Question Tag: Employment Years

a)
i) We have a negative correlation here, as shown by the negative coefficient of $x$ in the regression line. As the number of years employed with the company rises, the number of days absent in a year through sickness falls.
$y=15.6-1.2x$
The 15.6 represents the number of days of absence through sickness that an employee with zero years’ service is expected to suffer, so it is the number of days that an employee will need off through sickness in their first year of employment.
The -1.2 represents the gradient of the regression line, meaning that for each extra year’s service with the company, an employee will take 1.2 fewer days off sick per year. (2 marks)

ii) An employee who has been with the company for eight years is expected to require six days of sick leave per year. (2 marks)

iii) Limitations and problems of using the equation in practice:

• The regression line approach presupposes a linear relationship between the two variables: a sample of 50 workers has given us quite a strong correlation, but a strict linear relationship seems unlikely.
• A linear relationship may hold well within a small relevant range of data within which the equation may be useful in practice. But extrapolating outside the range will lead to serious inaccuracies. Thus, the equation would predict that an employee with more than 15.3/1.2 = 13 years’ service would have less than zero sick leave.
• If we use the equation to predict the future, we will use historical data to forecast the future, which is always risky.
• The regression line shows the expected number of days sick for a given employment period. But it is unlikely that all categories of workers will experience the same sickness pattern. The equation would be most useful if there were many employees all doing the same job in the same work conditions. (4 marks)

b)
i) Average Quarterly Variation Calculation:

Seasonal variations are short-term fluctuations in recorded values, due to different circumstances which affect results at different times of the year, on different days of the week, at different times of day, or whatever. For example, sales of ice cream will be higher in summer than in winter.
In this data, the highest output can be expected to be in the winter and the lowest in the summer. (5 marks)

ii) Forecast output = Trend + Seasonal variation
= 10,536 + 23.7
= 10,559.7 units (2 marks)

c)
i) Variable Overheads Expenditure Variance:

ii) Fixed Overheads Expenditure Variance:

iii) Fixed Overheads Volume Variance: