“Linear Regression Analysis and Plot: % OBESE vs. % DIABETIC”
- Import necessary libraries: The code begins by importing the required libraries:
– `statsmodels.api` for performing linear regression analysis.
– `matplotlib.pyplot` for creating plots.
– `numpy` to create a range of X values for the model line.
- Fit the linear regression model:
– It assumes that you already have `X` and `y` defined, where `X` is the independent variable (in this case, “% OBESE”) with a constant term added, and `y` is the dependent variable (“% DIABETIC”).
– It fits a linear regression model (`sm.OLS`) using the `X` and `y` data.
- Get the coefficients of the model:
– The code retrieves the intercept and slope coefficients from the fitted linear regression model.
- Create a range of X values for the model line:
– It generates a range of X values (`x_range`) using `np.linspace` that spans the range of the original “% OBESE” values.
- Calculate predicted Y values:
– The code calculates the predicted Y values (`y_pred`) based on the linear regression model by applying the intercept and slope to the `x_range`.
- Create a scatter plot of the data points:
– It creates a scatter plot (`plt.scatter`) of the original data points, where “% OBESE” is on the x-axis and “% DIABETIC” is on the y-axis. This visually represents the data.
- Plot the regression line:
– It overlays a red regression line (`plt.plot`) on the scatter plot, using the calculated `y_pred` values. This represents the linear regression model’s predictions.
- Add labels and a legend:
– The code adds labels to the x-axis and y-axis to provide context for the plot.
– It includes a legend to distinguish between the data points and the regression line.
- Show the plot:
– Finally, the code uses `plt.show()` to display the generated plot, allowing you to visualize the data points and the fitted regression line.