# Analysis of Using Quantitative Tools in the 57 largest German Companies listed in the Stock Exchange in 2006

Term Paper 2017 38 Pages

## Excerpt

## Table of content

1. Introduction

2. Analysis of Using Quantitative Tools

*2.1 Descriptive Statistics*

2.1.1 Histogram, Mean and Standard Deviation

2.1.2 Minimum and Maximum

2.1.3 Scatter Plot

*2.2 Inferential Statistics *

2.2.1 Linear regression

2.2.2 Multiple Regression

2.2.3 Multicollinearity

2.2.4 Outliers

3. A conclusion

List of References

## 1. Introduction

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Table 1 - Selected Data of the number of employees, EBIT, Revenue, Share Price and Market Capitalization of Daimler AG’s annual report 2015

Source: *https://www.daimler.com/documents/investors/berichte/geschaeftsberichte/daimler/daimler-ir-annual-report-2015.pdf*

According to Daimler Annual Report 2015 that we can find data about how many employees that Daimler AG have and whether or not the number of Daimler AG's employees gives impact on an increase or decrease of Daimler AG's revenue as well as earnings. As shown above Daimler AG involves five divisions such as Mercedes-Benz Cars, Daimler Trucks, Mercedes-Benz Vans, Daimler Buses and Daimler Financial Services. To facilitate a better comparison view between the number of employees, Earnings (EBIT) and Revenue the author decided to select the data with only arising the relevant data with objectives. As shown above from 2013 to 2015 in depart- ment of Mercedes-Benz Cars, Mercedes-Benz Vans and Daimler Financial Services there is a correlation between an increase of the number of employees with EBIT and Revenue. Conversely, in department of Daimler Trucks and Daimler Buses with the same period looks uncorrelated be- tween an increase of the number of employees and Revenue. In Daimler Group a correlation between the high number of employees with an increase of their share price and their market capitalization is shown where in 2012 the number of their employees about 279.972 increased about 284.015. This increase was followed by an increase of share price from 68,97 to 77,58 and of Market capitalization from 73 to 83. This is only one example from one German company. How- ever, we would analysis with using other specific data which included four variables and with 57 different German companies. Furthermore, in this paper we would also briefly proof how strong the correlation between one factor with other factors through SPSS software which would be used to observe their correlation with aid of descriptive statistics (e.g. Histogram, Mean, Variance, Min- imum, Maximum and Scatter plot) and inferential statistics (Linear Regression, Multiple Regres- sion, Multicollinearity and Outliers). According to Holcomb (2017), descriptive statistics usually are used by teachers, psychologists, marketing researchers and also administrators in all types of organizations to organize and summarize large amounts of data that need to be interpreted. While Inferential statistics are needed for making generalizations from samples to populations and can be used to compute a margin of error which is an allowance for the possible fluctuations because of sampling. For example, if a poll of 57 listed German companies which have an increase of company's revenues, earnings, market capitalization and share price, whether these variables can influence the number of participating employees in a company. When this sample has a margin of error of 4 percentage points, it can be confidently said that the true percentage of all these 57 listed companies who shows an impact of “the more increase of company's revenues, earnings, market capitalization and share price, the more number of employees would be hired” is between 51% and 59% (that is, 55% plus and minus 4%).

Before we continue into the analysis part which is situated in chapter two, we will inform you that as shown in table 2 we brought this data that is already selected from our main source from Handelsblatt which in advance recorded 500 largest European companies listed in the stock exchange but here it is only presented 57 German listed companies.

In this paper, statistical analysis of this data (table 2) which is the selected 57 German listed companies will be started by calculating descriptive statistics numbers that characterize features of those specific data and by presenting through tables or graphs. Then it will be continued to the inferential statistics and will be finalized with a conclusion in chapter 3.

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Table 2 - Selected Data of the number of employees, Earnings, Revenues, Share Price and Market Capitalization of 57 German listed companies in 2006

Source: http://tool.handelsblatt.com/tabelle/index.php?id=54&so=2d&pc=

## 2. Analysis of Using Quantitative Tools

### 2.1 Descriptive Statistics

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Table 3 - SPSS helps to find Mean, Median, Std. Deviation, Minimum and Maximum of collected data from the 57 German Companies listed in the Stock Exchange Source: SPSS Output

