In our discussion of Winter’s method, a monthlyseasonality of (say) 0.80 for January means that duringJanuary, air conditioner sales are expected to be 80% of thesales during an average month. An alternative approach tomodeling seasonality is to let the seasonality factor for eachmonth represent how far above average air conditioner saleswill be during the current month. For instance, if sJan 50, then air conditioner sales during January are expectedto be 50 less than air conditioner sales during an averagemonth. If sJuly 90, then air conditioner sales during Julyare expected to be 90 more than air conditioner sales duringan average month. Letst the seasonality for month t after month tdemand is observedLt the estimate of base after month tdemand is observedTt the estimate of trend after month t demandis observedThen the Winter’s method equations given in the text aremodified to be as follows (* indicates multiplication):Lt a * (I ) (1 a) * (Lt1 Tt1)Tt b * (Lt Lt1) (1 b) * Tt1st g * (II ) (1 g) * st12a What should I and II be?b Suppose that month 13 is a January, L12 30,T12 3, s1 50, and s2 20. Let a g b 0.5. Suppose 12 air conditioners are sold during month 13. At the end of month 13, what is the predic-tion for air conditioner sales during month 14?
Contingency Table
A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.
Binomial Distribution
Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.
In our discussion of Winter’s method, a monthly
seasonality of (say) 0.80 for January means that during
January, air conditioner sales are expected to be 80% of the
sales during an average month. An alternative approach to
modeling seasonality is to let the seasonality factor for each
month represent how far above average air conditioner sales
will be during the current month. For instance, if sJan
50, then air conditioner sales during January are expected
to be 50 less than air conditioner sales during an average
month. If sJuly 90, then air conditioner sales during July
are expected to be 90 more than air conditioner sales during
an average month. Let
st the seasonality for month t after month t
demand is observed
Lt the estimate of base after month t
demand is observed
Tt the estimate of trend after month t demand
is observed
Then the Winter’s method equations given in the text are
modified to be as follows (* indicates multiplication):
Lt a * (I ) (1 a) * (Lt1 Tt1)
Tt b * (Lt Lt1) (1 b) * Tt1
st g * (II ) (1 g) * st12
a What should I and II be?
b Suppose that month 13 is a January, L12 30,
T12 3, s1 50, and s2 20. Let a g
b 0.5. Suppose 12 air conditioners are sold during
month 13. At the end of month 13, what is the predic-
tion for air conditioner sales during month 14?
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