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by Ass oc . Prof. Sami Fethi

Department of Business Administration. FALL 20 10 - 11. by Ass oc . Prof. Sami Fethi. Demand Estimation. Demand Estimation.

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by Ass oc . Prof. Sami Fethi

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  1. Department of Business Administration FALL 2010-11 by Assoc. Prof. Sami Fethi Demand Estimation

  2. Demand Estimation • To use these important demand relationship in decision analysis, we need empirically to estimate the structural form and parameters of the demand function-Demand Estimation. • Qdx= (P, I, Pc, Ps, T) (-, + , - , +, +) • The demand for a commodity arises from the consumers’ willingness and ability to purchase the commodity. Consumer demand theory postulates that the quantity demanded of a commodity is a function of or depends on the price of the commodity, the consumers’ income, the price of related commodities, and the tastes of the consumer.

  3. Demand Estimation • In general, we will seek the answer for the following qustions: • How much will the revenue of the firm change after increasing the price of the commodity? • How much will the quantity demanded of the commodity increase if consumers’ income increase • What if the firms double its ads expenditure? • What if the competitors lower their prices? • Firms should know the answers the abovementioned questions if they want to achieve the objective of maximizing thier value.

  4. The Identification Problem • The demand curve for a commodity is generally estimated from market data on the quantity purchased of the commodity at various price over time (i.e. Time-series data) or various consuming units at one point in time (i.e. Cross-sectional data). • Simply joinning priced-quantity observations on a graph does not generate the demand curve for a commodity. The reason is that each priced-quantity observation is given by the intersection of a different and unobserved demand and supply curve of commodity. • In other words, The difficulty of deriving the demand curve for a commodity from observed priced-quantity points that results from the intersection of different and unobserved demand and supply curves for the commodity is referred to as the identification problem.

  5. The Identification Problem • In the following demand curve, Observed price-quantity data points E1, E2, E3, and E4, result respectively from the intersection of unobserved demand and supply curves D1 and S1, D2 and S2, D3 and S3, and D4 and S4. Therefore, the dashed line connecting observed points E1, E2, E3, and E4 is not the demanded curve for the commodity. The derived a demand curve for the commodity, say, D2, we allow the supply to shift or to be different and correct, through regression analysis, for the forces that cause demand curve D2 to shift or to be different as can be seen at points E2, E'2. This is done by regression analysis.

  6. Demand Estimation:Marketing ResearchApproaches • Consumer Surveys • Observational Research • Consumer Clinics • Market Experiments • These approaches are usually covered extensively in marketing courses, however the most important of these are consumer surveys and market experiments.

  7. Demand Estimation:Marketing ResearchApproaches • Consumer surveys: These surveys require the questioning of a firm’s customers in an attempt to estimate the relationship between the demand for its products and a variety of variables perceived to be for the marketing and profit planning functions. • These surveys can be conducted by simply stopping and questioning people at shopping centre or by administering sophisticated questionnaires to a carefully constructed representative sample of consumers by trained interviewers.

  8. Demand Estimation:Marketing ResearchApproaches • Major advantages: they may provide the only information available; they can be made as simple as possible; the researcher can ask exactly the questions they want • Major disadvantages: consumers may be unable or unwilling to provide reliable answers; careful and extensive surveys can be very expensive.

  9. Demand Estimation:Marketing ResearchApproaches • Market experiments: attempts by the firm to estimate the demand for the commodity by changing price and other determinants of the demand for the commodity in the actual market place.

  10. Demand Estimation:Marketing ResearchApproaches • Major advantages: consumers are in a real market situation; they do not know that they being observed; they can be conducted on a large scale to ensure the validity of results. • Major disadvantages: in order to keep cost down, the experiment may be too limited so the outcome can be questionable; competitors could try to sabotage the experiment by changing prices and other determinants of demand under their control; competitors can monitor the experiment to gain very useful information about the firm would prefer not to disclose.

  11. Purpose ofRegression Analysis • Regression Analysis is Used Primarily to Model Causality and Provide Prediction • Predict the values of a dependent (response) variable based on values of at least one independent (explanatory) variable • Explain the effect of the independent variables on the dependent variable • The relationship between X and Y can be shown on a scatter diagram

  12. Scatter Diagram • It is two dimensional graph of plotted points in which the vertical axis represents values of the dependent variable and the horizontal axis represents values of the independent or explanatory variable. • The patterns of the intersecting points of variables can graphically show relationship patterns. • Mostly, scatter diagram is used to prove or disprove cause-and-effect relationship. In the following example, it shows the relationship between advertising expenditure and its sales revenues.

  13. Scatter Diagram Scatter Diagram-Example

  14. Scatter Diagram • Scatter diagram shows a positive relationship between the relevant variables. The relationship is approximately linear. • This gives us a rough estimates of the linear relationship between the variables in the form of an equation such as • Y= a+ b X

  15. Regression Analysis • In the equation, a is the vertical intercept of the estimated linear relationship and gives the value of Y when X=0, while b is the slope of the line and gives an estimate of the increase in Y resulting from each unit increase in X. • The difficulty with the scatter diagram is that different researchers would probably obtain different results, even if they use same data points. Solution for this is to use regression analysis.

  16. Regression Analysis • Regression analysis: is a statistical technique for obtaining the line that best fits the data points so that all researchers can reach the same results. • Regression Line: Line of Best Fit • Regression Line: Minimizes the sum of the squared vertical deviations (et) of each point from the regression line. • This is the method called Ordinary Least Squares (OLS).

