Question

Hospitality Hotels forecasts monthly labor needs.

(a) Given the following monthly labor figures, make a forecast for June using a three-period moving average and a five-period moving average. (Round answers to 2 decimal places, e.g. 15.25.)

Month

Actual Values

January

35

February

45

March

44

April

44

May

46

3 - Period Moving Average = 44.67

5 - Period Moving Average = 42.8

(b) What would be the forecast for June using the naïve method? (Round answers to 2 decimal places, e.g. 15.25.)

Forecast for June = 46

(c) If the actual labor figure for June turns out to be 45, what would be the forecast for July using each of these models? (Round answers to 2 decimal places, e.g. 15.25.)

3 - Period Moving Average = 45

5 - Period Moving Average = 44.8

Naive method = 45

(d) Compare the accuracy of these models using the mean absolute deviation (MAD). (Round answers to 2 decimal places, e.g. 15.25.)

MAD (3-period) = ?

MAD (5-period) = ?

MAD (naive) = ?

(e) Compare the accuracy of these models using the mean squared error (MSE). (Round answers to 2 decimal places, e.g. 15.25.)

MSE (3-period) = ?

MSE (5-period) = ?

MSE (naive) = ?

Answer 1

I am calculating every part of the question to get clarity.

Ans - (a) 3 period of moving averages of June will be mean of a march, April and May i.e (44+44+46)/3 =44.67

The 5-period moving average will the average from January to May for June forecast i.e ( 35+45+44+44+46)/5=42.8

Ans (b) The forecast of June using the naive method will be the forecast of the actual value of may i.e 46.

Ans (c) If the value of June is 45 as per the question then the value of July using

The 3-period moving average will the mean of April may June i.e (44+46+45)/3 = 45

5 period moving average will be the mean of the past five months i.e ( 45+44+44+46+45)/5 = 44.8

The forecast of July using the naive method will be the value of June i.e 45.

Ans (d) The table will give a clear understanding of different values

Months	Real values	3 period MA	difference of 3 period	square of difference	5 period MA	difference of 5 period	square of 5-period difference	Naive method	difference of Naive	square difference of Naive
January	35
Feb	45							35	10	100
March	44							45	-1	1
April	44	41.33	2.67	7.13				44	0	0
May	46	44.33	1.67	2.79				44	2	4
June	45	44.67	0.33	0.109	44.8	0.2	0.04	46	-1	1

Ans (d) Now calculating MAD i.e Mean Absolute deviation

MAD 3 Period = (2.67+1.67+0.33)/3 = 1.55

MAD 5 Period = 0.2/1 =0.2

MAD (Naive) = (10+1+0+2+1)/5 = 2.8

Note- while calculating the MAD( Naive ) negative signs will be ignored. This difference is nothing but the error between the methods.

Ans (e) MSE 3 period  (7.13+2.79+0.109)/3 =3.34

MSE (5 Period) 0.04/1 =0.04

MSE (Naive) (100+1+0+4+1)/5 =21.2