Question 2

A recent study investigates the determinants of employees' satisfaction. The hypothesis tests to what extent satisfaction is linked to: the educational level of employees within firms; the employees' tenure within the same firm; the annual leave days of the employees; number of employees' promotions within the same company. Data is collected from 1,234 UK firms.

Their dataset contains the following variables:

• The dependent variable is the average level of work satisfaction in the firm that can range between 1 and 10.
• Employee's educational level (i.e., the average years of education of the firm's employees on a scale from 0 to 10)
• Employee's tenure within firm (i.e., the average years of tenure of the firm's employees on a scale from 0 to 10)
• Number of annual leave days per employee.
• Number of employees' promotions.

As part of the research the following linear regression has been produced (Table 1).

Table 1: Regression results on the determinants of salary

Independent variables	Dependent Variable
Level work satisfaction
Standardised coefficient Beta	Significance p-value
Employee's educational level	0.20	0.03
Employee's tenure	0.36	0.31
Number of annual leave days per employee	-0.05	0.148
Number of employee's promotion	4.40	0.072
R2 = 0.52
Number of observations = 1.234

1. Comment on the statistical significance, relative strength and direction of the relationships between the dependent variable and the independent variables. (30% of mark)

1. How well does the model predict/explain the level of work satisfaction of the employees?

What can be done to improve the model? (15% of mark)

1. What is variance and standard deviation, how do you measure it, and why are those

measures important? Provide examples. (15% of mark)

1. Which inferential test would you use to test a hypothesis between two categorical variables? Provide an example of this specific test to better explain the context in which you could use

them. (20% of mark)

1. The University College of Goldland has collected data about the salaries of two academic

Departments (Psychology and Arts) (20% of mark)

The following table shows the statistical summary.

Table 2: Summary Statistics

Statistics	Psychology	Arts
Mean	17,637	16,087
Median	15,769	14,423
Standard deviation	9,186	7,249
Skewness	1.307	0.552
Kurtosis	5.062	2.907
Minimum	2,3426	2,500
Maximum	48,0769	36,057
N. observations	40	35

Indicate and explain what you can conclude from the table about differences between the department in the distribution of the salaries. (20% of mark)