How to code ordinary least squares linear regression for a 3D scatterplot in Python?

Question

This is for a 3D scatterplot. The instructions state: Now that we have fit our model, which means that we have computed the optimal model parameters, we can use our model to plot the regression line for the data. Below, I supply you with x_fit and y_fit that represent the x- and y-data of the regression line, respectively. All we need to do next is ask the model to predict a z_fit value for each x_fit and y_fit pair by invoking the model's predict() method. This should make sense when you consider the ordinary least squares linear regression equation for calculating z_fit :

where are the computed model parameters. You must use x_fit and y_fit as features to be passed together as a DataFrame to the model's predict() method, which will return z_fit as determined by the above equation. Once you obtain z_fit , you are ready to plot the regression line by plotting it against x_fit and y_fit . My code so far is:

features = df[['x', 'y']]
response = df['z']

#perform linear regression model fitting

from sklearn.linear_model import LinearRegression

model = LinearRegression().fit(features, response)
model


print("Model Coefficients: ", model.coef_)
print("Model Intercept : ", model.intercept_)

Output:

Model Coefficients:  [ 8.02602396 15.95639323]
Model Intercept :  -8.632876775060822

This is where I'm stuck:

# Plot Curve Fit
x_fit = np.linspace(0,21,1000)
y_fit = x_fit

#ENTER CODE HERE#

Answer 1

# Plot Curve Fit
x_fit = np.linspace(0,21,1000)
y_fit = x_fit

#ENTER CODE HERE#

Assuming

theta1, theta2 = model.coef_
theta3 = model.intercept_

Equation

z_fit = (theta1 * x_fit) + (theta2 * y_fit) + theta3