Suppose the marketing department wants to
launch a new product (see picture) on the market. After select the design of the product and
decide about the taste of the product in the laboratory, how can we be sure
that the product will be admitted by the consumers? Machine learning can help you take good
decision about the tasting and the design of the product.
A sampling of consumer taste and score over 100
about the tasting and the designing of our product. At the end of the test they
admit or not to sell the product.
Set Sample of the
population
Tasting Score
|
Design Score
|
Y
|
34,62365962
|
78,02469282
|
0
|
30,28671077
|
43,89499752
|
0
|
35,84740877
|
72,90219803
|
0
|
60,18259939
|
86,3085521
|
1
|
79,03273605
|
75,34437644
|
1
|
45,08327748
|
56,31637178
|
0
|
61,10666454
|
96,51142588
|
1
|
75,02474557
|
46,55401354
|
1
|
76,0987867
|
87,42056972
|
1
|
84,43281996
|
43,53339331
|
1
|
95,86155507
|
38,22527806
|
0
|
75,01365839
|
30,60326323
|
0
|
82,30705337
|
76,4819633
|
1
|
69,36458876
|
97,71869196
|
1
|
39,53833914
|
76,03681085
|
0
|
53,97105215
|
89,20735014
|
1
|
Source: Adapted from Stanford ML
Course
Data visualization
We first of all realize that in general a
product with more than 50% designing score and more than 50% score tasting is selected
to be admitted.
Logistic regression is one of the
most useful supervise technique in classified problem. This method is used here to answer the
question.
The coefficients of the model are Theta_0=-25.16; Theta_1=0.206 and Theta_2=0.201 this shows that
our variables (tasting score and designing score) affect positively the
admission of the product.
Misclassification
matrix
Predicted Value
|
|||
Not
Admitted
|
Admitted
|
Total
|
|
Not
Admitted
|
35
|
5
|
40
|
Admitted
|
5
|
55
|
60
|
Total
|
40
|
60
|
100
|
The model misclassified 8% of
admitted product and 12.5% of not admitted product. Globally, the error rate is
10% ((5+5)/100) and the overall accuracy rate is 90% ((35+55)/100). This means
that we have 90% of chance to predict according to the model that a product
will be admitted in the market.
The decision boundary of the model is drawn in
the following figure. The figure implies that all points over the boundary line
are predicted to be admitted and
others are predicted to be not admitted.
The model predicts four false positive (points that are negative and the model
predict that they are positive) and five false negative (points that are
positive and model predicts that they are negative).
Application of the model to predict
the admission of a product with a tasting score of 50 and a designing score of
90, the admission probability is 96.38%
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