B Com > Business Mathematics and Statistics > Additive and Multiplicative Models, Business Mathematics and Statistics
Additive and Multiplicative Models, Business Mathematics and Statistics Video Lecture - Business Mathematics and Statistics - B Com
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FAQs on Additive and Multiplicative Models, Business Mathematics and Statistics Video Lecture - Business Mathematics and Statistics - B Com
| 1. What is the difference between additive and multiplicative models in business mathematics and statistics? |  |
Ans. Additive models are used when the relationship between variables is linear, meaning that the effect of one variable is simply added to the effect of another. On the other hand, multiplicative models are used when the relationship between variables is non-linear, meaning that the effect of one variable is multiplied by the effect of another.
| 2. How are additive models applied in business mathematics and statistics? | |
Ans. Additive models are commonly used in forecasting and time series analysis. They assume that the observed data can be decomposed into a systematic component and a residual component, where the systematic component represents the underlying trend and seasonality, and the residual component represents the random fluctuations.
| 3. When are multiplicative models more appropriate in business mathematics and statistics? | |
Ans. Multiplicative models are more appropriate when the relationship between variables is not strictly linear and cannot be adequately captured using additive models. For example, when the effect of one variable on another is proportional rather than additive, a multiplicative model may be more suitable.
| 4. What are the advantages and disadvantages of additive models? | |
Ans. The advantages of additive models include their simplicity and interpretability, as well as their ability to handle time series data with a constant variance. However, additive models may not capture non-linear relationships accurately and may not be appropriate for data with changing variance.
| 5. Can additive and multiplicative models be combined in business mathematics and statistics? | |
Ans. Yes, additive and multiplicative models can be combined to create hybrid models that capture both linear and non-linear relationships. These hybrid models, such as the additive-multiplicative seasonal decomposition of time series (AMSD), can provide a more accurate representation of the underlying data and improve forecasting accuracy.
Text Transcript from Video
all right so what's that talk about some
additive and multiplicative
relationships and really what this is is
just trying to figure out how you get
from one number the next so let's start
with a little chart here
and we'll just use some variables a and
B and then put some numbers on here 1 2
3 4 5 and then put some numbers down
here so 5 10 15 20 25 all right so all
you're looking for here is how do you
get from one number the next and so here
we have a rate of 1 2 5 and then the
second rate is 2 to 10 so in order to
get the second number all you have to do
is multiply the first number times 5 so
that is a multiplicative relationship
we're just taking whatever a is multiply
it by 5 and that will give us our beat
so let's explore a few more of these
alright so now we have another chart
here we have the number of rides and the
cost for doing that many rides so one
ride cost twenty two to three is cost
twenty six three rides plus 30 so here
if I multiply one by twenty two and then
try to apply that to the two two times
22 is 44 not 26 so you can't just
multiply your number of rides by a fixed
cost to figure out how much it's going
to cost you so here we're going to add
so to get from 22 to 26 I'm adding 4 and
to get to 26 to 30 I'm adding 4 so I can
find that last missing value I'm just
going to add 4 again so four rides would
cost you $34 in this type of
relationship what you have is you had
some other cost in there that is before
you actually get to ride a ride so if
you think you're going to like an
amusement park yet to pay to get in like
at the State Fair but then you pay for
each ride individually so you have the
cost to get in plus the cost of each
ride so let's do a couple more
these alright so we have two more tables
here and we have to decide first if this
is going to be multiplicative or
additive so looking at that first one to
get from 1 to 50 I can multiply by 50
but 2 times 50 isn't going to be 55 so
this is going to be additive so I'm
adding and in this case to get from 50
to 55 I'm adding 5 for each one so the 3
would be 64 would be 65 5 would be 70
and then I keep going to add 5 5 more
times which is 25 so 10 would be 95
looking at the second table to get from
1 to 15 I multiply by 15 to get so I
test up with 3 3 times 15 is 45 so this
is multiplicative so I'm multiplying by
15 so I just do that for the last 2 10
times 15 is 150 and then 5 times 15 is
75 so that is how you determine if
something has an additive relationship
or a multiplicative relationship
you
additive and multiplicative
relationships and really what this is is
just trying to figure out how you get
from one number the next so let's start
with a little chart here
and we'll just use some variables a and
B and then put some numbers on here 1 2
3 4 5 and then put some numbers down
here so 5 10 15 20 25 all right so all
you're looking for here is how do you
get from one number the next and so here
we have a rate of 1 2 5 and then the
second rate is 2 to 10 so in order to
get the second number all you have to do
is multiply the first number times 5 so
that is a multiplicative relationship
we're just taking whatever a is multiply
it by 5 and that will give us our beat
so let's explore a few more of these
alright so now we have another chart
here we have the number of rides and the
cost for doing that many rides so one
ride cost twenty two to three is cost
twenty six three rides plus 30 so here
if I multiply one by twenty two and then
try to apply that to the two two times
22 is 44 not 26 so you can't just
multiply your number of rides by a fixed
cost to figure out how much it's going
to cost you so here we're going to add
so to get from 22 to 26 I'm adding 4 and
to get to 26 to 30 I'm adding 4 so I can
find that last missing value I'm just
going to add 4 again so four rides would
cost you $34 in this type of
relationship what you have is you had
some other cost in there that is before
you actually get to ride a ride so if
you think you're going to like an
amusement park yet to pay to get in like
at the State Fair but then you pay for
each ride individually so you have the
cost to get in plus the cost of each
ride so let's do a couple more
these alright so we have two more tables
here and we have to decide first if this
is going to be multiplicative or
additive so looking at that first one to
get from 1 to 50 I can multiply by 50
but 2 times 50 isn't going to be 55 so
this is going to be additive so I'm
adding and in this case to get from 50
to 55 I'm adding 5 for each one so the 3
would be 64 would be 65 5 would be 70
and then I keep going to add 5 5 more
times which is 25 so 10 would be 95
looking at the second table to get from
1 to 15 I multiply by 15 to get so I
test up with 3 3 times 15 is 45 so this
is multiplicative so I'm multiplying by
15 so I just do that for the last 2 10
times 15 is 150 and then 5 times 15 is
75 so that is how you determine if
something has an additive relationship
or a multiplicative relationship
you
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