Q4 a) The sales manager of a company believes that the district sales (S.) of motor vehicles has been growing according to the model S = So (1 + g, where t is the time. Average sales is 50 units and average time is 4 years. He obtains the following OLS regression results: In S, = 3.6889 + 0.0583 t i. What is the estimate of the instantaneous and compound growth rate? ii. What is the estimate of So? ii. What will be the elasticity of sales with respect to time? iv. Suppose the researcher modifies the above equation and estimates the following regression: S, - 5.6731 + 2.7530 t Interpret the model. v. Compute elasticity of sales with respect to time for the model in part iv. Compare your results with the answer obtained in part ii.
Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
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