Regression

What is the Regression?
-- When we are to improve problems, it may be useful to identify relrationships among
the variables in many cases.(It may offer key-point of solving problem whether there are
relationships among variables or not)
-- Regression is to express and analyze a mathematical equation of describing a relationship.
That is, it is to fit a mathematical equation of describing a relationship between the
"Y(dependent variable)" and "X's(independent variable)"
-- Y=a+ bx+error where a=constant, b=slope

Classification of the equations of regression
-- Simple Linear Regression Analysis: there are one independent variable(predictor variable) and
one dependent variable(response variable)
-- Multiple Regression Analysis: there are more than two independent variables.
-- Curvilinear Regression Analysis: there are one independent variable and one dependent variable
(which has higher than 2nd order function)

Why use Regression?
-- To find the potential Vital Few "X's"
-- To predict/forecast the "Y"
-- To determine how to set the "X's" to optimize "Y"

When use Regression?
-- To screen passive data potential vital "X's"
Danger~!! Do not draw final conclusions using passive data. Follow up with a Design of Experiment.
-- To analyze the results of a Design of Experiment.

Equation of Regression
-- When we fitted observed total data by a mathematical equation, a and b must be determined
by the least total sum of variation that can't be explained by fitted regression equation.
(Method of least sum of square)
-- If all data is on the fitted regression equation, error is zero(0). But that occurs rarely because it is
optimal condition.
-- Also, if error(can't explain variation) is a small value relative to total variation, it can be understood
that explanation of data by Regression Model is sufficient.