Plots of the interaction effects that show the mean of house price at each of the 3 possible combinations of levels for a given pair of chosen factors: The non-parallel lines of yr_built:sqft interaction plots indicate that the effect of size depends on effect of yr_built–—as for those smaller-sized houses, the age of the houses creates big difference among the price; while for bigger houses, whether or not the houses are new doesn’t not affect the price that much. Likewise, the similar results holds for yr_built:grade interaction--- the effect of grade is dependent on the effect of yr_built––if the house are older, the grade doesn’t affect the price. However, if the houses are built after 2005, then the grade is positively correlated to the house price.
Next, we started our exploration of linear models fitting to respectively include the main effects, two-factor interactions as well as three-factor interactions. Consider all the main effects (Model1): Consider two-factor interactions (Model 2): Consider three-factor interactions (Model 3):
From the first three models, the p value concluded that there is high significance in only one parameter: sqft. None of the interaction terms were significant, which is surprising given the correlation we discovered in the previous interaction plots. We decided to view the problem from different angle by performing an ANOVA analysis. A Pareto/Coefficients plot for 3-factor model(Model3) was created to visualize the magnitude of factors’ coefficients. Since the model has 8 coefficients (intercept, main effects, and interactions) with only 8 observations and, p-values cannot be calculated for this model.
The coefficient values and the graphs indicated that the most important factors are sqft, the 3-factor interaction, grade, the interaction of grade and yr_built, and the interaction of sqft and yr_built. In reading the interaction variables, it is important to remember that the “low” values were coded as -1 rather than zero. Therefore, when the interacting factors are concordant, their product will be positive and we will see higher prices when both factors are high or low.
- Winter '18
- Rafeal Izzary