Regression Adjustments

Study: Meadowfoam

Meadowfoam is a flowering California native plant.

Can we effect the number of flowers produced by plants by providing extra light treatment, which varies in its intensity as well as it’s timing?

How would you describe the effect of intensity and timing? Would you fit an ANOVA or a regression model? Why?

A model for a categorical and continuous effect (ANCOVA):

\[ y_{ij} = \mu + \alpha_i + \beta_1 x_{ij} + \epsilon_{ij} \]

Each group has a linear model with the same effect on \(x\) and different effect on the categorical effect (two intercepts).

\[\begin{align} y_{i1} &= \mu + \alpha_1 + \beta_1 x_{i1} + \epsilon_{i1} = \mu_1 + \beta_1 x_{i1} + \epsilon_{i1} \\ y_{i2} &= \mu + \alpha_2 + \beta_1 x_{i2} + \epsilon_{i2} = \mu_2 + \beta_1 x_{i2} + \epsilon_{i2} \end{align}\]