Week 1: Multiple regression slices

Core idea: A coefficient describes how the prediction changes when one covariate moves and the other is held constant. The sliders choose the home represented by the gold point.

Slice the fitted plane

Change either covariate. The matching gold point moves; the other plot’s fitted line shifts because its held-constant value changed.

Predicted price = $153,643 + $310.81(Area) − $61,775(Bedrooms)

Living area2,000 sq ft

8004,000 sq ft

Bedrooms4 bedrooms

26 bedrooms

For a 2,000 sq ft home with 4 bedroomsPredicted price: $528,163

Move area; hold bedrooms constant

Bedrooms held at 4

Move bedrooms; hold area constant

Living area held at 2,000 sq ft

area slicebedroom sliceselected home

The same model in three dimensions

Both colored lines lie on one fitted plane and cross at the selected home.

Drag to rotate · arrow keys also work

Area: +$310.81

For one additional square foot, predicted price rises by $310.81 when bedrooms are held fixed.

Bedrooms: −$61,775

For one additional bedroom, predicted price falls by $61,775 when area is held fixed.

One plane, many slices

Every held-constant value creates another parallel line cut from the same fitted plane.