Function equation from sklearn linear regression / Calculating with coefficients gives different results than model.predict(x)

Question

I'm trying to get the equation of a linear regression model created with sklearn. However I get strange results when I try to calculate the prediction with the coefficients from the model by hand. I guess I made a mistake somewhere, but I couldn't figure it out by myself...

Here's my code:

# Many data points in Pandas DataFrame "filtered_data"

predictors = ["Druckwinkel korrigiert [°]", "Druckwinkel sq.", "Drehzahl [1/min]"]
regressant = "Kraft [N]"

x = filtered_data[predictors].to_numpy()
y = filtered_data[regressant].to_numpy()

model = LinearRegression()
model.fit(x, y)

print("Intercept:", model.intercept_)
print("Coefficients:", model.coef_)
print("R²:", model.score(x, y))

This prints:

Intercept: 150070.5970260448
Coefficients: [-1.28305930e+04  2.73978667e+02  1.48116871e-01]
R²: 0.9578737003844259

If I do

model.predict(np.array([28, 28**2, 2768]).reshape(1, -1))

I get

array([6023.2553988])

which seems reasonable. But if I use the coefficients and intercept to calculate Y like this:

def load(contact_angle, shaft_speed):
     return 150070.59702 - 12830.59299 * (contact_angle ** 2) + 273.97866 * contact_angle + 0.14811 * shaft_speed

load(28, 2768)

I get

-9901032.920822442

which is not at all what I expected...

Can anyone help?

Answer 1

I think you are predicting on [28, 28**2, 2768] and your manual calculation is passing [28**2, 28, 2768] .

To fix this:

def load(contact_angle, shaft_speed):
     return 150070.59702 - 12830.59299 * contact_angle + 273.97866 * (contact_angle ** 2) + 0.14811 * shaft_speed

load(28, 2768)