# Regression Analysis in Strategic Decision Making

Regression analysis is a powerful statistical approach that helps to predict the magnitude of one variable from the magnitude of other variables. Further, it provides a measure of how one variable is related to different variables. Thus, regression equations are plotted to estimate the value and direction of the dependent variable from the direction and values of the independent variable. The dependent variable is also called the criterion, while the independent variables are referred to as predictor variables. This is because the change in magnitude and direction of the independent variables will affect the dependent variable too. Hence, in brief the value of the dependent variable will be subjected to change if the magnitude and direction of independent variables changes. However, such cause and effect relationship may only be acknowledged if the dependent and independent variables are significantly correlated o each other (Freedman, 2005).

From the aspect of management decisions and managerial role profiles, regression equation may serve as a robust measurement of performance analysis. Each and every industry thrives to produce optimum performance and profitability. Hence, the employees of any organization are the backbone of any organization. The expertise, skills, knowledge and motivation are all key deciding factors in driving the productivity of an organization. From time to time, various managerial decisions need to be taken, to increase performance or downsize the workforce, which calls on for a critical analysis. Regression analysis provides a direction, which can influence the strategic decisions of management in a scientific way, without any opportunity of elemental bias. Understanding the factors which drive performance and at the same time understanding those factors which reduce the performance of employees, helps the management in their decision-making process.

Decisions can be taken to aid the employees with training and skills, it may implicate reducing the workforce, or change of managerial positions for the unit. Regression analysis would also help to understand the psychological and compensation issues which drive performance and productivity. Analyzing such variables helps management to relook into the compensation benefits of employees and designing of work. From the aspect of Ergonomics, it is hypothesized that performance and productivity of employees depend on a variety of factors. It is prudent, that for optimizing performance the “task should fit the man” and not the concept of “fitting the man to the task”. This is because a human being has physical, physiological and psychological limitations, which the management of any organization must accept. Therefore, they should look into those variables, which can be feasibly aligned to the employees. Regression analysis provides an estimation of such variables in the job place, which helps in improved performance of employees, within their physical, physiological and psychological limitations (Malakooti, 2013).

Regression equations are based on the philosophy of equation of the straight line and such equations are called linear regression equations. Linear regression equations are divided into two types, simple and multiple regression equations respectively. In simple regression equation the magnitude of the dependent variable is predicted from the magnitude of a single independent variable. On the other hand, in multiple regressions the magnitude of the dependent variable is predicted from the magnitude of a set of independent variables. Another form of logistic regression is based on non-linear kinetics, and it also helps in predicting the value of a dependent variable from the value/s of the independent variable. In the case of the logistic equation the two variables need not be correlated in a linear manner. Therefore, the general equation of a simple regression analysis is (Aldrich, 2005):

y= mx + C

Where, y represents the dependent variable

x represents the independent variable

m represents the slope of the straight line ( the coefficient of correlation)

C represents the y-intercept.

For finding the most likely value of one dependent variable from the set of values of one or more dependent variables, the correlation coefficient should be significant. A correlation coefficient may be positive or negative and has a value between -1 to +1. A positive correlation indicates that increasing the value of an independent variable, will also increase the value of dependent variable. On the other hand, a negative correlation coefficient indicates that increasing the value of the value of an independent variable will decrease the value of dependent variable. After a positive or negative correlation is estimated, it is important to evaluate whether such correlation coefficients are statistically significant (Aldrich, 2005).

The null hypothesis contends that there is no correlation between two variables considered for relational analysis, and any correlation has happened due to chance factors of random sampling. The null hypothesis is retained when the p-value is greater than at least 0.05. This means that out of 100 observations, more than 5 observations of such correlation has happened due to chance factors of random sampling. Hence, the null hypothesis would be retained and it will be contended that there is no relation between the two variables. It also means that such independent variable should not be included in the regression analysis.

