Forecasting absentee rate.

The foreman of a printing shop that has been in business five years is scheduling his workload for next year, and he must estimate the number of employees available for work. He asks the company statistician to forecast next year's absentee rate. Since it is known that quarterly fluctuations exist, the following model is proposed:

y= ₀ + ₁ x₁ + ₂ x₂ + ₃ x₃ +

where

y= Absentee rate = (Total employees absent / Total employees)

x₁=1 if quarter 1 (January - March)

0 if not

x₂=1 if quarter 2 ( April - June)

0 if not

x₃= 1 if quarter 3 ( July- September)

0 if not

(a)Fit the model to the data given in the following table.

(b)Consider the nature of the response variable, y. Do you think that there may be possible violations of the usual assumptions about ? Explain.

(c)Suggest an alternative model that will approximately stabilize the variance of the error term .

(d)Fit the alternative model. Check R² to determine whether model adequacy has improved.

Year Quarter1 Quarter2 Quarter3 Quarter4

1 0.06 0.13 0.28 0.07

2 0.12 0.09 0.19 0.09

3 0.08 0.18 0.41 0.07

4 0.05 0.13 0.23 0.08

5 0.06 0.07 0.30 0.05