1. Chapter 4: Demand Estimation The estimation of a demand function using econometric techniques involves the following steps
Identification of the variables
Collection of the data
Specification of the demand model
Estimation of the parameters using OLS
Development of forecasts (estimates) based on the model

2. Regression Analysis Line of Best Fit
Ordinary Least Square (OLS) Method: Minimize the sum of the squared deviations of each point from the regression line
The actual dependent variable (Y) is plus and minus 2se of the estimated dependent variable at an approximate 95% confidence

3. Significance Test to Estimated Coefficients (t-statistics)
H0: β=0 ( No relationship between X and Y)
Ha: β≠0 ( linear relationship between X and Y)
There are two ways of doing the testing:
Calculate the t statistic and compare it to the critical value
Use the p-value technique

4. Coefficient of Determination (R2)
It measures the proportion of the variation in the dependent variable that is explained by the regression line (the independent variable).
The coefficient of determination ranges from 0 (when none of the variation in Y is explained by the regression) to 1( when all the variation in Y is explained by the regression.

5. Statistical Validity of the Model (F-ratio)
It is used to test whether the estimated regression equation explains a significant proportion of the variation in the dependent variable.
The decision is to reject the null hypothesis of no relationship between X and Y ( that is, no explanatory power) at the k level of significance if the calculated F-ratio is greater than the Fk,1,n-2 value obtained from the F-distribution.

6. Association and Causation
The presence of association (correlation) does not necessarily imply causation.

7. Example 1
A 1984 study of cigarette demand in the following logarithmic regression equation:
where Q=annual cigarette consumption; P=average price of cigarette; Y=per capita income; A=total spending on cigarette advertising; w=dummy variable (w=1 to 1 after 1953 when American Cancer Assoc warned that smoking is linked to lung cancer, and w=0 otherwise.
R2=0.94, t-statisitcs are tp=-2.07; , tY=-1.05; , tA=4.48; , tw=-5.2.
Which variables have effect?
What does the coefficient of ln P represent?
Are cigarette purchase sensitive to income?

8. Example 2
The following rregresion was estimated for 23 quarters between 2000 and 2005 to test the hypothesis that tire sales (T) depend o new auto sales (A) and total miles driven (M):
where n=23 observation; R2=0.83; F=408; se=1.2; sintercept=0.32; sM=0.19; sA=0.41.
Does the regression and estimated coefficients make economic sense?
Discuss the statistical validity of the equation?
Are the coefficients on “miles driven” and “new auto sales” significantly different for 1.0? Explain.
Suppose “miles driven” is expected to fall by 2% and “new auto sales” by 13% due to expected recession? What is the predicted changes in sales quantity of tires? If actual tire sales dropped by 18%, would this be suprising?

9. Example 3 : Excel Exercise
Using the data for 6 US regions (Atlanta, Baltimore, Chicago, Denver, Erie and Fort Lauderdale) during 8 quarters, we estimate the following model using excel package:
where Q=quarterly sales; P=retail price (in cents); A=$1000 advertising expenditure; Po=rivals’ price (in cents); M=disposable income; t=trend.

10. Regression in Excel Enter data to each column
Under “Tools” menu select “Data Analysis”
Select “Regression” and click OK
Enter “Input Y Range” and “Input X Range” and click OK to run regression.

11. Regression Statistics
SUMMARY OUTPUT
Regression Statistics
Multiple R
R Square
Adjusted R Square
Standard Error
Observations 48
ANOVA df SS MS F
Significance F
Regression 6
1.09E+09
1.81E+08
9.94E-22
Residual 41
Total 47
1.17E+09
Coefficients
t Stat
P-value
Lower 95%
Upper 95%
Intercept
Price
7.45E-06
Advertising
Rival's Price
3.36E-06
Income
1.21E-14
Population
0.1253
Time Trend

12. Potential Problems in Regression
Equation Specification
Linear versus Nonlinear Models
Omitted Variables
Multicollinearity
Two or more explanatory variables are highly correlated
Autocorrelation
Error terms are highly correlated
Simultaneity and Identification