The intercept as a starting point, seedling growth

Question

A greenhouse tracks a seedling and fits its height against the number of days since planting:

$\widehat{\text{height in cm}} = 2 + 0.5 \cdot (\text{days since planting}).$

What height does the model predict on day zero, and does that intercept have a sensible meaning?

Accepted Answer

Set days to zero: \widehat{	ext{height}} = 2 + 0.5 	imes 0 = 2 	ext{ cm.} The intercept 2 cm is the predicted height on the day of planting. That is meaningful: day zero is a real, observed moment, and a seedling genuinely has some starting height when it goes into the soil. The slope 0.5 then says the plant grows about half a centimeter per day. This is the friendly case for an intercept: the input value zero is not only realistic but is actually part of the data you would have collected, so reading the intercept as "starting height" is fair. Contrast this with a model where zero sits far…

The intercept as a starting point, seedling growth

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