The reduced model coefficients are given in
Table. VII. Another way to test the quality of two
models is to compare their coefficient of
determination (R squared), which measures the
proportion of total variation explained by the
regression model. With regard to deal with Multiple
Linear regression, the R squared is not accurate
enough since it would always increase when a new
variable is added to the model. We’ll focus on the
modified version (Adjusted R squared), which works
the as R squared. The larger the adjusted R squared
is, the better the model fit.
Table 8: Metics for the model.
Reduced Model (with
interaction)
Full Model (with
interaction)
AIC 206.41 210.34
R squared 0.8473 0.826
While viewing the variables of the model, we
could make another interpretation with interaction.
P
50
: If the company consider setting price at 50, they
will induce 519.513 less sales than setting price at 70.
P
60
: If the company consider setting price at 60, they
will induce 792.621 more sales than setting price at
70. A
0
: the 3 million advertising policy would bring
175.677 less sales than 3.5 million advertising policy.
C
1:
stores in city1 will bring 46.527 less sales than that
of city4. V: if the company considered setting price at
50, each unit increase in Store Volume is associated
with an increase of (15.202+18.037) in total sales. If
the company considered setting price at 60, each unit
increase in Store Volume is associated with an
increase of (15.202-14.042) in total sales. If the
company considered setting price at 70, each unit
increase in Store Volume is associated with an
increase of 15.202 in total sales.
According to the multiple linear regression, the
variables Price, Advertising, City Index, Store
Volume and interaction between Price and Store
Volume can determine the total sales of the Product–
K-pack. As a matter of fact, this regression model is
not perfect even though we did the bootstrap re-
sampling technique to reduce the bias. In the future,
if one could collect more data from the
SMARTFOOD company, a better regression analysis
can be formed, e.g., split data to carry out cross
validation and construct complex nonlinear model
(neural networks). The training data set would be
used to construct models and the test data set would
be used to evaluate the quality of linear models. Then,
the over-fitting problems might be eliminated and the
precision of regression analysis would be improved.
In addition, we need to reveal more variables which
might also affect the total sales of product. The more
variables the model includes, the better performance
one can obtain.
4 CONCLUSION
In summary, we investigate K-Pack’s 4-month
marketing performance based on multivariate linear
regression. According to the analysis, the feasibility to
sales prediction is verified and the impacts of efficacy
of marketing mix on the sales are demonstrated. In the
future, to construct a more robust and improve the
performance, we can consider more variables as well
as enlarging the sample quantities. Besides, it is
necessary to pay attention to the marketing strategy of
competitors, detect market changes timely as well as
given questionnaires to customers regularly Market is
full of change. we have to pay attention to everything
about it, i.e., the prediction will be more reliable and
closer to the fact. Overall, these results offer a
guideline for sales prediction for a specific case.
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