**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.