The business problem facing the director of broadcasting operations for a television station was the issue of standby hours (i.e. hours in which unionized graphic artists at the station are paid but are not actually involved in any activity) and what factors were related to standby hours. The study included the following variables:
Standby hours (Y)—total number of standby hours in a week
Total staff present (X¹)—Weekly total of people-days
Remote hours (X²)—Total number of hours worked by employees at locations away from the central plant
Data were collected for 26 weeks; these data are organized and stored in Standby.
Copy data on to an excel sheet.
|Standby||Total Staff||Remote||Dubner||Total Labor|
Go to data and select the data analysis add in. Click on it and select regression.
Now we can answer the question using the table:
From the results obtained we can write the regression equation as follows:
Y = -330.831 + 1.76X1 – 0.13X2 Where, Y= standby hours X1= Total staff present X2= Remote hours b0= -330.67 b1= 1.76 b2= -0.13
The slope b1 means that with a 1 unit increase in total staff present the standby hours increase by 1.76 units.
The slope b2 means that if 1 unit of change is seen in remote hours then the standby hours would decrease by 0.13 units.
Thus we can conclude that standby hours are directly proportional to total staff present while remote hours and standby hours are inversely related.
The slope b0 has no practical meaning as time is never negative. And to have an intercept for time is absurd.
Total staff present = 310 Remote hours = 400 Y=1.76*310 – 0.13*400 = 493.6 hours
Yhat =Y± tn-2,α/2) sY
To calculate t α/2 select the function TINV in excel and put α =0.05 while degree of freedom as 23 (=n-2-1).
t23,0.05 = 2.06 Yhat = 493.6 + (2.06*35.38) = 566.27 Or Yhat = 493.6 - (2.06*35.38) = 420.93 Confidence interval = (420.93, 566.27)