(Data file: Minn Land) Another variable in this data file
is the region, a factor with six levels...

Question

(Data file: Minn Land) Another variable in this data file
is the region, a factor with six levels that are geographic identifiers. 

Assuming both year and region are factors, consider the
two mean functions given in Wilkinson–Rogers notation as: 

(a) log(acre Price) ∼ 
year +  region 

(b) log(acre Price) ∼ year + region + year:
region Explain the difference between these two models (no fitting is required
for this problem).

Aditi · Accepted Answer

SOLUTION
As can be seen, the most noticeable distinction that stands out right away is the presence of the year: region pairing. The model in question is referred to as a main effects model in the aforementioned textbook. Because the impact of the continuous regressor is the same regardless of the level of the component, model 
(a) is a lot easier to understand than models that take into account interaction. The interaction model is represented by the 
(b) model, on the other hand. The signal for an interaction is the colon ":" in a sentence. The multiplicative interaction is represented by the additional regressor.
In conclusion,

(Data file: Minn Land) Another variable in this data file is the region, a factor with six levels that are geographic identifiers. Assuming both year and region are factors, consider the two mean...

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