  17. In the table, Y1 refers actual or observed sales revenue of $44 mn associated with the advertising expenditure of $10 mn in the first year for which data collected. In the following graph, Y^1is the corresponding sales revenue of the firm estimated from the regression line for the advertising expenditure of $10 mn in the first year. The symbol e1 is the corresponding vertical deviation or error of the actual sales revenue estimated from the regression line in the first year. This can be expressed as e1= Y1- Y^1. Regression Analysis

  18. Regression Analysis • In the graph, Y^1is the corresponding sales revenue of the firm estimated from the regression line for the advertising expenditure of $10 mn in the first year. • The symbol e1 is the corresponding vertical deviation or error of the actual sales revenue estimated from the regression line in the first year. This can be expressed as e1= Y1- Y^1.

  19. Regression Analysis • Since there are 10 observation points, we have obviously 10 vertical deviations or error (i.e., e1 to e10). The regression line obtained is the line that best fits the data points in the sense that the sum of the squared (vertical) deviations from the line is minimum. This means that each of the 10 e values is first squared and then summed.

  20. Simple Regression Analysis • Now we are in a position to calculate the value of a ( the vertical intercept) and the value of b (the slope coefficient) of the regression line. • Conduct tests of significance of parameter estimates. • Construct confidence interval for the true parameter. • Test for the overall explanatory power of the regression.

  21. Simple Linear Regression Model Regression line is a straight line that describes the dependence of the average value of one variable on the other SlopeCoefficient Random Error Y Intercept Dependent (Response) Variable Independent (Explanatory) Variable Regression Line

  22. Ordinary Least Squares (OLS) Model:

  23. Ordinary Least Squares (OLS) Objective: Determine the slope and intercept that minimize the sum of the squared errors.

  24. Ordinary Least Squares (OLS) Estimation Procedure

  25. Ordinary Least Squares (OLS) Estimation Example

  26. Ordinary Least Squares (OLS) Estimation Example

  27. The Equation of Regression Line • The equation of the regression line can be constructed as follows: • Yt^=7.60 +3.53 Xt • When X=0 (zero advertising expenditures), the expected sales revenue of the firm is $7.60 mn. In the first year, when X=10mn, Y1^= $42.90 mn. • Strictly speaking, the regression line should be used only to estimate the sales revenues resulting from advertising expenditure that are within the range.

  28. Crucial Assumptions • Error term is normally distributed. • Error term has zero expected value or mean. • Error term has constant variance in each time period and for all values of X. • Error term’s value in one time period is unrelated to its value in any other period.

  29. Tests of Significance:Standard Error • To test the hypothesis that b is statistically significant (i.e., advertising positively affects sales), we need first of all to calculate standard error (deviation) of b^. • The standard error can be calculated in the following expression:

  30. Tests of Significance Standard Error of the Slope Estimate

  31. Tests of Significance Example Calculation Yt^=7.60 +3.53 Xt =7.60+3.53(10)= 42.90

  32. Tests of Significance Example Calculation

  33. Tests of Significance Calculation of the t Statistic Degrees of Freedom = (n-k) = (10-2) = 8 Critical Value (tabulated) at 5% level =2.306

  34. Confidence interval • We can also construct confidence interval for the true parameter from the estimated coefficient. • Accepting the alternative hypothesis that there is a relationship between X and Y. • Using tabular value of t=2.306 for 5% and 8 df in our example, the true value of b will lies between 2.33 and 4.73 • t=b^+/- 2.306 (sb^)=3.53+/- 2.036 (0.52)

  35. Tests of Significance Decomposition of Sum of Squares Total Variation = Explained Variation + Unexplained Variation

  36. Tests of Significance Decomposition of Sum of Squares

  37. Coefficient of Determination • Coefficient of Determination: is defined as the proportion of the total variation or dispersion in the dependent variable that explained by the variation in the explanatory variables in the regression. • In our example, COD measures how much of the variation in the firm’s sales is explained by the variation in its advertising expenditures.

  38. Tests of Significance Coefficient of Determination

  39. Coefficient of Correlation • Coefficient of Correlation (r): The square root of the coefficient of determination. • This is simply a measure of the degree of association or co-variation that exists between variables X and Y. • In our example, this mean that variables X and Y vary together 92% of the time. • The sign of coefficient r is always the same as the sign of coefficient of b^.

  40. Tests of Significance Coefficient of Correlation

  41. Multiple Regression Analysis Model:

  42. Relationship between 1 dependent & 2 or more independent variables is a linear function Multiple Regression Analysis Y-intercept Slopes Random error Dependent (Response) variable Independent (Explanatory) variables

  43. Multiple Regression Analysis

  44. Multiple Regression Analysis Too complicated by hand! Ouch!

  45. Multiple Regression Model: Example Develop a model for estimating heating oil used for a single family home in the month of January, based on average temperature and amount of insulation in inches.

  46. Multiple Regression Model: Example Excel Output For each degree increase in temperature, the estimated average amount of heating oil used is decreased by 5.437 gallons, holding insulation constant. For each increase in one inch of insulation, the estimated average use of heating oil is decreased by 20.012 gallons, holding temperature constant.

  47. Multiple Regression Analysis Adjusted Coefficient of Determination

  48. Interpretation of Coefficient of MultipleDetermination • 96.56% of the total variation in heating oil can be explained by temperature and amount of insulation • 95.99% of the total fluctuation in heating oil can be explained by temperature and amount of insulation after adjusting for the number of explanatory variables and sample size

  49. Testing for Overall Significance • Shows if Y Depends Linearly on All of the X Variables Together as a Group • Use F Test Statistic • Hypotheses: • H0: 1 = 2 = … = k = 0 (No linear relationship) • H1: At least one i  0 ( At least one independent variable affects Y ) • The Null Hypothesis is a Very Strong Statement • The Null Hypothesis is Almost Always Rejected

  50. Multiple Regression Analysis Analysis of Variance and F Statistic

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