tiger7789 / linear-and-nonlinear-regression-analysis-of-boardgame

Analyzing board game features using R's regression tools

Board Game Rating Regression Analysis

This R code focuses on regression analyses to study the relationship between board game ratings (avg_rating) and several potential predictors such as year of release, time of play, weight, age, and number of votes, among others. I will break down the code for you.

Step 1: Multiple Linear Regression

A linear regression model reg1 is created with avg_rating as the dependent variable and year, avg_timeplay, and weight as independent variables. Residual plots are then generated to visually inspect the residuals (errors).

Step 2: Diagnosing Heteroscedasticity

This step focuses on diagnosing the potential heteroscedasticity in the residuals (i.e., if the spread or variance of residuals changes across different levels of the independent variable). A new regression model reg2a is created with avg_rating predicted by avg_timeplay.

Step 3: Outlier Detection and Handling

A regression model reg3 is constructed with avg_rating being predicted by min_players, age, and num_votes. After plotting residuals, outlier detection is applied and two potential outliers are removed. Then, a new regression model reg3C is constructed without these outliers, and its summary is compared with that of reg3.

Step 4: Checking Multicollinearity

Correlations among several quantitative variables are computed. Another regression model reg4b is created and checked for multicollinearity using the variance inflation factor (VIF). Based on the VIF, min_timeplay is removed and a new regression model reg4f is created.

Step 5: Presenting Results

This step mainly focuses on presenting results using the stargazer package, which provides a nice table of regression outputs. The regression models presented compare avg_rating against avg_timeplay, min_players, and max_players.

Step 6: Polynomial Regression on Age

Polynomial regression is employed here, examining how the age of the board game (in years) might predict its rating. Four models of increasing polynomial degree (from linear to quartic) are created and summarized in a table.

Step 7: Polynomial Regression on avg_timeplay

This step examines how the average time of play (avg_timeplay) predicts the rating using polynomial regression. Four models are created, just as in Step 6.

Step 8: Combined Polynomial Regression

A regression model reg8 is created with a fourth-degree polynomial term of age and avg_timeplay as predictors.

Step 9: Splines Regression

Splines regression is utilized to provide a flexible way of modeling the relationship between avg_rating and avg_timeplay. The bs function is used to generate the spline basis functions, and three models of increasing degree are created. Knots for the splines are based on quantiles of avg_timeplay.

Step 10: Simulation-based Evaluation

A simulation-based approach is taken here to estimate the mean squared error (MSE) for the linear regression model that predicts avg_rating using the weight of the board game. The code iterates through the process of splitting the data into training and testing sets, fitting a linear regression model on the training set, and evaluating its MSE on the testing set. The average MSE across the 30 iterations is then computed. The same process is then applied to polynomial models of increasing degree, but this part of the code is truncated.

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Overall, this R code conducts comprehensive regression analyses examining the relationship between board game ratings and several potential predictors. It uses both linear regression and more advanced methods like polynomial regression and splines regression. The code also incorporates simulation-based techniques and visualization to assess model performance and diagnose potential issues.