Modelling

Overall Regression Results

Table 1 suggests that the gradient boosting model had the best overall performance, with a somewhat low train RMSE and the lowest test RMSE. The random forest model had the lowest train RMSE, but a higher test RMSE, suggesting possible overfitting.

Table 1. RMSE results for each model

Method	Train RMSE	Test RMSE
Linear Regression	0.634	0.634
Auto. Lin. Reg.	0.634	0.634
GLMM	0.620	0.630
Regression Tree	0.640	0.633
Random Forest	0.323	0.635
Boosting	0.597	0.626
XGBoost	0.545	0.630

Linear Regression Coefficients

Figure 1 shows the estimated coefficients from a baseline linear regression model. Notably, all of the size levels have statistically significant effects at the 0.05 significance level. For example, large chains have a 0.921 lower rating than single location restaurants on average. Moreover, two of the price levels have statistically significant effects: Very High and Unknown, compared to the baseline level of Low. Review count also has small, but statistically significant effect

Figure 1. Coefficients and their 95% confidence interval for the baseline linear model

Variable Importances

Figure 2 shows the rankings of each variable in the random forest, boosting and XGBoost models. There is a lot of variations between the rankings, but overall, size level appears to be the most important.

Figure 2. Differences in Variable Importance Rankings Over Models