Predicting plant height after ten weeks

Question

A gardener models a plant's height against how many weeks it has been growing: \widehat{	ext{height in cm}} = 6 + 1.2 \cdot (	ext{weeks}). What height does the model predict at 10 weeks?

Accepted Answer

Insert the input, 10 weeks, into the line: \widehat{	ext{height}} = 6 + 1.2 	imes 10 = 6 + 12 = 18 	ext{ cm.} The intercept 6 cm is the plant's height at week zero, and the slope 1.2 says it grows about 1.2 cm per week. After 10 weeks the model predicts 18 cm. A decimal slope changes nothing about the method: multiply it by the input just as you would a whole number. Here 1.2 	imes 10 = 12, then add the starting 6. Takeaway. Decimal slopes work the same way: 6 + 1.2 	imes 10 = 18 cm, slope times input, then add the intercept.

Predicting plant height after ten weeks

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