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All Rights Reserved to Kardan University 2014 Kardan.edu.af 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. 2 Q dx = (P, I, P c, P s, 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.

All Rights Reserved to Kardan University 2014 Kardan.edu.af 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. 3

All Rights Reserved to Kardan University 2014 Kardan.edu.af Demand Estimation: Marketing Research Approaches 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. 4

All Rights Reserved to Kardan University 2014 Kardan.edu.af Purpose of Regression 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 5

All Rights Reserved to Kardan University 2014 Kardan.edu.af Regression analysis is Concerned with the study of the dependence of one variable (dependent variable) on one or more other variables (explanatory variables) with a view to estimate or predict the average value of the dependent variable Regression analysis used for observation of relationship between two or more than two variables

All Rights Reserved to Kardan University 2014 Kardan.edu.af 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. 7

All Rights Reserved to Kardan University 2014 Kardan.edu.af Scatter Diagram-Example 8 Scatter Diagram

All Rights Reserved to Kardan University 2014 Kardan.edu.af 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 9

All Rights Reserved to Kardan University 2014 Kardan.edu.af 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. 10

All Rights Reserved to Kardan University 2014 Kardan.edu.af 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 This is the method called Ordinary Least Squares (OLS). 11

All Rights Reserved to Kardan University 2014 Kardan.edu.af Simple Linear Regression Model 12 average value Regression line is a straight line that describes the dependence of the average value of one variable on the other Y Intercept Slope Coefficient Random Error Independent (Explanatory) Variable Regression Line Dependent (Response) Variable

All Rights Reserved to Kardan University 2014 Kardan.edu.af Ordinary Least Squares (OLS) 13 Model:

All Rights Reserved to Kardan University 2014 – Y = β 0 + β 1 X 1 + β 2 X 2 This is an exact relationship whose meaning is that the variation in the quantity demanded are fully explained by changes in price (X1) and income (X2). But the influence of other factors may be there, so for which we introduce Random Variable (ui) in the model. So our Multiple regression model will be; Y = β 0 + β 1 X 1 + β 2 X 2 + u i And estimated Regression line shall be Y = b 0 + b 1 X 1 + b 2 X 2 An example for Model with Two Explanatory Variables ^ ^^

All Rights Reserved to Kardan University 2014 Formulas to calculate estimates of parameters Beta`s whereas x 1 = X 1 – X 1 x 2 = X 2 – X 2 y 1 = Y – Y b0b0 ^ ^ ^

All Rights Reserved to Kardan University 2014 Kardan.edu.af Ordinary Least Squares (OLS) 16 Estimation Procedure

All Rights Reserved to Kardan University 2014 Kardan.edu.af Ordinary Least Squares (OLS) 17 Estimation Example

All Rights Reserved to Kardan University 2014 Kardan.edu.af Ordinary Least Squares (OLS) 18 Estimation Example

All Rights Reserved to Kardan University 2014 Kardan.edu.af The Equation of Regression Line The equation of the regression line can be constructed as follows: Y t ^ = X t When X=0 (zero advertising expenditures), the expected sales revenue of the firm is $7.60 mn. In the first year, when X=10mn, Y 1 ^ = $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. 19

Q.DPrice (X1)Income (X2) Example

YX1X2yx1x1 x2x2 (y) 2 (x 1 ) 2 (x 2 ) 2 yx 1 yx 2 x1x2x1x Y = ΣY/n X 1 = ΣY/nX2 = ΣY/n = 800/10= 60/10 = 8000/10 = 80= 6 = 800

All Rights Reserved to Kardan University 2014 By putting the values in the given formulas we get b 0 = b 1 = b 2 = So Estimated Multiple Regression model is Y = b 0 + b 1 X 1 + b 2 X 2 Y = X X 2 ^ ^ ^ ^^^

All Rights Reserved to Kardan University 2014 The Coefficient Of Multiple Determination R 2 It shows the percentage of total variation in Y explained by the explanatory variables (X 1 & X 2 ) The coefficient of multiple determination is denoted by capital R 2. In three variable model the coefficient of determination is R 2 (y, x 1 x 2 )

All Rights Reserved to Kardan University 2014 The value of R 2 lies between 0 and 1. The higher R 2 the greater the percentage of the variation of Y explained by the regression plain that is the better the goodness of fit of the regression plain to the sample observations. The closer R 2 to zero the worse the fit. THE COEFFICIENT OF MULTIPLE DETERMINATION R 2

All Rights Reserved to Kardan University 2014 Formula to calculate R-square ·For this we have the following formula ·R 2 = b 1 ( Σyx 1 ) + b 2 (Σyx 2 ) Σ y 2 Now by putting values in the following formula, which we have already calculated in previous slides, we get R 2 = 0.89 What does this mean….? ^ ^

All Rights Reserved to Kardan University 2014 Kardan.edu.af Regression Analysis in Practice Suppose we have an Employment (Labor Demand) Function as follows: N=Constant+K+W+AD+P+WT N: employees in employment K: capital accumulation W: value of real wages AD: aggregate deficit P: effect of world manufacturing exports on employment WT: the deviation of world trade from trend. 26

All Rights Reserved to Kardan University 2014 Kardan.edu.af Using Multiple Regression Analysis: When the Dependent Variable (Y) that we seek to explain depends on more than one independent variable, that is called Multiple Regression Analysis. For example, the firm’s Sales Revenue (Y) may be postulated to depend not only on the firm’s advertising expenditures (X 1 ) but also on its expenditures on Quality Control (X 2 )

All Rights Reserved to Kardan University 2014 Kardan.edu.af Y Sales X 1 Advertising X 2 Quality Control x1x1 x2x2 yx1yx1yx2yx2yx1x2x1x2 x12x12 x22x sum= Mean=50105 B1= B2= B0= Y = X X2

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All Rights Reserved to Kardan University 2014 Correlation coefficient Kardan.edu.af

All Rights Reserved to Kardan University 2014 Correlation “Co” means two, to see the relationship between two variables. The value of r lies between -1 and +1. If r = 0.2 it means positive r/s If r = -0.2 it means negative r/s If r = 1 perfect positive correlation If r = -1 perfect negative correlation Kardan.edu.af

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