Regression Analysis Model in Sales Forecasting

Regression Analysis Model in Sales Forecasting

In the current business environment, future expectations are more essential than the events that were happening in the past. However, the past events are important in predicting the future events. In business, the amount of sales that the business makes in the market determines its profitability and potentiality of growth. Decision-making in any organization depends on how well the organization is able to make predictions about the future since current decisions affect future events. Various statistical methods have been developed in the forecasting of future business environment based on historical statistical data. Decision-making is essential in any organization whether in government or in business and forecasting is critical in decision-making (Mentzer & Moon 2005). In the prediction of sales, regression model provides diverse insights that affect the demand. As such, the model is very useful in sales forecasting. For a regression model to be effective, it must be created and evaluation of the model must be done in an informed way. In management, forecasting is important in the allocation of resources, determining risks and opportunities. Predictions assist management of production scheduling and inventory planning. Sales forecasting is fundamental in determining promotional strategy that will be used in the market (Shim et al 2011).

There are three methods commonly used in forecasting sales. They include time series model, cause and effect models and judgmental models. A regression model is a cause and effect model since it investigates functional relationships between different variables. Cause and effects models are used where there are strong relationships between different variables. For example, in determining the demand of product there are various factors that affect the demand for example price, advertising, income and population. To predict future demand, historical data is used to explain the relationship and to make forecasts on future demand. Cause and effect models are used in both forecasting and policy decisions. There are two variables in cause and effect models, these are the dependent and independent variables. This paper seeks to analyze the regression model as used in forecasting sales. Theoretical and statistical foundations, and the various benefits and shortcomings arising from the model will also be central to this study. Furthermore, the model applications in various fields will be an essential part of this discussion.

Theoretical Foundations of Regression Model

A regression model is a cause and effect model, which uses the independent and dependent variables to explain the cause and effect relationship between the two variables. Regression can either be simple or multiple, where a simple regression involves one independent variable and multiple regressions involve more than one independent variable. The earliest version of the regression model was the least squares method developed by Gauss and Legendre. It was developed to determine astronomical observations. Besides, this model was developed to include the version of Gauss-Markov Regression Theorem (Dahiya 2000). Karl Pearson developed regression further where regression was done towards the mean. Least squares method is a method used to minimize errors in the overall solution of every equation. It involves drawing of a line of best fit where the squared deviations are minimized between the observed value and the fitted value. There are two categories of least squares method, which include the ordinary least squares method and the non-linear least squares method. Gauss published the method in 1809 where he stated that the mean of the squared deviations and the errors are uncorrelated with equal variances (Guerard et al 2007). In a linear regression analysis, the relationship between the regressor and the response variable is linear. It has been used in many applications and mostly in forecasting where it is used to develop a predictive model of an observed data. It is also used to quantify the strength of relationship between the independent and dependent variable. In a standard linear regression model, there are a number of assumptions about the independent and dependent variables and their relationship. However, in every application, some of the assumptions are relaxed while others are eliminated. Linear regression model major assumptions include weak exogeneity where the independent variables are assumed to be fixed without errors while in reality the model’s independent variables vary on the line of best fit. The assumption that the relationship between the regressor variable and the dependent variable are linear does not hold in all the situations. There are various regressions that use the linear regression model. They include the polynomial regression. In polynomial regression, it uses linear regression to fit the independent variable arbitrary to the polynomial function. However, critics have criticized the polynomial regression due to its tendency to over fit the independent variable. It may result in unrealistic solutions, which may be biased, and the result of the estimation process produce untrue results. The linear regression analysis assumes that the variance of the mean deviations is constant (Wang & Jain 2003). The variances of the deviations are not constant in reality and they keep varying. In common, a line of best fit, the errors vary along the line and are not equal, hence, disqualifying this assumption. The errors are not evenly distributed on the line of regression but they are scattered. As such, the assumption should be taken to be proportion to the mean rather than the assumption that it is constant. The assumption of constant variance has led the linear regression mode to produce inaccurate results due to the increased standard errors. Linear regression also assumes that errors are uncorrelated which creates a bias in the data used. The polynomial regression as a linear regression model uses nonlinear independent variables but applies the linear equation (Berk 2004).

