I recently gave a text paper with 4 different colors (White, Green, Blue, and Pink). I want to know if any of the colors have an effect on the probability that a student earns an A. In addition to the color of the text paper, I included the homework grades(1-100) of the students at the time of the text. The R output for the additive model is shown below:

Call:

glm(formula = A ~ HW + Color, family = binomial, data = Exam_Grades)

Coefficients:

Estimate Std. Error z value Pr(>|z|)

(Intercept) -4.240774 1.422965 -2.980 0.002880 **

HW 0.052096 0.015417 3.379 0.000727 ***

ColorG 0.022861 0.619375 0.037 0.970557 

ColorB -0.006197 0.620401 -0.010 0.992030 

ColorP 0.168470 0.622751 0.271 0.786756 

---

Null deviance: 147.20 on 106 degrees of freedom

Residual deviance: 127.48 on 102 degrees of freedom

AIC: 137.48

Coefficients:

 Estimate Std. Error z value Pr(>|z|) 

(Intercept) -4.54930 2.21255 -2.056 0.0398 *

HW 0.05591 0.02612 2.140 0.0324 *

ColorG 2.83670 3.27858 0.865 0.3869 

ColorB 0.79650 3.59232 0.222 0.8245 

ColorP -3.28400 4.94710 -0.664 0.5068 

HW:ColorG -0.03204 0.03771 -0.850 0.3955 

HW:ColorB -0.00935 0.04119 -0.227 0.8204 

HW:ColorP 0.03891 0.05601 0.695 0.4873 

---

 Null deviance: 147.20 on 106 degrees of freedom

Residual deviance: 125.54 on 99 degrees of freedom

AIC: 141.54

A logistic regression model includes the interaction effect between the homework grade and the color of the exam. Conduct a likelihood ratio test to determine if the interaction term is needed. Does it agree with using AIC to choose between the two models?

calculate the BIC of the model with interaction.