## Introduction

We can use `sklearn.linear_model.LinearRegression`

to do linear regression in Python. The following is the core syntax of using sklearn.

lm.fit(IVs, DV)

Where,

IVs: the independent variables

DV: the dependent variable

## Example for Linear Regression Model

The following is the linear regression model, including household income as `IV`

s and purchase intention as `DV`

.

\[f(x)=b_0 +b_1 \times Price+b_2 \times Household \ Income \]

The following is the hypothetical data, including purchase intention as `DV`

and prices and household income as `IV`

s.

Purchase Intention | Prices | Household Income |
---|---|---|

7 | 5 | 7 |

6 | 6 | 5 |

5 | 7 | 4 |

5 | 8 | 6 |

3 | 9 | 3 |

4 | 10 | 3 |

## Step 1: Prepare the data

The following Python code generates the hypothetical data and then changed it into appropriate format.

```
import numpy as np
from sklearn.linear_model import LinearRegression
lm = LinearRegression()
# Input hypothetical data
Purchase_Intention=(7,6,5,5,3,4)
Prices=(5,6,7,8,9,10)
Household_income=(7,5,4,6,3,3)
# change it into the format we want
DV= np.transpose([Purchase_Intention])
print("DV: \n",DV)
# change it into the format we want
IVs=np.concatenate(([Prices], [Household_income]), axis=0)
IVs=np.transpose(IVs)
print("IVs: \n",IVs)
```

Output:

DV: [[7] [6] [5] [5] [3] [4]] IVs: [[ 5 7] [ 6 5] [ 7 4] [ 8 6] [ 9 3] [10 3]]

## Step 2: Use `lm`

from `sklearn.linear_model`

.The following is the Python code of adding the IVs and DV in the `lm.fit()`

.

```
# apply sklearn.linear_model
result = lm.fit(IVs, DV)
print("Result is as follows:")
print("Intercept:\n",result.intercept_)
print("Regression Coefficients:\n", result.coef_)
```

Output:

Result is as follows: Intercept: [6.73880597] Regression Coefficients: [[-0.44776119 0.34701493]]

## Step 3: Write out the regression model

We can write out a model with the estimated regression coefficients.

\[f(x)=6.73-0.45 \ Price+0.35 \ Household \ Income \]

We can see that price is negatively related with purchase intention, while household income is positively related with purchase intention.