Steps in Regression Analysis

The regression analysis involves a process that is carried out using distinct clear steps. Since the model is carried out to forecast a future event, it must state the specific problem. Like in marketing, the problem statement may be forecasting the demand of a certain product for the next five months. In a marketing regression model, the problem statement includes specification of the concrete product whose demand is to be estimated. This is because the general market demand cannot be used to determine the demand of a specific product. The general market factors and the unique factors facing the demand of the product are different. It will be the problem that will be solved in the regression analysis. After stating the problem, the relevant potential variables are selected. For example, in a marketing regression analysis, the problem previously stated as determining the demand of the product for the next five months (Chatterjee & Hadi 2006). The various variables relevant to this analysis include all the factors that affect the demand of the specific product. The general factors that affect the demand of a product include price, income, population, taste and preferences, competition and availability of substitutes. These create the variables that may be used in a regression analysis to forecast the demand. For example, the demand of bread for the next five months will be affected by the own price, price of cakes and buns, other competing brands of bread in the market, and people’s income. This is an example of a cause and effect regression model since the objective will be to use the variable to explain the demand. For example, in our case, the effects of price, income, competition, availability of substitutes and other factors will be examined on the effect they have on demand. The regression may be multiple regressions where the regression is done on all the factors affecting the demand or can be a simple regression where each variable is taken and its effect on the independent variable analyzed. In our case, the simple regression model will explain the effect of price alone on demand of bread, or the effect of availability of substitutes on demand of bread. In a multiple regression, all the factors affecting the demand of bread are taken into account (Wang & Marvin 2002). The next step in regression analysis involves data collection of the variables that have been selected. This is because regression is a quantitative technique, which uses data in analysis. The data include the price of the product, price of related product and price of other substitutes for the last few months as determined in the model. After data is collected, a model that fits the analysis is specified. This model may be either multiplicative or additive depending on the effects of the regressor variables on the response variable. The choice of the model is also dependent on the relationship between the independent and dependent variables. The fitting method is determined after specifying the model. Determination of the fitting method is determined on the reliability, simplicity and the model specified. The fitting model used may be the ordinary least squares method, linear regression, simple regression, polynomial regression and general linear regression (Aladjev & Haritonov 2004).

The simple regression analysis is the one, which contains only one independent variable. It is the simplest form of regression. It involves a single linear equation where all the standard deviations of the equation are drawn on a single graph. The intercepts of the independent and dependent variable are fitted in the single equation. The equation of a simple linear equation may take the form of y = a + bx and its goal will be to establish the points on this linear equation which minimizes the mean of squared deviations. In least squares method, the aim is to fit data between the observed and the fitted value in a model. The mean of squared deviation that minimizes the errors in the overall solution is found by data fitting. There are two types of least squares method, which are the ordinary least squares method and the non-linear least squares method. The choice of method depends on whether the relationship between the regressor variable and the response variable is linear or nonlinear. The ordinary least squares method is used mainly in forecasting and uses linear equations to find the mean of the squared deviations. The nonlinear least squares method uses numerical algorithms and the equations are expressed in power form. The last step in a regression analysis is to ultimately do the estimations based on the data and the fitting that has been done. Based on the line of best fit that has been drawn, one is able to do a prediction of the future (Cox et al 2005). In sales forecasting, regression analysis provides more information than a time series analysis. Regression model analysis provides a framework where the various variables affecting the independent variable are evaluated while in a time series the various effects are based on periods. Regression analysis facilitates the use of correlation analysis, which enables relationship of demand and the external factors to be found. For example, in an equation y = a +bx₁+ bx₂ + bx₃ +………bx_n it displays that there is a relationship between the independent variable y and the dependent variables x₁, x₂, x₃,…x_n. Since only historical data is available, we do not have the true values of the independent variable. Therefore, an estimated model is developed to represent the true values of the model. In sales forecasting the regression model is used to in several applications. First, it is used to explain the behavior of the system. For example, the model may help to identify which factors are related to demand that may help to explain why the demand fluctuates. Regression model also assists in explaining the importance of some factors within the system, which business organization can use to improve sales. For example, in the various factors affecting demand a few factors may have a higher influence on the level of demand than others may. In demand estimation regression model, the effect of price on future demand may have more influence than the income of the individual. Therefore, the firm can make a decision on reducing the price of the product a little to achieve the higher sales. The regression model is also important in the forecasting of demand and the main aim of regression in demand estimation is forecasting rather than explanatory. Like in any other regression analysis, in sales forecasting, one must understand the process of creation and evaluation of the model. Poor model creation and evaluation causes the analyst to make mistakes in the forecasting which might costly to the company use the information provided. For example, the sales regression analysis requires a model that captures all the data that may be affecting the demand. If the model leaves out some critical information about the demand of the product it may misguide decision-making by the firm about the demand of the product (Poitras 2010).

