In an effort to determine the relationship between annual wages, in £000, for employees and the number of days absent from work because of sickness, a large corporation studied the personnel records for a random sample of 12 employees. The paired data are provided below:
Employee Annual wages (£'000) Days missed
1 25.7 4
2 27.2 3
3 23.8 6
4 34.2 5
5 25.0 3
6 22.7 12
7 23.8 5
8 28.7 1
9 20.8 12
10 21.8 11
11 35.4 2
12 27.2 4
Determine the correlation coefficient and test to see whether the number of days missed is related to annual wages, at the 5 per cent level of significance. If it is, find the regression equation for predicting the number of likely absence in days. Interpret its coefficients and use it to predict the likely absence of an employee earning £25,000.
Is the relationship between wages and days missed significant at the 5% level?
Plot the relationship on a graph
What is the linear regression equation?
If the wage is 25,000, how many days will be missed by an employee?