Linear regression vs polynomial regression v01

Linear Regression VS Polynomial Regression
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★Linear Regression:
The variable and the independent variable are linear, as with input and output, it is a linear
relationship.
[Step]
Used the LinearRegression of sklearn.linear_model to construct the model.
Used the fit method to fit the input data (X_train) and the output data (y_train) to construct
a linear model
Used the predict method to predict the results trained by this linear model.
#1) Import linear regression
from sklearn.linear_model import LinearRegression
#2)Create a linear regression model
LinearRegression_model = LinearRegression()
#3) Train the model based on input and output data
LinearRegression_model.fit(X_train, y_train)
#4) Predicted value of training data
y_pred = LinearRegression_model.predict(X_test)

★Polynomial Regression:
It is an evolution based on linear regression. The independent variable will be transformed into
n linear regressions, just as the input and output are not linear.
When the polynomial power is larger, it means that the fit of the input and output is higher.
However, this polynomial power is limited. If the polynomial power is too large, then predicted
result will be diverged.
[Step]
Used the PolynomialFeatures of sklearn.preprocessing and fit_transform to transform the input
data (X_train)
Used the LinearRegression of sklearn.linear_model to construct the model.
Used the fit method to fit the trnasform data (X_Poly_reg) and the output data (y_train) to construct
a linear model
Used the predict method to predict the results trained by this linear model.
#1) Import linear regression
from sklearn.linear_model import LinearRegression
#2) Import polynomial regression
from sklearn.preprocessing import PolynomialFeatures

#3) Convert the input data to be trained
Poly_reg = PolynomialFeatures()
X_Poly_reg = Poly_reg.fit_transform(X_train)
#4)Create a linear regression model
Linear_Poly_model = LinearRegression()
#5) Train the model based on the converted input and output data
Linear_Poly_model.fit(X_Poly_reg, y_train)
#6) Predicted value of training data
y_pred = Linear_Poly_model.predict(X_test)

★Assuming the annual salary corresponding to the seniority of the
university from the assistant to the professor (the following data is
for reference only).

The Assistant is divided into Assistant-1 and Assistant-2.
Assistant-1 is the annual salary of 300,000 NT for the 1st year of assistant
Assistant-2 is the annual salary of 400,000 NT for the 2nd year of assistant
The Lecturer is divided into Lecturer-1, Lecturer-2 and Lecturer-3.
Lecturer-1 is the annual salary of 600,000 NT for the 1st year of Lecturer
Lecturer-2 is the annual salary of 700,000 NT for the 2nd year of Lecturer
Lecturer-3 is the annual salary of 800,000 NT for the 3rd year of Lecturer
The Assistant Professor is divided into Assistant Professor-1, Assistant Professor-2
and Assistant Professor-3.
Assistant Professor-1 is the annual salary of 1,000,000 NT for the 1st year of Assistant Professor
Assistant Professor-2 is the annual salary of 1,100,000 NT for the 2nd year of Assistant Professor
Assistant Professor-3 is the annual salary of 1,200,000 NT for the 3rd year of Assistant Professor

The Associate Professor is divided into Associate Professor-1, Associate Professor-2,
Associate Professor-3, Associate Professor-4 and Associate Professor-5.
Associate Professor-1 is the annual salary of 1,400,000 NT for the 1st year of Associate Professor
Associate Professor-2 is the annual salary of 1,500,000 NT for the 2nd year of Associate Professor
Associate Professor-3 is the annual salary of 1,600,000 NT for the 3rd year of Associate Professor
Associate Professor-4 is the annual salary of 1,700,000 NT for the 4th year of Associate Professor
Associate Professor-5 is the annual salary of 1,800,000 NT for the 5th year of Associate Professor
Professor is only one level, indicating that the annual salary after serving as a professor
is 3,000,000 NT.

Frank, Peter, John learned that a university is hiring lecturers,
assistant professors, and associate professors.
Frank is a lecturer with 1 year of experience, and total seniority is 4.5 years. He
expects an annual salary of 660,000 NT.
Peter is an assistant professor with 1 year of experience, and total seniority is
7.5 years. He expects an annual salary of 1,480,000 NT.
John is an associate professor with 5 year of experience, and total seniority is 14.5
years. He expects an annual salary of 2,000,000 NT.
Calculate the estimated annual salary of 3 people through linear
regression and polynomial regression.

★[Linear regression - estimated results]
Frank: Below the expected annual salary
Estimated 650,310 NT
Expectation 660,000 NT
Peter: Below the expected annual salary
Estimated 1,094,513 NT
Expectation 1,480,000 NT
John: Higher than expected annual salary
Eestimated 2,130,987 NT
Expected 2,000,000 NT
Conclusion: Using linear regression estimates, only John is above the expected annual salary, while
Frank and Peter are below the expected annual salary.

★[Polynomial (2 times) regression - estimated results]
Conclusion: Using polynomial (2) regression estimates, only John is above the expected annual salary,
while Frank and Peter are below the expected annual salary.

Frank: Higher than expected annual salary
Expected 660,000 NT
Conclusion: Using polynomial (3) regression estimates, Frank and John are higher than expected annual
salary, and Peter is lower than expected annual salary.

Conclusion: Using polynomial (4th) regression estimates, only John is above the expected annual
salary, while Frank and Peter are lower than expected annual salary.

Conclusion: Using polynomial (6 times) regression estimates, Frank and John are higher than expected
annual salary, and Peter is lower than expected annual salary.

Conclusion: Using the polynomial (7) regression estimates, only John is above the expected annual
salary, while Frank and Peter are below the expected annual salary.

Estimated 645088 NT

Conclusion: Using the polynomial (10) regression estimates, only John is above the expected annual

★Polynomial (20 times) regression - estimated results]
Conclusion: Using polynomial (20) regression estimates, only John is above the expected annual salary,
while Frank and Peter are below the expected annual salary.

Frank: Higher the expected annual salary
Conclusion: Using polynomial (30) regression estimates, Frank and John are higher than expected

Frank: Higher the expected annual salary
Estimated 4,078,739,520,000 NT
Conclusion: Using polynomial (100 times) regression estimates, Frank and John are higher than expected

★Conclusion
1. When the input and output data have approximate slopes, linear
regression can be used to predict the result, but the accuracy is
still insufficient.
2. Using linear regression to polynomial regression (2 to 10 times),
comparing the estimated annual salary with the expected annual
salary of 3 people, Frank's expected annual salary may be higher
than the estimated annual salary. John's expected annual salary is
completely lower than the estimated annual salary. Peter's expected
annual salary is higher than the estimated annual salary, so Peter
need to adjust the expected annual salary to meet market demand.

3. From the simulation results of polynomial regression, the fit of
7 to 10 times are very high, so we can refer to the estimated annual
salary using these multiple regressions.
4. From the simulation results of polynomial regression (20 times),
it is estimated that the annual salary of the previous paragraph
has deviated somewhat, even to the polynomial regression (100 times).
Most of the estimated annual salary deviates from the original data.
The annual salary is also completely distorted and cannot be
referenced, so the function of too high a number of times causes
over-fitting, so that the predicted result is divergent.

Linear regression vs polynomial regression v01

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Linear regression vs polynomial regression v01