Managerial Economics By Mr. Tahir Islam

Demand Estimation by regression analysis  What is regression The term regression was first introduced by Francis Galton In a famous paper Galton found that there was a strong tendency for all tall parents to have tall children and for short parents to have short children Meaning that average height of children born tends to move towards the average height of the parents This is universal law of Galton and is confirmed by his friend Karl Pearson Regression means to move towards the center to average

Regression analysis 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 Regression analysis

 In order to introduce regression analysis,  suppose that a manager wants to determine the relationship between the firm’s advertisement expenditures and its sale revenue  The manager wants to test the hypotheses that higher the advertising expenditures leads to higher sale for a firm  Manager wants to estimate the strength of the relationship (i.e. how much sales increase for each dollar increase in advertising expenditures)  The manager collects data on advertising expenditure and on sales revenue in specific period of time Introduction to Regression analysis in Managerial Economics

Suppose that advertising and sale data are given below for 10 years Year (t) Advertising Exp (X) Sales Revenue (Y) If we now plot each pair of advertising-sales value on a graph, with advertising expenditures measured along the horizontal axis and sales revenue measured along horizontal axis Introduction to Regression analysis in Managerial Economics ( cont…)

Advertising expenditure Sales

Introduction to Regression analysis in Managerial Economics ( cont…) Advertising expenditure Sales ^ Y

Introduction to Regression analysis in Managerial Economics ( cont…)  We gets points or dots in figure  This is known as a scatter diagram  It shows the spread of the points in the X-Y plane  There is a positive relationship between the level of firm’s advertising expenditure and its sales revenue  Relationship between them is linear  One way to estimate the relationship is visual inspection  Draw a straight line among these points in such away that these points are cluster around the straight line  By extending a line to the vertical axis, we can estimate the firm sale revenue with zero advertisement

Introduction to Regression analysis in Managerial Economics ( cont…)  Where as the slop of line presents the linear relationship between sale revenue and advertisement i.e. how much sale revenue would increase for one dollar increase in advertisement  This will give us a rough estimate of relationship between these two variables  The manager could use this information to estimate how much sale revenue of the firm would be if its advertisement expenditure were anywhere between $9 million and $15 million

 Regression analysis is a best statistical technique for obtaining the line that best fits the data points  Regression line is obtain to minimize the difference/deviations between each points and regression line  This method is called “method of least square” Introduction to Regression analysis in Managerial Economics ( cont…)

 Y refers to actual or observed sale revenue of $44 million associated with advertising expenditure of $10 million in first year  Y is estimated sale for a firm for advertising expenditures of $10 million in first year  The term “ e” in the figure is the corresponding vertical deviation or error and is equal to the difference between the actual value and estimated value of the firm  The formula for error is e =Y-Y  Since there are 10 observation points in figure, we have 10 such vertical deviations or errors Introduction to Regression analysis in Managerial Economics ( cont…) ^ ^

Demand Estimation by regression analysis As we know that demand plays a vital role in managerial making decision, so correct estimation about demand is important as well as a problem Although many techniques are used for estimating demand but the most common method for estimating demand in managerial economic is regression analysis This method is more objective, provide more complete information and is generally less expensive

Demand Estimation by regression analysis In this section we summarize and review the method of estimating demand by regression analysis We discuss 1.Model specification 2. Data requirements 3. Functional form 4. Evaluation of econometric results obtain

Demand Estimation by regression analysis 1.Model specification Model specification is first step in estimating demand function This involves identifying most important variables that affect the demand for a commodity Usually we include explanatory variables a. price of commodity b. consumer income c. numbers of members in a family d. price of related goods e. level of advertisement expenditure f. availability of credit incentives and consumers price expectation are

Demand Estimation by regression analysis But specification of demand function for different goods are different Demand function for expensive durable goods, such as automobiles and houses Explanatory variables are a.Credit terms b.rate of interest c.Income level

Demand Estimation by regression analysis (cont…) Demand function for seasonal equipment, such as air conditioner, swimming suits and cold beverages Explanatory variables are a. weather conditions b. Income level of consumer

Demand Estimation by regression analysis (cont…) Demand function for capital goods such as machinery and factory buildings Explanatory variables are a. rate of profits b. capital utilization c. wage rate d.Income level of investor The researcher must avoid omitting important variables Other wise he or she will obtain biased results

Demand Estimation by regression analysis (cont…) 2.Collecting data on variables Collecting of data is another step to estimate the demand function Data can be collected for each variable over the time (yearly, quarterly and monthly) is called time series data Data for different economic units (individuals, households) at particular point of time i.e. for a particular year, month or and year is called cross- sectional data

Demand Estimation by regression analysis (cont…) If data about variables are incorrect then researcher can not make a best estimation Specifying the form of the demand function The third step in estimating demand by regression analysis is to determine the functional form of the model Linear model is the simplest and realist form of demand function Qx =ao +a 1 px + a 2 I +a 3 N +a 4 PY +…………) In above equation a’s are parameters to be estimated

Demand Estimation by regression analysis (cont…) Testing the Econometrics results The fourth and final step in the estimation of demand by regression analysis is to evaluate the regression results First, the sign of each estimated coefficient must be checked to confirm whether it matched economic theory Tests are used to find the value of parameters, usually we use t-statistic