Question

In: Statistics and Probability

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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