a. Create a logistic regression model using Radius, Concave, Radius*Radius, and Radius*Concave as explanatory variables to estimate the probability that a mass is malignant. Submit the logistic regression model and the likelihood ratio test results, including the log-likelihood (or deviance) values.
b. Even though in Part A Wald’s test shows the highest p-value for Radius, it is typically best to attempt to keep the simplest terms in the model. Generally, keeping simpler terms in the model makes the model easier to interpret.*Thus, we suggest as a first attempt keeping Radius in the model and eliminating the variable with the next highest p-value. Create a logistic regression model using Radius, Concave, and Radius*Concave as explanatory variables to estimate the probability that a mass is malignant. Submit the logistic regression model and the likelihood ratio test results, including the log-likelihood (or deviance) values. Conduct the drop-in-deviance test to determine if Radius*Radius should be included in the model.
c. Use a scatterplot to compare Radius to Radius*Radius and calculate the correlation between these two terms. Are these variables highly correlated?
d. Chapter 3 discusses multicollinearity (highly correlated explanatory variables). Explain whether you believe Radius is important in the logistic regression model. Why is the p-value for Radius so large in Part A but very small in Part B?
e. Create a logistic regression model using Radius and Concave as explanatory variables to estimate the probability that a mass is malignant. Submit the logistic regression model and the likelihood ratio test results, including the log-likelihood (or deviance) values. Conduct the drop-in-deviance test to determine if Radius*Concave should be included in the model.
f. Create a logistic regression model using only Concave as an explanatory variable to estimate the probability that a mass is malignant. Submit the logistic regression model and the likelihood ratio test results, including the log-likelihood (or deviance) values. Conduct the drop-in-deviance test to determine if Radius should be included in the model.
g. Submit a final model and provide a justification for choosing that model.