Robustness and Errors Regression Analysis

The theory of robustness in regression analysis has three approaches. They include the qualitative, infinitesimal, and quantitative. They are important in evaluation of the ordinary least squares method, which is used in demand forecasting. Robustness of the regression model provides important information on univariate and multivariate robust data analysis. These techniques are important in evaluation of the model proneness to extreme values. The technique is important in evaluation of the effectiveness of the coefficients used in the model. The model uses the SAS software, SPSS software and S-PLUS software packages to simulate the available data in the model (Shekhar 2008). Errors in the model arise from mistakes in model specification. They may also arise from incorrect use of a variable by omitting a variable or including an irrelevant model. Another potential source of errors in a linear regression analysis is wrong assumptions, which may lead to misspecification of the model. If the assumption of a common mean and common variance does not hold, they may cause serious deviations of the model due to the assumption of normal distribution. If the mean or the variance varies, it will mean that the distribution of the model is not normal and may result in serious errors in the process of estimation. Robustness of the model is the ability of the model to resist against the natural deviations arising from the natural assumptions in the model. These assumptions include the assumption of independence, normality and the constant mean and variance referred to as (homoscedasticity). The errors that arise from these assumptions may rise due to typing errors, transmission or copying. The concept of robustness has three approaches, which are the qualitative, quantitative and infinitesimal robustness. In qualitative robustness, the errors result from small changes in the distribution. These small changes in empirical distribution in the model may result in gross errors and gross changes in the estimator (Finger 2007). The qualitative robustness ensures continuity, which is a sufficient and necessary condition in ensuring that none of the slight changes causes a gross change in the estimator. Infinitesimal and quantitative robustness results, from misspecification of the model and errors in entering the data. These errors include omission of data, typing errors and transmission errors they may result in a gross change in the estimator.

Statistical Foundations of the Regression Model

Learning a certain phenomenon in marketing facilitates prediction the decision consequences that a firm will take to manipulate future outcomes. Regression model is based on empirical observations and the test of these observations is done empirically. Since regression analysis tests the functional relationship between the dependent variable (regressors) and the independent variables (response), the empirical data is collected on all the variables. Regression analysis is a mathematical estimation that establishes the relations between the regressor independent and the response variables. In a simple regression analysis, only one independent variable is involved, for example, the effect of price on demand of a product. Multiple regression involves more than two independent variables, for example, in a demand estimation procedure the regression may involve the price and advertising (Sen & Srivastava 1990). Simple regression analysis equation y = a + bx

Multiple regression analysis equation y = a + bx₁ +bx₂ + bx₃….bx_n

The least squares method of regression is the most commonly used model in forecasting. Least regression analysis involves an attempt to find a line of best fit of the observed data.

u= y – y’

y’ = a + bX

To define the error in the least squares method the difference between the observed value and the estimated value is found in our example above. We have denoted it with U and                    U= Y – Y’.

Where                Y = observed value of dependent variable.

Y’ = estimated value based on y’= a + bX.

The line of best fit minimizes the mean squared deviations of the estimated value and the observed value. The equation below shows the minimum squared deviations

∑ y = ∑a + ∑ bx

The solution obtained minimizes the errors along the line of best fit.

The regression can involve more than one independent variable in a multiple regression analysis. The equation of a multiple linear regression analysis involves two or more independent variables like follows

Y = a + bx1 + bx2 +bx3…….bxn

There are various assumptions in the model which are the assumption of normally distributed residuals, the residual has a constant variance and that the residuals are not linearly correlated.

