Models

Modeling involves the use of historical data that helps come up with a function that will aid in predicting future values, for example a business may want to know the value of sales in the future so that the stocks levels are not in excess or too low that they may not meet the demand of the consumers.

Models are widely used in almost all the industries to make forecast on various issues, however proper models must be estimated in order to reduce uncertainty in prediction, the first step is to specify the model to be estimated, Model specification is made on the basis of existing economic theories or existing hypothesis, therefore improper specification of models will lead to wrong conclusions when the model is used to **forecast** or explain relationships between variables.

The wrong mathematical form of a model may be chosen, example we have to choose whether the mathematical form of the model is linear or non linear, therefore choosing the wrong mathematical form will lead to errors in the model.

Single and multiple relationships have to be determined whereby we choose the relationships between the dependent variable and independent variable or variables, however this choice will depend on the complexity of the relationship, the purpose of the model, availability of data, computational facilities available and the resources available. Also the existence of errors such as omission errors, mistaken mathematical forms and omission of variables will lead to incorrect conclusions.

From the above discussion therefore it is clear that model specification is the most important but

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yet the most difficult, incorrect specification may be as a result of imperfect statements in the hypothesis or theory, knowledge limitation of factors to be included in a particular model and finally the obstacles that may be faced such as unavailable data.

Bayes:

Thomas Bayes was born in 1702 and he was both a mathematician and also a minister in the Presbyterian Church, he studied logic and theology in the University of Edinburgh. He later introduced his theory on probability where he helped explain both conditional and marginal probability. His theory gives a guide to the calculation of probability of occurrence of two random events given the probability of their occurrence.

His theory has been used in computer programming especially in the health industry, it most commonly used in diagnosis for various diseases in the health industry which helps medical practitioners to establish with certainty the health disorders among patients.

Skewed:

A normal distribution is symmetrical with a bell shaped curve when the values are represented in a chart, however when we have asymmetry we describe the data as negative skewed or positively skewed, negative skewed data means that the majority of observations are on the lower levels of the scale used, however positive skewed means that majority of observations are on the upper levels of the scale used.

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In a normal distribution the mean is equal to the mode; in negative skewed data the mode is greater than the mean while in positive skew the mode is less than the mean. Therefore we can establish whether data is skewed by observing the values of the mean, median and mode; however we can also calculate the value of skew ness in the data to determine positive or negative skew.

Deviation:

Standard deviation is the measure of dispersion from the mean, it measure the value of deviations of data from the means. Larger values of standard deviations means that data deviates more from the mean while a small value of standard deviation means that data deviates less from the mean.

To achieve a large value of standard deviation then this means that data must deviate more from the mean, in order to achieve large standard deviation then we should measure values of data that has large differences between elements of data example values like 0, 100, 1000, 5000,20. This data will give a large value of standard deviation.

To achieve a small standard deviation value then the data will deviate less from the mean, for example if we collect the following elements of data which are 12, 11, 13, 14, 10, 9 ,8 12 and 14 then this set of data will have a small value of standard deviation.

Risk:

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Risk avoider:

A risk avoider is a situation where an individual completely avoids an action that may lead to loss or damage, example in my case I will not buy any company shares because there may be a devaluation of the shares that may result into the loss of my invested money.

Risk taker:

A risk take is an individual that may take actions that may probably result into losses or damages, in my case I am a risk take in some situations example I ride my bike without any protective gear on.

Risk neutral decision maker:

Attending school is a risk neutral decision I make, this is because there is no risk involved in this activity.

From the above discussion therefore I am both a risk taker and risk avoider in different situations, the risks levels change with each situation in my day to day activities.

Forecasting:

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In business forecasting is an important tool used in management, the most common forecast is the sales level forecast, it is used to determine or estimate future sales levels, example a car sales company that finances its car stocks using both capital and loan from banks will need to have proper forecast in order to avoid high cost of borrowed capital if the stock is higher than sales over a period of time.

The model used to forecast takes into consideration the income level in the country, interest rates, seasonal adjustments in demand for cars and finally the price of cars. Using historical data the model is estimated to help in forecasting. Forecasting has been helpful in determining the level of capital to be borrowed depending on the expected demand levels as the variables increase or decrease. However this model can improved by adding other independent variables such as the inflation rate and consumer tastes and preferences of the different car models

Delphi:

the Delphi approach is a decision making tools that involves gathering information from a number of experts with the aim of achieving an accurate model for business decision making, the company I work with uses this technique whereby various department heads are asked to come up with estimates and then the results are discussed and the final estimate is used. This is a method that reduces biasness in estimation.

in a company where such a system does not exist to make accurate decision, it can be simple to implement, the first step is to get a group of experts who will estimate example sales levels, the next step is to provide them with the information on what is to be estimated, after the experts finish estimating a group discussion is held and this is where the median estimate is taken and results discussed. When this is done experts are then expected to come up with another __independent__ estimate and in the final meeting of the group a consensus is reached on what estimate to be used in the business.

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This approach therefore reduces bias in estimation and therefore ensures that a business makes the right decision.

Sensitivity:

Sensitivity analysis involves analyzing mathematical __models__ with the aim of quantifying the variations in the model, estimated **models** may produce uncertain results and through sensitivity analysis a company is able to reduce uncertainty. It is an important tool in that modeling involves the use of past data to estimate future outcomes; however this may not be the case in future and therefore may lead to uncertainty.

at work sensitivity analysis is used to check the consistence of a model through use of different samples, this involves selecting different samples from existing data and estimating the model, this is a way of reducing uncertainty on the model that will finally be used to forecast, the outcomes of each model are analyzed and decisions are made regarding the consistence of the models. It is useful in that it helps reduce uncertainty and therefore aid in making proper decisions.

