Model soybean growth with GAM

In this exercise you will model the average leaf weight on a soybean plant as a function of time (after planting). As you will see, the soybean plant doesn't grow at a steady rate, but rather has a "growth spurt" that eventually tapers off. Hence, leaf weight is not well described by a linear model.

Recall that you can designate which variable you want to model non-linearly in a formula with the s() function:

y ~ s(x)

Also remember that gam() from the package mgcv has the calling interface

gam(formula, family, data)

For standard regression, use family = gaussian (the default).

The soybean training data, soybean_train is loaded into your workspace. It has two columns: the outcome weight and the variable Time. For comparison, the linear model model.lin, which was fit using the formula weight ~ Time has already been loaded into the workspace as well.

Fill in the blanks to plot weight versus Time (Time on x-axis). Does the relationship look linear?
Load the package mgcv.
Create the formula fmla.gam to express weight as a non-linear function of Time. Print it.
Fit a generalized additive model on soybean_train using fmla.gam.
Call summary() on the linear model model.lin (already in your workspace). What is the \(R^2\)?
Call summary() on 'model.gam. The "deviance explained" reports the model's unadjusted \(R^2\). What is the \(R^2\)?
- Which model appears to be a better fit to the training data?
Call plot() on model.gam to see the derived relationship between Time and weight.

Take Hint (-30 XP)

Exercise

Model soybean growth with GAM

Instructions