Analysis Of Employee Working Hours Dataset

Descriptive Statistics

Dear Lee,

I went through the dataset and I have a made a complete analysis of the same. The answers for your questions are attached below. Hope this will provide you with the insight that you need and will help you in overcoming your problems. 

Regards.

John Frank.

An overall summary of the employee working hour can be written as follows:

The required summary statistic table is :

Fig 1: Descriptive statistics

Column1
Mean	45.26888889
Standard Error	0.462535883
Median	40
Mode	40
Standard Deviation	9.811867779
Sample Variance	96.27274932
Kurtosis	2.924597195
Skewness	1.555322843
Range	61
Minimum	28
Maximum	89
Sum	20371
Count	450
!st quartile	40
3rd quartile	50
IQR	10

Average working time of each employee is 45.2688 hours. This average working hour can deviate in a range of 9.811 hours employees can deviate from their average working hour with 9.811 hours (Wildemuth 2016). Maximum number of employees woks for 40 hours. 50% of the employees work more than 40 hours and 50% of them works less than that. 255 of the employees work less than 40 hours and 25 % of the employees woks more than 50 hours. Median is less than mean that means distribution of working hours is left skewed which implies that the worker tends to work less regarding hours (Chang 2015). The maximum working hour for an employee is 89 hours and the minimum working hour is 28 hour. The total range of working hour is 61. The total number of employee is 450.  The frequency table and box and whisker pot can be attached with the said report.

It is clear from the histrogram that there are 6 divisions of the hours of work starting from the range of 28 – 38.16667 and ending in 78.83333 – 89. The frequency distribution for each of the group is is also shown in the table. 

The plot clearly shows that there is a whisker in the said frequency division.

There are 450 employees in total and number of people who are very satisfied with their job are 206 in number (Norman,  Mello and Choi  2016). A frequency table for the dataset is given below:

Table 2: Frequency distribution of the dataset.

Row Labels	Count of Moderately satisfied
A little dissatisfied	29
Moderately satisfied	194
Very dissatisfied	20
Very satisfied	206
Grand Total	449

A bar chart showing the frequency distribution of the whole dataset will be like: 

Therefore. Assuming p to be the proportion of people who are most likely to retain their job, then:

p = 0.547.

So, 1 – p = 0.542.

Therefore. Standard deviation of proportion is 0.023 and standard error is 0.046.

Hence, the upper and lower limit of this proportion are (0.41, 0.50).

It can be said here that people who are likely to retain their job are 0.046 in proportion and this proportion can vary with a highest limit of 0.50 and in the lowest limit of 0.41.

1. Work hour may also be related to gender (Kuppuswamy and Bayus  2018).  A linear relationship between the said variables can be said like:

Frequency Distribution

Y = a + b*x where y is the dependent variable and x is the independent variable. a and b are regression constants. The calculated table is:

Fig 2: Regression calculation.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.303019
R Square	0.091821
Adjusted R Square	0.089794
Standard Error	0.471741
Observations	450
ANOVA
	df	SS	MS	F	Significance F
Regression	1	10.07987	10.07987	45.29467	5.2E-11
Residual	448	99.6979	0.22254
Total	449	109.7778
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	1.1135	0.105094	10.59532	1.47E-23	0.906962	1.320038	0.906962	1.320038
X Variable 1	-0.01527	0.002269	-6.73013	5.2E-11	-0.01973	-0.01081	-0.01973	-0.01081

It can be said from calculation that intercept or a is 1.113 and p value for this is 1.47E-23 which is less than 0.05 (Colchero et al.  2016.). Therefore, the intercept value can be accepted. Again, X-variable value or b is -0.015 with p-value 5.2E-11 which is again less than 0.05. Therefore, X-variable value can again be accepted. F-statistic for the regression analysis is 45.29 and F-significant value is 5.2E-11 which is less than f statistic value (Ladd et al.  2014.). Therefore, the regression fit is statistically significant. The R-square value is 0.09 which means that the estimates can differ within a range of 0.09.The regression line can be interpreted as: 

Y = 0.003 + (-0.015)*x.