Costs:

sunk costs are those costs that are incurred by a firm and they cannot be recovered in future, relevant costs are those cost that are considered in decision making and **they** will reduce or increase depending on decision made, for this reason therefore sunk costs are not affected by management decisions while relevant costs are affected by decisions made in a firm. an example of a sunk cost is where a firm acquires a business license, this cost cannot be recovered in the future and therefore management decisions should always avoid such costs, relevant cost include costs incurred in acquiring new processing equipments and their running costs.

DEA:

DEA is a linear programming method that is used to estimate production in future using the

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**Models**

most efficient method, it is a method that is used in cases where there is multiple output and inputs in the production process, it is anon parenthesis method of estimation and very useful in decision making especially production plans.

The advantage of this method is that there is no need to specify mathematical forms, it is a useful method in determinant relationships between variables, it is possible to include multiple outputs and inputs and finally it can be used to determine points of inefficiency in the production process.

This method will therefore be useful to a company that has different inputs and different output in the production process, the company will be in a position to determine the most efficient way to produce and that the company will be in a position to detect cases of inefficiency in the production process.

Solver:

We allocate the units as follows and because the supply is greater than the demand then we include a dummy variable:

DETROIT

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MIAMI

SN FRAN

DUMMY

TOTAL

UNITS

COST

UNITS

COST

UNITS

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COST

__UNIT__

COST

NY

80

15

20

17

0

29

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Models

0

0

100

UT

0

14

40

15

50

22

60

0

10/18

Models

150

TX

0

16

0

18

0

21

125

0

125

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**Models**

TOTAL

80

60

50

185

375

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Therefore we have to allocate the following units to each plant:

DETROIT

MIAMI

SN FRAN

TOTAL

NY

80

20

0

100

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Models

UT

0

40

50

90

TX

0

0

0

0

TOTAL

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80

60

50

The total cost is therefore 3240

Functions:

The most useful data analysis formulas include the average function, variance, standard deviation, median, maximum, minimum and the sum. The sum function will give the total for all values included in the worksheet; this can help to calculate the total of thousand units of data with accuracy and at light speed and this ensures accuracy and minimum time used to calculate the totals. The other important function is the average function that helps find the mean of a given data set, the values provided are accurate.

The standard deviation and the variance functions are data analysis *function* that helps to determine the dispersion of data from the mean; this is an important function in that it helps in making proper and accurate conclusions about a given data set. Finally the minimum function helps determine the smallest value in the data set while the maximum value helps determine the maximum value in a given data set.

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DATA ANALYSIS:

The first most important function is the sort function, this function helps in arranging data in an ascending or descending order and therefore helps determine the minimum and maximum values in a given data, it helps in determining percentage of data that is below a given range. The other important function is the text to column function, this function helps to turn data from other sources into excel data, example when data is transferred from a word document into an excel worksheet, one is required to specify the symbols that are between columns and therefore helps reduce the work of having to copy and paste each data unit into the excel worksheet. The group ungroup and subtotal functions are also important in analyzing data; they also help in analyzing a data set.

DEMOS:

The demo section gives guidelines on the various functions in excel, one of the most important function is the add function which involves selecting the data you want to add and an empty cell at the bottom and then clicking on the symbol ∑, this automatically adds up the selected area and the total is reported on the empty cell earlier selected.

The other most important demo is how one can specify the a function on one cell and then auto fill to other cells, example if we have tow series of data and want to add them up to the next column then we can specify the functions in the first cell and then auto fill the function into the other cells.

QUEUE:

I always queue for services or products, one of the most common include ATM queues, bank and food and services Queues, these queues are due to high demand for services and products in certain areas and they can only be reduced if there are more places that offer the same services and products.

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The queue I dislike however the ATM queue is where sometimes I have to wait for a long period of time, there is always an alternative to withdraw cash from inside the bank but people still make long queues to access ATMs.

LP5 DESCISION TREE:

a decision tree is a statistical diagram drawn to show the possible outcomes and their probabilities, it is important in determining the possibility of an outcome and it is used in decision making, example a firm may be faced with a business plan that may result to many outcomes, the outcomes may also have other possible out comes, below is an example of a decision tree:

the advantages of a decision tree is that it helps in decision making, the highest earning and highest possible outcome is chosen and therefore helps to predict and give probabilities of certain outcomes. The disadvantages of using a tree diagram is that it depends on already established possibilities and possible outcomes and therefore may limit decisions made under uncertainty.

From the above tree diagram it is evident that the probability at each stage is 100% for both situations, example the probability of a and b is 50% + 50% = 100, the same case with C and D where 25%+75% = 100. We can now determine the probability of A happening and at the same time C happening and this will be derived by multiplying probability of A and probability of C, in this case it will be 50% X 25%. Therefore the decision tree will help in decision making.

LP5 CHARTSGRAPHS:

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Charts and graphs are diagrammatical presentations of data and values, this representations helps in making conclusion about the data and also shows the frequencies, trend and the increase or decreasing nature of time series data. There are various types of graphs and charts and they include line graphs, bar charts, and pie charts and scatter diagrams. For this reason therefore graphs are useful in summarizing given data values and also they help in making conclusions about data.

the disadvantages of using graphs is that they require accurate measure of values and in some cases where the data range is wide the physical appearance may not reflect the true nature of the data, for this reason therefore graphs and charts may mislead interpretations about data.

The following are examples of graphs and charts:

Below is a line graph:

Below is a bar chart

Below is a pie chart

References:

Nelder J and Mead R (1995) A Simplex Method for Function Minimization, McGraw Hill press, N ew York

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