SuperPart Industries is a renowned and fictitious automobile parts manufacturer with 9800 employees and bears no resemblance to any existing organization. SuperPart wishes to study its full-time workforce by developing an employee profile that measures factors such as income, career progress and job-satisfaction. It is a survey of a random sample of 400 staffs conducted via inter-office mail. The executive Manager of the Company is the planning maker and manages company demand and employees’ welfare (Strohmeier 2013). Manager takes planning to prosper his company and satisfy his employees in various ways. He is in charge of assisting Human Resources matters.
The executive manager of the company is interested about the running process of his company. He is concerned about the demand, choices and needs of the employees of his company. He would like to go through all the conclusions drawn by the report and prepare the future planning. Manager suspected few matters and he tried to have some guidelines. He also has some factor like age, working years, job satisfaction, union membership oriented queries. After all, he needs to stop the resignation of employees in the coming sessions and optimize the satisfaction level of the employees.
The report provides the detailed validation of Manager’s suspicions and answers his queries. It would definitely help Executive Manager in next meeting or discussion. The report provides updated excel data sheet, necessary calculations and graphs for perfect visualization.
The summary measures of age of the employees is given below:
|
Summary Measures |
|||||
|
Min. |
1st Qu. |
Median |
Mean |
3rd Qu. |
Max. |
|
18 |
32 |
38 |
39.41 |
46 |
69 |
Relation between age and Occupation:
Estimate Std.Error t-value Pr(>|t|)
(Intercept) 40.0154 1.32272 30.252 <2e-16***
Occupation2.Prof’nal 0.06037 1.86351 0.032 0,974
Occupation3.Tech/Sales -1.9628 1.93513 -1.014 0.311
Occupation4.Admin 0.01538 1.87061 0.008 0.993
Occupation5.Service -0.18780 2.38140 -0.079 0.937
Occupation6.Prod’n -0.71909 1.96356 -0.366 0.714
Occupation7.Laborer -1.42163 1.87790 -0.757 0.449
Harrell Jr, F.E., 2015. Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis. Springer.
Residual standard error: 10.66 on 393 degrees of freedom
Multiple R-squared: 0.005154, Adjusted R-squared: -0.01003
F-statistic: 0.3393 on 6 and 393 DF, p-value: 0.9159
Here, the linear regression model is-
Age = 40.01538 + 0.06037*(2.Prof’nal) – 1.96275*(3.Tech/Sales) + 0.01538*(4.Admin) -0.18780*(5.Service) – 0.71909*(6.Prod’n) – 1.42163*(7.Laborer).
This summary measure reflects that the values of t-test of different labels of Occupation are negligible except manager. Occupation 1, Manager effects significantly age factor. The summary table indicates that manager, Professional, admin have positive linear relationship with age but laborer, production, service, technical and sales sector workers have negative linear relationship with age.
The linear regression model shows that due to very small value of multiple R2 (0.005154), overall the two regressing factors age and occupation does not have significant linear relationship (Harell 2015).
Relation with age and working hours:
Call:
lm(formula = age ~ WorkHrs)
Residuals:
Min 1Q Median 3Q Max
-21.462 -8.066 -1.066 6.873 27.605
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 44.8983 2.4473 18.346 <2e-16
WorkHrs -0.1208 0.0526 -2.297 0.0222
Residual standard error: 10.55 on 398 degrees of freedom
Multiple R-squared: 0.01308, Adjusted R-squared: 0.0106
F-statistic: 5.274 on 1 and 398 DF, p-value: 0.02216
The linear model between age and Working Hours is given as-
Age = 44.8983 – 0.1208*(WorkHrs).
The small value of multiple R2 (0.01308) shows that a very insignificant linear relation lies between age and working hours. It infers that the aged peoples, that is, above 50 has comparatively less working hours than young people. The young person, whose age is below 50, especially 40 to 50 provides maximum working hours to the company.
Relation between age and Income previous taxes:
Call:
lm(formula = age ~ PreTaxInc)
Residuals:
Min 1Q Median 3Q Max
8.945 -7.823 -1.162 5.866 31.779
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 30.90497 1.89138 16.340 < 2e-16
PreTaxInc 0.17163 0.03671 4.675 4.03e-06
Residual standard error: 10.34 on 398 degrees of freedom
Multiple R-squared: 0.05205, Adjusted R-squared: 0.04967
F-statistic: 21.85 on 1 and 398 DF, p-value: 4.032e-06
The linear model between age and the income previous taxes is given as-
Age = 30.90497 + 0.17163*PreTaxInc.
Clearly, here age has an insignificant linear relationship with the income before taxes.
Brief Descriptions of the relations between age and working hours, age and occupation, age and before-Taxes income:
We have calculated the summary measures between age and three factors like Occupation, the number of hours worked and Before-Taxes income one by one. The linear model between age and occupation shows that though age has significant relation with manager but overall no significant linear relation was observed. Similarly, no significant multiple regressing values between the models age and number of hours worked, age and Before-Taxes income show the insignificant linear relationship between age and those two factors.
Job Satisfaction:
summary(JobSat)
Very Sat 2.Mod Sat 3.Little Dissat 4.Very Dissat
185 171 27 17
This graph and summary measures of different levels of job satisfaction indicate that most of the employees of the foundation are satisfied. Almost half of the satisfied employees are moderately satisfied and the rests are Very satisfied. Some candidates are little dissatisfied and few candidates are very dissatisfied to work in this financial company.
