1
x
iSlide26
Computing the Least Squares Parameters
b0 and b1Slide27
b
0
=-14.36
b
1
= 72.718Slide28
Least
Squares Uses CalculusSlide29
Least squares minimizes the sum of squared deviations from the line
.Slide30
Summary
Theory vs. practiceLinear RelationshipDeterministicRandom, stochastic, ‘probabilistic’Mean is a function of xRegression Relationship
Causality vs. correlation
Least squares