Qu 4. 25 marks A personnel manager for a large corporation feels that there may
ID: 3055569 • Letter: Q
Question
Qu 4. 25 marks A personnel manager for a large corporation feels that there may be a relationship between absenteeism, age and life status (single, married, divorced and other) of workers. He would like to develop a model to predict the number of days absent during a calendar year for workers using the independent variables above. A random sample of 20 workers was selected with the results presented below. Days Absent Age Life Status 15 40 10 18 27 61 37 23 46 58 29 67 64 40 57 28 60 39 Single Divorced Married Married Other Other Other Single Single Married Other Married Divorced Divorced 20 14 32 26 18 35 24Explanation / Answer
a)
Looking at the output above, we get the equation as Days absent=-4.34+0.387*Age+4.47*Single+2.95*Married+20.53*Divorced
b)
r=0.8743
c)
Yes. Looking at the significance F, we can conclude that overall model is significant
d)
r^2=0.7643
e)
MSE=45.97
f)
Looking at the p-values, we can see that age and Divorced are only significant
g)
Absent days=-4.34+0.387*54+4.47*0+2.95*0+20.53*1=37.088. Hence, 37 days.
Days absent Age Single Married Divorced 15 27 1 0 0 40 61 0 0 1 10 37 0 1 0 18 23 0 1 0 9 46 0 0 0 20 58 0 0 0 14 29 0 0 0 32 67 1 0 0 26 64 1 0 0 8 40 0 1 0 18 57 0 0 0 8 28 0 1 0 35 60 0 0 1 24 39 0 0 1 11 35 1 0 0 21 45 1 0 0 5 23 0 0 0 9 48 0 0 0 49 55 0 0 1 3 39 1 0 0 SUMMARY OUTPUT Regression Statistics Multiple R 0.874258274 R Square 0.76432753 Adjusted R Square 0.701481538 Standard Error 6.779964256 Observations 20 ANOVA df SS MS F Significance F Regression 4 2236.23127 559.0578176 12.16191367 0.000131974 Residual 15 689.5187297 45.96791531 Total 19 2925.75 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept -4.337969341 6.185131001 -0.701354481 0.493820123 -17.521264 8.84532532 Age 0.387079755 0.127154756 3.044162613 0.008200518 0.116055808 0.658103702 Single 4.46778732 3.929072822 1.137109828 0.273331748 -3.906833161 12.8424078 Married 2.951417182 4.614277837 0.639627107 0.532063178 -6.883683217 12.78651758 Divorced 20.53243251 4.566397205 4.496418422 0.00042633 10.79938727 30.26547776