Multivariate linear regression: a concrete-strength prediction plane

Now use two input features — cement content and water content — to predict the same output, 28-day concrete compressive strength. Adjust three parameters to change the orientation and height of the regression plane.

Intercept w₀ (MPa): Cement coefficient w₁: Water coefficient w₂:

Show 12 training residuals Show training mean squared error

Drag inside the plot to rotate the view. A residual is measured vertically along the strength axis, not perpendicular to the plane.

Held-out cement: Held-out water: Predicted strength: Residual: not revealedTraining MSE: hidden

Synthetic observationsLinear prediction planeTraining residualsHeld-out observation

Compare with the 2D model: Adding water content changes a line into a plane. The plane is still linear in the features and parameters. Why might a nonlinear feature such as the water-to-cement ratio be worth considering later?

Synthetic instructional dataset. The signs of the cement and water effects are engineering-motivated, but these observations and parameter values are simulated, not sourced from Yeh's experiments. This toy linear model is not a mix-design formula or a validated strength-prediction method.