Demand Analysis

1
Chapter 3

• Demand Analysis

2
Regression Analysis

• Regression analysis estimates the demand
  equation.
• Used to forecast effects of anticipated changes
  in prices, income, advertising, etc. on demand.

3
Elasticities

• effect of an independent variable X on quantity
  Q for any explanatory variable x

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Price Elasticity
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Price Elasticity and MR
P
elastic
unitary elastic
inelastic
D
MR
Q
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Cross-price Elasticity

• QX 22,000 ? 2.5PX 4PY ? 1M 1.5A

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Income elasticity

• Advertising elasticity

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Nonlinear Demand

• Taking natural logarithms

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Regression Analysis

• Finds the equation that best fits the data.
• May be linear

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• Or nonlinear

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Sum of Squared Errors (SSE)

• The deviations of observed Q from predicted
  Q(P) are residual errors.
• Squaring and summing these errors gives the
  (SSE).
• Least Squares Regression chooses the coefficients
  ?0 and ?X for the equation which minimize the SSE.

QX ?0 ?XPX
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Interpretation of Results

• t-statistics number of standard deviations ?b
  that the estimated coefficient is from zero (H0).

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Goodness of Fit

• R2 measures how much of the deviation in the data
  is explained by the equation.
• The total deviation is measured by the total sum
  of squared errors TSS deviations of observed
  values Q from the mean .
• The coefficient of determination is the
  proportion of the total deviation explained by
  the regression.

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• Note that 0 ? R2 ? 1. The closer R2 is to 1, the
  more explanatory power the equation has.
• R2 may be low because the TSS is large.

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Using R2

• R2 can be used to compare the results of two
  different specifications of the equation, if the
  have the same independent variables.
• If the two equations have a different number of
  independent variables, then the adjusted R2 is
  used.

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Estimating Nonlinear Equations

• The data must be converted by taking the natural
  log of each variable.
• A linear regression techniques can then be used
  on the logged data.

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Forcasting

• To forecast with a nonlinear specification, the
  value of the independent variables must be
  entered in their logged form.
• The result is a value for lnQ. To get Q, take
  the antilog
• Q elnQ
• If lnQ 6.215, then Q e6.215 500.

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Auction of Airwaves

• Data to access data go to the CD or Bb.
• Click Tools, Data Analysis, Regression.
• Enter data for dependent variables lnP in Input
  Y.
• Enter data for independent data lnQ and lnPop in
  Input X.
• Hit Enter.

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Regression Results
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Insert values for Pop and Q
Link
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Table 3-8 Data

• Data
• Open Excel
• Run the regression
• Check your results

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Table 3-8 Regression Results
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Table 3-9 Data

• Data
• Regression

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Table 3-9 Results
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Project 1

• Groups of up to four members
• Read directions carefully
• Excel guide in EXCELREG.doc
• Use assigned data to analyze regressions
• Write 2-3 page business report that addresses the
  questions in the assignment
• Provide calculations and regression results in
  appendix. Send Excel file to Drop Box.

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Instructions

• Send me an email with the names in your group
• I will set up a group on Bb with an assigned data
  set
• Your group can then communicate and exchange
  documents through the group page.