6. A cafe owner wishes to improve on the efficiency of his cafe. One aspect that needs to be looked into is that of the rate at which customers are being served by the staff. The table below shows the number of weeks that eight employees have been working at the cafe and the average number of customers that each served per hour. Weeks at cafe 8 5 15 3 10 2 13 6
Customers served 18.4 12.2 32.3 10 21 8.2 28.1 16.5
a. Draw a scatter diagram for the given set of data. Define the variable C to represent the average number of customers an employee served per hour and the variable w to represent the number of weeks that employee has been working at the cafe.
b. The owner decides to use a straight line to model the data. Is the owner justified? Give a reason for your answer.
c.
i. Calculate the correlation coefficient for the given data set.
ii. Use the method of least squares to determine the line of best fit.
iii. Graph the regression line on the scatter diagram in part a.
d. Estimate how many customers an employee should be able to serve in one hour if they have been working at the cafe for
i) 9 weeks
ii) 50 weeks
iii) What constraints can you see this model having?