Chapter 2 of 7

Interpreting the Coefficients

What each number in the equation actually means

Let's break down the estimated regression equation from the additive model. What does each coefficient tell us?

Estimated regression equation
y^=1.4b0+3.04b1×salary+10.8b2×outfield\hat{y} = \underbrace{-1.4}_{b_0} + \underbrace{3.04}_{b_1} \times \text{salary} + \underbrace{10.8}_{b_2} \times \text{outfield}

There are three coefficients. Let's look at each one.


b₀ is the predicted market value for a goalkeeper earning €0M salary.

024681012Annual Salary (M€)01020304050Market Value (M€)GoalkeeperOutfieldb₀ = -1.4
b₀ (Intercept) €0.0M

When salary = 0 and position = goalkeeper, the model predicts a market value of €-1.4M.


b₁: for each additional €1M in salary, market value increases by b₁ M€ — regardless of position.

4681012Annual Salary (M€)01020304050Market Value (M€)GoalkeeperOutfield+€1M+3.04+€1M+3.04
b₁ (Salary Effect) +€0.00M

The slope is identical for both lines. Whether goalkeeper or outfield, an extra €1M in salary predicts an increase of €3.04M in market value.


b₂: the position (being an outfield) effect — at any salary level, outfield players are worth b₂ M€ more than goalkeepers.

4681012Annual Salary (M€)01020304050Market Value (M€)GoalkeeperOutfieldb₂ = 10.8
b₂ (Being an Outfield Effect) +€0.0M

The gap is the same at every salary level. This is what "additive" means — position shifts the prediction by a constant amount.


Plug in any salary + position to get a prediction.

4681012Annual Salary (M€)01020304050Market Value (M€)GoalkeeperOutfield
y^=1.4+3.04×7.0+10.8×1\hat{y} = -1.4 + 3.04 \times 7.0 + 10.8 \times 1
Predicted Market Value €0.0M

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