You run a customer service operation that takes telephone calls from customers s

Question

You run a customer service operation that takes telephone calls from customers seven days a week. You currently have the same number of employees each day of the week, but you’re wondering whether your staffing should vary by day of week. You ask your analyst to compile data over the past two months on the total minutes that your staff spends on the telephone plus documenting the calls. The analyst runs a regression in which each day’s total minutes is the dependent variable. The specification is: ,

Mt = a + bTt + cMont + dTuet + eWedt + fThurt + gFrit + hSatt

where the independent variables are a constant term, a linear time trend T that increases in value by one each passing day, and a dummy variable for each day of the week other than Sunday – that is, Mont takes the value one if a data point is for Monday and takes the value zero if the data point is for any other day of the week, Tuet takes the value one if a data point is for Tuesday and takes the value zero if the data point is for any other day of the week, etc. The results from the regression are the following:

(a) Interpret the estimated coefficient of -2.15 for the time variable T. Answer:

(b) Interpret the estimated coefficient of 469.75 for the dummy variable for Monday.

Answer:

(c) State whether the estimated coefficient of the dummy variable for Monday is statistically significant at the 5% significance level, by reference to its p-value. Answer: (d) We’re not asking you to commit yourself to your staffing plans, but do you conclude that there is convincing evidence that the customer service load is higher or lower on any of the days of the week than it is on another day? Explain. Answer:

(d) We’re not asking you to commit yourself to your staffing plans, but do you conclude that there is convincing evidence that the customer service load is higher or lower on any of the days of the week than it is on another day? Explain.

Explanation / Answer

a) Interpret the estimated coefficient of -2.15 for the time variable T:

There is negative correlation between Mt and T i.e. Mt decreases for every increase in T by 2.5 units

b) There is positive correlation between Monday and Mt

c) p value not given

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