Relation with Union membership of the employees with their job satisfaction:
Firstly, the graph indicates that the no union members are greater in number than yes union members. The Yes members of union and very satisfied are comparatively in greater ratio than the members who are not the member of Union and are very satisfied. The employees who are in no union category are greater in number who are very satisfied than moderately satisfied. However, in case of “yes union” category, the number of very satisfied employees are less in number than moderate satisfied category. Dissatisfied employees are also greater in number in case of the employees who are the members of the union. Both very and moderate satisfactory level if taken together, then the number of employees in “No Union” is greater than “Yes Union” members are. It is that, the unsatisfied employees are present in more number in “yes category” than “no category”.
It is easy to say that those who are not the members of any Union are much satisfied to this job.
Relation between Job Satisfaction and the Working Hours of the employees:
The graph and box plot shows that the median of working hours in case of very satisfactory level, moderate satisfactory level and very dissatisfactory level are either 40 or very near to 40. However, the median value of the little dissatisfied employees is around 44. Therefore, we cannot find any direct relationship between amount of working hours and job satisfaction level.
We also observed that the spread of working hours of the employees in very satisfaction level is comparatively greater than other levels of satisfaction.
One Sample t-test
data: EmpYears
t = 20.689, df = 399, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
90 percent confidence interval:
7.975233 9.356367
sample estimates:
mean of x
8.6658
The one-sample t-teat of average working years of the employees show that mean of average working is 8.668 and 90% confidence interval of employing years is (7.975233,9.356367). The excel sheet shows that the number of employees who are working in the company in the confidence interval is 15 in number. It is less than 10% of the sampled 400 employees. The t-value of the years of employment is 20.689, therefore the employees who are 44 in number can leave the company (more than t-value). Therefore, the suspect of company that next year more than 10% of the members are going to leave the company is true. Notec that, we have taken 90% confidence interval in order to find 10% level of significance of the members.
45.4325
The graph shows that the estimated means of the working hours in case of both “No Union” and “Yes Union” category are near 45 and almost same to each other. The overall mean of working hours is 45.4325. Therefore, we can state that the average of overall and category wise working hours of all the employees are near 45.
The estimated number of employees who are not the members of Labor Union and whose working hour per week is greater than 40 hours is 152.
The estimated number of employees who are not the members of Labor Union and whose working hour per week is greater than 50 years is 65.
The number of non-unionized workers whose number of working hours per week is greater than 45 is 118.
summary(MemUnion)
No Union Yes Union
331 69
Therefore, among 331 No Union workers, 118 workers work more than 45 hours per week.
The summary of the membership of labor union among 400 workers shows that the number of Union employees is 69. 20% of total employee is 80. Therefore, the number of total union employee is less than 20%. It can be said that the total number of union membership is less than 20% and the statement of union that the proportion of unionized staff nationally was at least 20% is not true. The suspicion of the manager is valid.
The company has a goal to reduce the overall average working week and to increase the level of job satisfaction. Next year, they intend to perform a follow-up study on these variables in particular. They would like to estimate the average working week for all employees to within one hour and the proportion of satisfied workers for the whole company to within 1%. To calculate the probability of success of planning of the company, we should apply t-test. However, t-value gives the score 90.453 with 399 degrees of freedom at 95% C.I (44.44506, 46.41994). According to the online sample size calculator, within the defined confidence interval the sample size should be 4. Hence, to obtain change of the satisfaction level of the employees due to average working hours in a week within 1% of the whole company, the sample size 400 is large enough.
t.test(WorkHrs)
One Sample t-test
data: WorkHrs
t = 90.453, df = 399, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
44.44506 46.41994
sample estimates:
mean of x
45.4325
Conclusion:
As a conclusion, the report advices the reporter that he have to take care more about the younger employees, as they are the backbone of the company. In connection with per week working hours, before-taxes Income, they should get company’s reconstructed policy. Not only that, those workers who are labor, technical staffs, service worker are looking for more job satisfaction. Company should take care the lower graded officials; otherwise, they could leave the company. Company must reconsider the reasons that why employees are finding sometimes themselves dissatisfied. Variability of membership of labor Union, weekly working hours is the reason behind it. Company should rectify the drawbacks and take necessary plans. The interrelation of different factors is the main resources behind it. Manager should observe the necessary calculations and plots to identify the correlation among several factors and the outcomes. Proper steps simultaneously can transform the situation of the company.
References:
Bazeley, P., 2013. Qualitative data analysis: Practical strategies. Sage.
Harrell Jr, F.E., 2015. Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis. Springer.
McNeil, A.J., Frey, R. and Embrechts, P., 2015. Quantitative risk management: Concepts, techniques and tools. Princeton university press.
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Powers, D. and Xie, Y., 2008. Statistical methods for categorical data analysis. Emerald Group Publishing.
Stark, J., 2015. Product lifecycle management. In Product Lifecycle Management (Volume 1) (pp. 1-29). Springer International Publishing.
Strohmeier, S., 2013. Employee relationship management—Realizing competitive advantage through information technology?. Human Resource Management Review, 23(1), pp.93-104.
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