Linear Regression Analysis and Interpretation

Instructions.

In this exam, you will complete a linear regression analysis using Python and interpret the

results. Follow each step carefully, and in a clear and structured summary, interpret the

results of your analysis. Use the following guiding points for your interpretation: Please use VS Code to show your answers.

$1.$ Why is it important to first inspect the dataset before proceeding with analysis?

$2.$ Why is it necessary to preprocess the data before fitting the model? Discuss the

impact of missing values on a regression model.

$3.$ Why do we split the data into training and testing sets, and how does it help in

evaluating the model?

$4.$ What does the R$-$squared value tell us about the model's performance, and how

would you interpret a low versus a high R$-$squared score in this context?

$5.($A$)$ How do the coefficients help in understanding the impact of each feature on

house prices? $($B$)$ If $`$Rooms$`$ has a coefficient of $15,000,$ what does this imply?

$6.$ Why Linear Regression?$**$ Why is linear regression an appropriate model for this

problem? Explain why a decision tree, which can capture non$-$linear relationships,

might not be as suitable for this scenario.

$7.$ Describe the relationship between the features $(`$Rooms$`,`$Age$`,$

$`$DistanceToCityCenter$`)$ and the target variable $(`$Price$`).$

$8.$ Discuss the effectiveness of the model based on the R$-$squared and MSE values.

Submit your interpretation summary in a PDF document. Make sure to format your

document clearly and label each section.

Dataset

We will use a housing dataset to predict house prices based on several features, such as

the number of rooms, square footage, and the age of the property.

Dataset Information:

$-$ Target Variable: $`$Price$`($price of the house in thousands of dollars$)$

$-$ Features: $`$Rooms$`,`$Age$`,`$DistanceToCityCenter$`$

Step $1$: Import Libraries and Load Data

$1.$ import the required libraries: $`$pandas$`,`$numpy$`,`$matplotlib$.$pyplot$`,$ and

$`$sklearn$.$linear$\_$model$`.$

$2.$ Load the dataset $($e$.$g$.,$ from a CSV file$)$ and display the first five rows of the data.

Step $2$: Data Preparation

$1.**$Handle missing values$**$ if any are present by filling them in with the median or

dropping them.

$2.$ Select $`$Rooms$`,`$Age$`,$ and $`$DistanceToCityCenter$`$ as the features $($independent

variables$)$ and $`$Price$`$ as the target $($dependent variable$).$

Step $3$: Split the Data

$1.$ Split the data into training and testing sets using an $80/20$ split.

Step $4$: Build and Train the Linear Regression Model

$1.$ Initialize the $**$Linear Regression$**$ model.

$2.$ Fit the model to the training data.

Step $5$: Make Predictions and Calculate Metrics

$1.$ Predict the prices using the test data.

$2.$ Calculate and display the $**$Mean Squared Error $($MSE$)**$ and the $**$R$-$squared $($R$^2)**$

value.

Step $6$: Interpret the Model Coefficients

$1.$ Display the $**$coefficients$**$ of the linear regression model to understand the

relationship between each feature and the target variable.