The manager of a department store is investigating the relation between the number of salespersons in duty during a week, X, and the value of merchandise lost (shrinkage) per week, Y in $'000. The investigation was done over 12 consecutive weeks, with a different number of sales staff on duty each week, but constant during each week. Week 1 2 3 4 5 6 7 8 9 10 11 12 X 20 21 22 23 24 25 25 20 22 24 26 28 Y 2.0 2.3 1.8 1.7 1.7 1.2 1.7 2.6 2.1 1.1 1.0 0.4 Determine the linear relation between number of sales staff and value of shrinkage per week, and plot this on the scattergram diagram. [3 marks] Find the standard error of the estimate for this data. [3 marks] Interpret the coefficient of determination between the two variables. What is the correlation coefficient ? [3 marks] Predict the shrinkage per week when there are 27 staff on duty. [3 marks] If additional part-time floor-walkers could be hired during peak periods at a cost of $ 50 per week, how many extras would the firm hire ? [3 marks]