Question

Based on the forward selection output, is there evidence of multicollinearity?

Table 1

BMI : F-statistic = 281.05, P-value = 0, R² = 0.082

weight: F-statistic = 209.76, P-value =0, R²=0.063

TypeA: F-statistic = 19.13, p-value =0, R²=0.006

Table 2

BMI weight: partial F= 3.46, p-value=0.063, R²=0.083

BMI TypeA: partial F=16.87, p-value=0, R²=0.087

Answer 1

From table 1, it is clear that the independent variable BMI, weight and type A are significant to be considered in the model because their respective p values are equal to 0, which are significant.

From table 2, it is clear that the p value for the interaction term of BMI and weight is 0.063, which is not significant enough at 0.05 level of significance to consider it as significant interaction.

P value for the interaction term BMI Type A is significant because its corresponding p value is 0. Therefore, there is an evidence of multicollinearity between BMI and type A variable because the interaction term is significant with coefficient of determination value of 0.087, but we need further confirmation with the help of VIF value

Calculation for variance inflation factor

we know that VIF=

setting R squared value for BMI Type A interaction = 0.087

we get

VIF = 1/(1-0.087) = 1/0.913 = 1.095

It is clear that the VIF value corresponding to the interaction term BMI Type A is 1.095, which is less than 10. Therefore, we can say that there is not enough evidence for multicollinearity because the VIF is less than 10.