11.The number of meals consumed in a school canteen is recorded each day for two weeks....

11.The number of meals consumed in a school canteen is recorded each day for two weeks.

week	day	number of meals
1	monday	252
	tuesday	265
	wednesday	281
	thursday	242
	friday	229
2	monday	258
	tuesday	270
	wednesday	289
	thursday	251
	friday	237

n-point moving average value for n is 5.

(i) a)Explain why a suitable value for n is 5

ii) b) explain why centring will not be necessary

iii) c) Calculate all the 5-point moving average values and insert them in appropriate places in the table above.

d)Use values from your table to find an estimate for the seasonal component for Wednesday

Solutions

Expert Solution

i). a). Since, we have 5 days a week considered. Moving averages are an estimate of trend pattern that remove seasonality. Here, 5 days a week will show a seasonal pattern over week. Taking average of 5 observations will eliminate the possible seasonal pattern over week and will be able to give true estimate of trend.

ii). b. As, n = 5 is an odd number it will correspond to 3rd observation (that wll be centered itself) or centering will not be necessary.

iii). c).

week	day	number of meals	5 MA
1	monday	252
	tuesday	265
	wednesday	281	253.8
	thursday	242	255
	friday	229	256
2	monday	258	257.6
	tuesday	270	259.4
	wednesday	289	261
	thursday	251
	friday	237

is the 5 point moving average corresponding to 3rd - 8th observation.

d). We can take the moving averages to estimate the seasonality.

week	day	number of meals	5 MA	y - 5MA	y / 5MA
1	monday	252
	tuesday	265
	wednesday	281	253.8	27.2	1.11
	thursday	242	255	-13	0.95
	friday	229	256	-27	0.89
2	monday	258	257.6	0.4	1.00
	tuesday	270	259.4	10.6	1.04
	wednesday	289	261	28	1.11
	thursday	251
	friday	237

There are two types of model: Additive and Multiplicative.

Addtive ; y = trend + seasonality + error

Here, seasoanlity is estimated by column y - 5MA (actual - 5MA)

Multiplicative: y = trend*seasonality*error

Here, seasonality is estimated by column y/5MA = (actual/5MA)

Please rate my answer and comment for doubt.

orchestra answered 1 year ago

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