Validation of the Model

After generating the model, an evaluation is done to validate the use of the model for statistical purposes. Various methods have been developed to evaluate the regression model. They include coefficient of analysis, standard error of the residue, f-test, t-test, Ex-post forecast and review of the assumptions. Coefficient of determination evaluates the changes in the independent variable due to the changes in the dependent variable. It is denoted by R (squared), it measures total deviations and sum of the total residuals. The variance and squared error of the residuals utilize the analysis of variance (ANOVA). It measures the minimization of the squared deviations in a regression model. The sum of the squared errors and the standard error of the model are measured. The model aims at minimizing the squared deviations of the estimated value from the observed value. Hence, the more the deviations are less, the more the validity of the model is. The use of hypothesis has been utilized to test the validity of the model. These hypothesis testing methods include analysis of variance and f-distribution and t-distribution. Confidence levels are developed when we are testing the hypothesis. Ex-post forecast is where various statistical evaluations are performed on the model to determine its validity. Ex-post forecast is a prediction for the periods for which data is already available. There is a number of software that has been developed to simplify the regression analysis. These includes the Microsoft excel the SPSS and S-PLUS, they are used to simplify the regression analysis by automatic analysis of the data (Knopov & Korkhin 2011).

Uses of the Regression Model, Strengths and Weakness

Sales forecasting is usually done using various methods as discussed above. Sales must be forecasted in the right way to ensure that proper strategies are adopted to meet the demands of the market and also to maximize profit for the business. Different methods can be used to forecast sales of any business at any particular time. The business will adopt the method that is convenient to the management and the method that the business understands that it will be correct. Regression model is one of the sales forecasting model that is common with many business that analyze their data using qualitative versus quantitative methods and the time series methods (Schoner & Uhl 2011). As it is stated above, regression model is a cause and effect analysis or a statistical technique that establish the relationship between two or even more quantitative variables. The method considers two values; one is the dependent variable that the research wishes to establish while the other is the independent variable or the explanatory variable. The independent variable is the one whose values are known and available. The technique is able to establish the relationship by getting the equation that relates to the two variables. A simple regression model will be able to establish the relations between the two variables by indicating that the independent variable and the dependant variable are linearly related. The dependent variable must be continuous meaning it has to be able to take any value or close to continuous while the independent variable can take any of the value either continuous or discrete. This can be mathematically said to have linear equation Y= a + bX (where a and b are constant). It can be explained that dependant variable y is linearly dependant on independent variable x. The other regression model is the multiple regression models that relate to more than two variables. This regression provides equation that predicts variation of more than two independent variables Y= a + bX₁+ cX₂+ dX₃. The independent variable y depends on the three independent variables (Schoner & Uhl 2011).

Strengths of Regression Analysis

The use of regression analysis to forecast on sale has several advantages. Business people will use the analysis to predict the future sales of their product and, hence, to be able to meet the demand when due. One of the advantages of the regression model is that it provides accurate results. Managers are able to predict the sales volumes accurately and come up with the objective measures of the connection between the explained variable and the explanatory variables. It enables managers to avoid using personal judgmental purely in making a decision which can in most cases be misleading. The use of the regressions analysis usually gives more accurate results that will be reliable in decision-making. The other parties can also empirically test the findings either by the same data or separate data without resolving on personal opinions. After management obtains the results electronically, then they use the computers that have the some software packages for statistics like R-square and the student t-value statistics. The managers will be able to determine the accuracy of the results they obtain from the regression analysis and, hence, the reliability of the results for predictions purposes (Witten & Frank 1999). Another advantage of the regression model is that managers of businesses can be able to use multiple regressions to examine how different independent variables explain characteristics of the dependent variable. The concerned party can test for all the factors they may think that are likely to affect the dependent factor or variable (Gujarat 2011). It makes regression model a better model for analysis than other models because it is able to test for more than one factor that affects the dependent factor. When more than one independent factor is used the accuracy of the information is improved. Regression analysis has made the work of sale forecasting very accurate. Data is analyzed within a short period and the results provided. Many businesses are able to predict the future of their sales accurately and, hence, are able to meet the required demand when the time for it comes. Some of the businesses that realize that they are likely not to be able to make sales in the future will engage more in advertising and activities that will ensure they maintain their customers (Gujarat 2011).

