- Sure, let's go through each question in detail with Python code:
- 1. Identify the dependent variable and the independent variables:
- ```python
- # Dependent variable
- dependent_variable = 'Performance Index'
- # Independent variables
- independent_variables = ['Hours Studied', 'Previous Scores', 'Extracurricular Activities', 'Sleep Hours', 'Sample Question Papers Practiced']
- ```
- 2. Find the relation of the dependent variable with each independent variable (Hint: Correlation). Explore more about correlation:
- ```python
- import pandas as pd
- # Assuming df is your DataFrame containing the dataset
- correlation_matrix = df.corr()
- dependent_variable_correlation = correlation_matrix['Performance Index']
- ```
- This will give you the correlation coefficients between the dependent variable ('Performance Index') and each independent variable.
- 3. Create a basic linear regression model and fit it using Python:
- ```python
- from sklearn.linear_model import LinearRegression
- # X contains independent variables, y contains the dependent variable
- X = df[independent_variables]
- y = df[dependent_variable]
- # Create and fit the model
- model = LinearRegression()
- model.fit(X, y)
- ```
- 4. From the above model created, find the coefficients and intercept of the variables created:
- ```python
- coefficients = model.coef_
- intercept = model.intercept_
- ```
- The `coefficients` array will contain the coefficients for each independent variable, and `intercept` will give the intercept value of the linear regression model.
- 5. Understand the difference between the interpretation of simple linear regression and correlation. Explain with an example from the dataset:
- Simple linear regression finds the relationship between one independent variable and the dependent variable, while correlation measures the strength and direction of the relationship between two variables.
- For example, if we want to find the relationship between 'Hours Studied' and 'Performance Index':
- ```python
- correlation_hours_studied = df['Hours Studied'].corr(df['Performance Index'])
- ```
- Here, `correlation_hours_studied` will give you the correlation coefficient between 'Hours Studied' and 'Performance Index'.
- 6. Calculate the predicted values of your dependent variable and observe how good you are getting the results:
- ```python
- predicted_values = model.predict(X)
- # You can then compare predicted_values with actual values (y) to evaluate the model
- ```
- You can use metrics such as mean squared error, R-squared, or visualizations to evaluate how well your model is performing.
- Let me know if you need further explanation or assistance with any part!
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