Estimating Demand Functions. Chapter 4. 1. Objectives of Demand Estimation. determine the relative influence of demand factors. forecast future demand. make production plans and effective inventory controls. 2. Major approaches to Demand Estimation. a. Marketing Research.
Estimating Demand Functions
1. Objectives of Demand Estimation
2. Major approaches to Demand Estimation
Advantage: provides useful data for the introduction of new products
Regression Analysis is usually:
4 a.Given Sales (Yt in ‘000 units) and Advertising Expenditures (Xt) (in mill. $) data as follow:
4c. Interpretation of Regression Coefficients
-- is the intercept term which represents the value of the dependent variable when Xt=0.
-- has no economic meaning when its value lies outside the range of observed data for Yt. Note: Data Range=> 25-63
- the slope of the regression line
- represents the change in the dependent variable (Yt) related to a unit change in the independent variable
=5.14 means that a $ 1 million dollar increase in ad expenses will result in an increase in sales by 5140 units.
4d. Overall Measures of Model Performance
Notice that R2 is adjusted for the degrees of freedom- the number of observations beyond the minimum needed to calculate a given regression statistic.
For example, to calculate the intercept term, at least one observation is needed; to calculate an intercept term plus one slope coefficient, at least two observations are required, and so on.
=.761 means that 76.1% of the variation of in sales is explained by the variation in advertising expenditures.
Note:One would like R2 to be as high as possible. R2, however, depends on the type of data used in the estimation. It is relatively higher for time series and smaller for cross-sectional data.
For a cross-section data, R2 of .5 is acceptable.
F-Statistic- a statistical test of significance of the regression model.
F- Test of Hypotheses
Accept Ho if F-calculated < F-table
Reject HO if F-calculated> F-table
F-table is defined for df1=k-1, df2=n-k)
at a= .05 (conventional) or a=.01, or any other level of significance.
[k= # of parameters (2), n= # of observations (7)]
F(1, 5) at a= .05 = 6.61,
Reject Ho since F-cal>F-table, i.e.
the regression model exhibits a statistically significant relationship.
Accept Ho if t-lower<t-cal<t-upper critical Value.
Reject Ho if t-cal < t-lower or t-cal> t-upper critical value.
Decision: Reject Ho since t-cal> t-upper value from the table or t-cal<t-lower value. There is a statistically significant relationship between sales and advertising
Multiple Regression has more than one independent variable.
Example: Earnings=f(Age, ED, JOB Exp.)
Use a variety of statistical software (Minitab, Excel, SAS, SPSS, ET, Limdep, Shazam, TSP)
=-72.06 -.21Age +2.25ED +1.02JEXP
(-2.1) (-1.93) (8.86) (4.07)
(The numbers in parenthesis are t-values).
R2 = .874
Test the significance of each of the variables.
Interpret the meaning of the coefficients.
5.The regression coefficients which are obtained from a linear demand equation represent slopes (the effect of a one unit change in the independent variable on the dependent variable
Problems in Regression Analysis arise due to:
more of the classical assumptions of the linear regression model.
E(etet-1)= 0 ==> no autocorrelation
systematically uncorrelated with the
error term in another period
If this assumption is violated i.e.
E(etet-1)=0 => autocorrelation problem
The variance of the error term et is the same for each
E(Set)2= s2 = 1 =>heteroscadasticity
To reduce multcollinearity:
transform the functional relationship.
(large std errors)