Weakness of Regression Analysis

Regression analysis is widely used in forecasting sales. It provides accurate and reliable data that enable business people to predict the future demand of the business of their products. However, despite the widely acceptance of this method, it has some limitations that hinder some people from using it and even those using it have to cope up with. The business person can decide to use linear or multiple regressions to forecast the sale depending on the factors affecting the sales of that business. The linear regression only focuses on the linear relationships between the independent and the dependant variables. It assumes that there is a linear or straight line relationship between these variables. This assumption may not always be correct. For instance, relationships that exist between income and age are not straight but curved. It simply means the income that a person has does necessarily increase with his or her age. The income of person tends to increase at the early age when the person has the energy to work, flattens out in the later adulthood of person when the person has almost climax of his or her life and declines in the late part of life when the person is almost retiring. The graphical representation is not straight but curved as the age of person rises (Ferber 1974). The other weakness of the linear regression model is that it only considers the mean of the dependent variable. The approach only looks at the relationship between the mean of the dependent variable and the independent variables .For instance, when analysis the relationship between the maternal characteristics like age and the weight of an infant at birth, the linear regression will consider the mean weight of the babies born to mothers of various ages. The linear analysis does not consider the extreme situation of the dependent variables. For example, his analysis will not consider the fact that babies are at risk when their weights are very low. The mean that the linear regression considers does not fully describe a single variable. Similarly, linear regression does not completely describe the relationships that exist between or among variables. In addition, linear regression does not consider the data that are outlying. It is not sensitive to this kind of data. Outliers are data that are surprising and they can be univariate or multivariate (Witten & Frank 1999). For instance, it can happen after the analysis of age and income when there is a person with age 120 years and who made $20 million. On the other hand, multivariate outlier could be a person of 18 years old who made $ 200000. In this scenario, the age or income given is not extreme but the very few people aged 18 years are able to make such amount of money (Ferber 1974). The outlying values in the statistics have a great effect on the regression. The linear regression model can only work with data that are independent. It means that the score of one item has no relations to the score of the other item or function. This assumption by the linear regression happens to be the case with most of the data must not always the case. The assumption is not always sensible. Two of the major instances of the data that are not sensitive to this assumption of the linear regression are the clustering in space and time. An example of the data of the clustering in space is the student test score. The data about students’ performance can be analyzed and it will have various like classes, grades, schools and school districts. The characteristics of the student will tend to the same because these students come from the same areas, taught by the same teachers and are involved in almost the same activities. It simply means that the data of such analysis cannot be independent. Moreover, the data on the clustering in time will also not be independent (Lawrence & Arthur 1990). An example is where the same object is measured in many times. In the study of diet and weight, for example, the same person may be measured many times (Gaughan 2009). The data collected in such a situation will not be independent because the way a person weighs on occasion will be dependent on what the weight of the same person in other occasions was. Multiple regression analysis of the sale data has the disadvantage in analyzing the data. The model requires input value for every independent variable. The technique that exists that can be used to interpolate the missing data from the observations will reduce the accuracy and make it hard to predict. In some situation, information given for all the independent data may not be correct or accurate and it may only be obtained sequentially (Kahn 2006). This will make it hard for the model to forecast the incident. However, it will not be seen as a great threat because the value of the independent variable will be available when the situation occurs. The techniques of regression in analyzing the sales data in order to be able predict the future values are very demanding. The method will require quantitative data relating to the several people or items (Gaughan 2009). This quantitative data may require to be collected from the field and analyzed. The data required in terms of the total sale made during a particular season may require not to be easily available and, hence, time for collection of this data must be created. It would simply mean that for this approach to be used time will be consumed and the method is also expensive to use. In addition, the regression model is likely to arrive at the conclusion that the there exists a strong relation between two or more variables whereas the contribution of the other crucial factors could have been captured. For example, the sale of some items may be dependent on the climatic condition of a place. If this factor is not one of the independent variables of the sale regression model, then the conclusion will not be correct. This kind of error is called snooping (Buckner 1998). It means that the tool must be used with a lot of care. The regression model is only limited to the relations where certain factors have effect on one certain factor. If there exists circular relation where the relation between the explained and explanatory variable is circular and each factor influences the other, the regression model may not be applicable. For instance, if sales volume will affect the number of customers and at the same time the number of customers has an influence on the sale volume, the regression analysis cannot be used in this scenario. Another weakness of the regression analysis model is that the observations made must give enough contrasting evaluation to enable easy establishment of the influence independent variables which they have on dependent variables (Guerard & Guerard 2005).