On the other hand, alternate hypothesis contends that there is the significant correlation between two variables considered for relational analysis, and the correlation has not happened due to chance factors of random sampling. The alternate hypothesis is retained when the p-value is less than at least 0.05. This means that out of 100 observations, less than 5 observations of such correlation could happen due to chance factors of random sampling. Hence, the probability of null hypothesis would be considered too low and would be rejected. On the other hand, the alternate hypothesis will be retained and it will be contended that there is the significant relation between the two variables. It also means that such independent variable should be included in the regression analysis (Aldrich, 2005).

Hypothetical Case Study

The management of company “X” is bothered by the production of valves for the last two months, which have significantly decreased. The company decided to downsize the workforce to meet the desired profitability. However, they called upon the Works Manager and asked for his opinion. The management thought that the manufacturing department had some senior employees, and, therefore, age might be a causative factor for such performance. On the other hand, the company introduced a new technology for the production of valves. The Works Manager apprehended that employees may have some complexities, in adjusting to the new technology. Management was very serious and asked the Works Manager to provide an immediate report.

The Works manager suspected that either age or complexity may be a hindrance to production, but that should be verified. The Works manager went up to the manufacturing unit and collected relevant data, regarding the age of employees and complexities faced by them. The complexity rating was evaluated by a qualitative question “How do you rate the complexity of the new technology?” The rating was put on a scale of 1 to 3 and the production of each employee was based on the output sheets in their daily performance register. The Works Manager employed a random sampling methodology, interviewed and collected data from 10 individuals. The data was used to frame the regression equation based on R programming software. The hypothetical data is represented in Table 1.

Production

(number of valve units produced in last 5 days) Complexity

(Scale of subjective rating 1, 2, or 3 Age

(in years)

10 3 23

12 3 40

17 1 38

9 3 42

14 2 26

16 1 40

10 2 21

9 3 35

8 3 39

16 2 42

Table 1: Indicates the data collected from 10 individual employees engaged in the production of valves. The production of valves was estimated for the last 5 days.

Regression Equation

The regression equation framed considered age and complexity as the independent variables and production (number of units produced) as the dependent variable

Multiple Linear Regression – Estimated Regression Equation

Production= -3.4524932053913 Complexity+0.085639802540353 Age+17.077597204504

Multiple Linear Regression – Ordinary Least SquaresVariable Parameter S.E. T-STATH0: parameter = 0 2-tail p-value 1-tail p-value

Com[t] -3.452493 0.753475 -4.582093 0.002537 0.001269

Age[t] 0.08564 0.076459 1.120081 0.299633 0.149816

Constant 17.077597 3.282439 5.202716 0.001249 0.000625

Variable Partial Correlation

Com[t] -0.866003

Age[t] 0.389854

Constant 0.891364

Multiple Linear Regression – Analysis of Variance

ANOVA DF Sum of Squares Mean Square

Regression 2 78.710749 39.355375

Residual 7 24.189251 3.455607

Total 9 102.9 11.433333333333

F-TEST 11.388845

p-value 0.006298

Analysis

The regression analysis clearly indicated that production was significantly related to the perception of complexity. More the individual felt complexity with the new technology, reduction in production would occur. This was evidenced by the negative correlation coefficient of complexity, which was statistically significant also (p<0.05). On the other hand, age was not at all related to the production of valves (although equation shows a positive correlation, but it was not statistically significant). Moreover, the regression equation is also statistically significant as the p-value was 0.006298.

Therefore, the Works Manager went up to the management with this report and suggested training programs to be implemented for making the employees more versant with the new technology. Further, he also suggested that there is no need to downsize the employees based on age, because it was not a determining factor for production of valves.

Discussion and Conclusion

The above situation and analysis indicated that regression equation helps to formulate the strategic action plan, without any bias of management. However, it may also be speculated that there can have various driving factors which influence the production or any dependent variable and identifying all the independent variables concertedly may impose a problem.

References

Aldrich, John (2005). “Fisher and Regression”. Statistical Science, 20 (4), 401–417

Freedman, D. (2005).Statistical Models: Theory and Practice, Cambridge University Press Malakooti, B. (2013). Operations and Production Systems with Multiple Objectives. John

Wiley & Sons

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