Regression is a statistical method used to model the relationship between a dependent variable and one or more independent variables.
Linear regression is a regression model that assumes a linear relationship between the dependent variable and the independent variable. This linear relationship can be represented by the equation of a straight line:
Y = a + bX + ε
where:
- Y is the dependent variable
- a is the constant term
- b is the regression coefficient
- X is the independent variable
- ε is the error term
Examples of linear regression in the manufacturing industry:
- Predicting the number of products that can be produced in a given time based on the number of available workers.
- Estimating production costs based on the amount of raw materials used.
- Forecasting product demand based on historical sales data.
Non-linear regression is a regression model that assumes a non-linear relationship between the dependent variable and the independent variable. This non-linear relationship can be represented by various equations, such as parabolic, exponential, and logarithmic.
Examples of non-linear regression in the manufacturing industry:
- Predicting the learning curve for a new manufacturing process.
- Estimating the relationship between product defect rate and production speed.
- Forecasting the impact of changes in raw material prices on company profitability.
Here are some key differences between linear and non-linear regression:
| Feature | Linear Regression | Non-Linear Regression |
|---|---|---|
| Relationship between variables | Linear | Non-Linear |
| Equation | Straight line | Various equations |
| Applications | Proportional relationships | Non-proportional relationships |
| Advantages | Simple and easy to understand | More accurate for complex relationships |
| Disadvantages | Less accurate for complex relationships | More complex and difficult to understand |
Choosing the right regression model
The appropriate regression model to use depends on several factors, such as:
- The nature of the relationship between the dependent and independent variables
- Availability of data
- Expertise and resources available
It is essential to perform careful data analysis before selecting a regression model.
Additional resources:
- https://opentextbc.ca/introductorybusinessstatistics/chapter/regression-basics-2/
- https://machinelearningmastery.com/
- http://scikit-learn.org/stable/modules/generated/sklearn.linear_model.LinearRegression.html
- https://susiloharjo.web.id/machine-learning-libraries/
Note:
- The examples provided above are just a few of the many applications of linear and non-linear regression in the manufacturing industry.
- There are many statistical software packages available to help you conduct regression analysis.