Application of the Regression Model in Market Decision-making

Regression model has been used in several areas as well as in predictions about the future sales of products. Some of places that the regression analysis has been widely used are the time series forecasting method. Data is analyzed moving averages and exponential smoothing averages. The data is then further analyzed using the regression model (Mendenhal &Sincich 1993). The data of all sales made in all previous months are analyzed and the data is put in the regression model to determine the future or predictions of the sales. The manufacturer or the managers are able to know the amount of product that they produce. This analysis will also enable the managers to know what has to be produced in the market and ensure that the market demand is met (Guerard & Guerard 2005). It will ensure that there are no excess products in the market that will affect the product prices and areconsequently affecting the economy. The analysis will also enable managers to know what is to be stored in the warehouses waiting for to be sold in the future. What is required in the future will also dictate the amount of raw materials required to be purchased to ensure a continuous flow of production. Another day to day application of the regression model is the constrained regression procedure for estimating market potentials (Shim 2000). The clear justification of the constraining estimate is the presence of information from sources other than from the statistics that are just developed. For example, the basic problem may be described as the relationship of people in certain areas and their income. The income of people will influence the total sales that people make in a given situation (Blattberg & Allenby 2010). The regression analysis in this case will be used to establish the relations that exist between the population in certain areas and the income of these people. Income is one of the factors that affect the demand of the product and, hence, when the income of people in a certain area is high, the sale in that area is likely to be high. Regression analysis model will be very important in establishing such relations. In the same analysis about the population and the income, the population is also a major factor in influencing the product demand (Buckner 1998). The regression analysis will be used to establish the effect the population has on the product sale in the certain areas (Mun 2006). The managers will be able to know the effect of the population and whether the sales of the company are directly related to the population. The knowledge of how the population affects the sales in the market will enable managers to make an informed decision on where to sell his products. Heterogeneity of the consumers has been clearly brought out by the regression analysis. The consumers’ behaviors are a very important factor in the marketing decision-making. Consumers will behave differently in various situations and, hence, there is a need to understand how they affect the sales of products. Marketing decision will depend on the regression results that arrived from the data collected and analyzed. Further, regression model can be used to indicate the slow moving products. Managers of the business will be able to make a decision on the stocking of such products and avoid oversupply in the market .The regression model will also be used in the monitoring of the risky of the unauthorized payments that may be received by the business (Blattberg & Allenby 2010).

In conclusion, sale forecasting is very important in any business unit. The businesses are established with the primary goal of making profits and improving the welfare of the public and business as well. Therefore, it is very crucial to establish what the customers require in a particular time and what the business is able to produce. The managers are able to know when to produce, whom to produce to, when to take the product to consumers and how many the products to sell. As it is discussed above, the product market is affected by many factors at all times. However, the way and the magnitude of the effects are different to different factors. It makes important to use forecasting model to establish the relationship that exists in the independent variable and the dependent factors. Most of the business will apply the regression analysis to forecast the sales at a certain time of the accounting period. The regression model will involve a number of steps that must be keenly followed to ensure proper decision is made (Krajewski et al 2011). Decision-making in any organization is very important and, hence, the reason why such decisions are only left to the senior management to make. This is because marketing decision would either result into total flourishing of the business or bring it down. Product manufacturing is a very expensive task and managers must be able to ensure that only what is produced is required by the market especially business that deals with perishable products (Horngren et al 2012). The acquisition of raw materials must be made in the right time to avoid congestion in the store and the loss of value of the raw materials waiting for processing. All these decisions can only be made if a proper forecast of sales in the future is made in the right way that will give accurate results that are reliable to decision-making. The steps involved in regression analysis are tedious and time consuming. It has been made easy by the regression software that will analyze the data and give the finding within a very short period of time. The time consumed in the collecting the data and expenses incurred can be easily reduced to reasonable values if all the data are properly kept in a logical way to ease the work of retrieving the data when required. The data for the business is supposed to be kept properly in the machine and given some backup systems to ensure the information is safe. Wrong forecast of information can be very dangerous to business. Managers must be very careful on the data that they will rely on in making their decision. Some companies that inaccurately regress their data. It can result into losses and even closure of the business. The two types of the regression analysis are used in a different situation depending on the nature of the market. However, the linear regression is really used because it deals with only two factors whereas in most cases the sales of certain products are affected by more than one factor. In addition, though the regression analysis has several advantages and many businesses are at great use, it has several challenges that may hide its effectiveness. Therefore, despite the challenges that are associated with the use of the regression analysis, the advantages the model has are far beyond the challenges. Business people will make data analysis very easy and the employees enjoy doing the work. The contention of employees in the workplace has a great impact on their productivity. Moreover, when the future becomes predictable, it is easy for the manager to plan with employees and set targets that are realistic and achievable in a certain period of time (Horngren et al 2012).