Short information about Table 3, here we have in total 57 valid data without any missing data. 57 valid data show the number of companies that were already analyzed in SPSS and result the value of Mean, Median, Standard Deviation, Minimum and Maximum. In our sub chapter, they will be more explained. And to remember, the main purpose of this study is to find and identify relationship between the number of Employees, Market capitalization, share price and Earnings of selected Companies using the SPSS (Statistical Package for the Social Sciences) and

### 2.1.1 Histogram, Mean and Standard Deviation

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Figure 1 - Histogram (Frequency-Number of employees)

Source: SPSS File

The histogram in the figure above shows the frequencies of the observed number of Employees. The number of Employees that is lower than 100000 representing the top 35% of the observed Frequency, and bigger than 200000, representing the minimum of the Staff members. On the horizontal line are Number of employees and on the vertical line the corresponding frequencies (how many times a certain value has been observed).

The distribution of the Employees is clearly skewed to the right, as there are relatively very few com- panies that employs a lot of Workers to manage their operations. We called a positively skewed distri- bution.

Which is located slightly to the right of the peak of the frequencies, since the distribution is skewed to the right. Actually, the mean best describes the central tendency of a variable when the variable is fully symmetrical for the distribution of employees above the mean is about 73296.88. However, it is not in our example. It is obvious that the mean is being dragged in the direct of the skew. In these situations, the median is generally considered to be the best representative of the central location of the data. The more skewed the distribution, the greater the difference between the median and mean, and the greater emphasis should be placed on using the median as opposed to the mean.

The most basic measure for dispersion is called standard deviation. The standard deviation measures how concentrated the data are around the mean. Standard deviation can be difficult to interpret as a single number on its own. Basically, a small standard deviation means that the values in a statistical data set are close to the mean of the data set, on average, and a large standard deviation means that the values in the data set are farther away from the mean. In our case the Standard deviation is greater (Std.dev. =107990.038) than the Mean (M=73296.88).

A large standard deviation can be a goal in certain situations where most of the companies choose to use highly qualified technology rather than hiring more employees or they choose to allocate a specific business processes to a specialist external service provider so they can reduce Operational and Recruitment costs and concentrate on core process rather than the supporting ones .

Looking at the chart, it is obvious that there is one value that lies far to the right side of all the other data. This data point is an outlier. Outliers can have a disproportionate effect on statistical results, such as the mean, which can result in misleading interpretations.

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Figure 2 - Histogram (Frequency-Revenue)

Source: SPSS File

The histogram shows the frequencies of the observed Revenue. In the figure 2, we have a high peak that represent 35% of lowest revenues.

The distribution is positively or right skewed (the tail on the right side of the distribution is longer than the left side) In a positively skewed distribution the mean is pulled toward the right tail of the distribution.

The Standard deviation is greater (Std.dev. =29084, 8825) than the Mean

(M=29084, 8427) → a large Standard deviation means that the values in the Data set are farther away from the mean. In this situation, a large standard deviation isn’t necessarily a bad thing; it just reflects a large amount of variation in the group that is being studied.

Looking at revenue of every company, including the small one and the big one, the standard deviation may be very large.

On the other hand, if narrowing the group down by looking only at the small companies, the standard deviation will be smaller, because in this group the companies have revenue that are less variable. The figure shows a positive outlier at 150000, 0000

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Figure 3 - Histogram (Frequency-Share price)

Source: SPSS File

The histogram in the figure above shows the frequencies of the observed Share price. On the horizontal line are share price and on the vertical line the corresponding frequencies.

This plot represents data with a well-defined peak that represent 12% of the Share price that is also close in value to the median and the mean.

While there are "outliers," they are of relatively low frequency. There is a symmetrical shape where the median (MD=19.800000) and the mean (M=22.410526) are almost the same and are together in the center of the curve.

Most of the data are clustered around the center, while the more extreme values on either side of the center become less rare as the distance from the center increases (i.e. About 68% of values lie within one standard deviation (σ) away from the mean; about 95% of the values lie within two Standard devi- ations and about 99.7% are within three standard deviations. This is known as the empirical rule or the 3-sigma rule.). Skewness is normal that means it involves a perfectly symmetric distribution.

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Figure 4 - Histogram (Frequency-Earnings)

Source: SPSS File

The histogram represents the frequencies of the observed Earnings. On the horizontal line are Earnings and on the vertical line the corresponding frequencies. We have one peak that represent more than 25% of earnings.

The data in Figure is right skewed; the mean is 931.249123, and the median is 423.200000; a mean higher than a median is common for right-skewed data because the extreme higher values pull the mean up but do not have the same effect on the median.

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