Worker influence levels can be classified into 4 levels like influences always, influences at times, influences much of the times, and never influences (Solon, Haider and Wooldridge  2015). Again, there are 152 people who always influences, 66 people who influences much of the times, 181 peoples who influences much of the times and 51 people who never influences. The frequency distribution of the whole dataset will be like:

Table 3: Frequncy distribution of influence of the workers.

Row Labels	Count of Sometimes
Always	152
Much of the time	181
Never	51
Sometimes	65
Grand Total	449

A bar chart depicting the frequency distribution here will be like: 

Figure 4: Frequnecy distribution of influence.

Therefore, it can be said that most of the workers influences company decisions. Mostly of them do that always. There are only a very low number of workers who doesn’t have any influence at all (Plesinger et al.  2015).

Work hours can be related to education years, salary, work years and years of experience in Cuteen. The relation equation or the regression equation can be written as:

y = a + b*x₁ + cx₂ + d*x₃,

where, y is the dependent variable, x is the independent variable, a is the intercept of regression and b, c and d are the regression co efficient.

The required calculated table is: 

Fig 3: Regression table. 

Regression Statistics	Column1
Multiple R	0.190687108
R Square	0.036361573
Adjusted R Square	0.0298797
Standard Error	9.664168273
Observations	450

ANOVA	Column1	Column2	Column3	Column4	Column5
	df	SS	MS	F	Significance F
Regression	3	1571.782253	523.927418	5.60973259	0.000879492
Residual	446	41654.68219	93.3961484
Total	449	43226.46444

Column1	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	42.25530642	1.249459475	33.8188691	3.594E-125	39.79974731	44.71086552	39.79974731	44.71086552
X Variable 1	0.138186906	0.033857344	4.08144551	5.3036E-05	0.071647165	0.204726648	0.071647165	0.204726648
X Variable 2	-0.035420588	0.056579799	-0.6260289	0.53161625	-0.146616704	0.075775529	-0.146616704	0.075775529
X Variable 3	-0.041514931	0.066593935	-0.6234041	0.53333768	-0.172391799	0.089361937	-0.172391799	0.089361937

It can be said from the calculation that intercept or a is 42.25530642 and the corresponding p value is3.594E-125 which is less than 0.05 and that means the intercept value can be accepted (Boos and Osborne  2015.). Again, b or coefficient of x1 is 0.138186906 and the corresponding p – value is 5.3036E-05 which is less than 0.05 that is the value will be accepted. C or co-efficient of x2 is 0.035420588 and the corresponding p-value is 0.53161625 which is less than 0.05 and therefore, the value can be accepted. D or coefficient of x3 is 0.041514931 and the corresponding p-value is 0.53333768 which is more than 0.05. therefore, the intercept value cannot be accepted. Again, regressed F-statistic value is 7.899 and the significant f_value is 3.82E-05 which is less than f statistic value and therefore, the regression value can be accepted here (Thiem  2014). The R-square value is 0.05 that means the fitted value can deteriorate within a range of 0.05. The fitted regression line is :

Y = 42.25 + (0.1381)*x₁ + (0.0354)*x₂ .

A scatter plot can be shown among the dependent and the independent variables.

Scatter plot between working hours and salary.  

References:

Solon, G., Haider, S.J. and Wooldridge, J.M., 2015. What are we weighting for?. Journal of Human resources, 50(2), pp.301-316.

Boos, D.D. and Osborne, J.A., 2015. Assessing variability of complex descriptive statistics in monte carlo studies using resampling methods. International Statistical Review, 83(2), pp.228-238.

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Colchero, M.A., Popkin, B.M., Rivera, J.A. and Ng, S.W., 2016. Beverage purchases from stores in Mexico under the excise tax on sugar sweetened beverages: observational study. bmj, 352, p.h6704.

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Norman, C., Mello, M. and Choi, B., 2016. Identifying frequent users of an urban emergency medical service using descriptive statistics and regression analyses. Western Journal of Emergency Medicine, 17(1), p.39.

Phoa, F.K.H., Chou, S.K. and Woods, D.C., 2017. Summary of effect aliasing structure (SEAS): new descriptive statistics for factorial and supersaturated designs. arXiv preprint arXiv:1711.11488.

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