**relationship between a dependent variable and multiple independent variables**

**linear relationship between the dependent variable**

**best-fit hyperplane that represents the relationship between the independent variables and the dependent variable**

**method of ordinary least squares**

**model might predict the price of a house with a size of 1500 square feet, 3 bedrooms, and located in a certain area to be $250,000**

**how each independent variable contributes to the prediction of the dependent variable**

**Multiple linear regression** is an extension of simple linear regression that allows for the analysis of the **relationship between a dependent variable and multiple independent variables**. It assumes a **linear relationship between the dependent variable** and each independent variable while considering the effects of all independent variables simultaneously.

The multiple linear regression model aims to find the **best-fit hyperplane that represents the relationship between the independent variables and the dependent variable**. It calculates the coefficients or parameters of the regression equation, including the intercept and slopes for each independent variable.

The regression equation can be represented as:

```
y = b0 + b1x1 + b2x2 + ... + bn*xn
```

Where:

y is the dependent variable (housing price).

b0 is the intercept, which represents the predicted value of y when all independent variables are zero.

b1, b2, ..., bn are the coefficients, representing the effect of each independent variable (size, number of bedrooms, location) on the dependent variable.

x1, x2, ..., xn are the independent variables (size, number of bedrooms, location).

The coefficients are estimated using the method of **ordinary least squares (OLS)**, similar to simple linear regression. The estimated coefficients provide insights into the strength and direction of the relationships between the independent variables and the dependent variable.

The output of multiple linear regression is the predicted values of the dependent variable based on the independent variables. For example, the **model might predict the price of a house with a size of 1500 square feet, 3 bedrooms, and located in a certain area to be $250,000**.

Multiple linear regression allows us to analyze **how each independent variable contributes to the prediction of the dependent variable** while considering the potential interactions and combined effects of multiple variables. It is widely used in various fields, including economics, finance, real estate, social sciences, and engineering, to gain insights into the relationships between variables and make predictions based on multiple predictors.

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