Question

1) Please find the partially completed multiple regression analysis below, which explores the relationship betwen the sales (in hundreds) and the independent variables price(in dollars), promotional expenditure(in hundreds of dollars) and the quality score (0-100) for a very popular Cbristmas season toy The regression equation is Sales -3432-0.23 Price + 2.7" Promotional exp + 0.22 Quality Predictor Constant Price Promotional exp 2.704 Quality Coef Standard Errorl SE Coef T P VIF 343.20 62.59 -0.23358 0.0373 2.415 1.047 10.387 0.2204 0.1429 R-Sq = Analysis ot Variance Source Regression Residual Error Total DF SS MS F 2847.78 15 3933.40
Is there a problem with multi-collinearity among independant variables in the analysis?

Answer 1

Answer

We have three independent variables, namely price, promotional exp and quality. For multi-collinearity, we have to check the variation inflation factor or VIF value for each indpendent variable.

Rule of thumb for VIF says that VIF value above 4 needs to checked further for multi-collinearity, but a VIF value of 10 or above indicates a serious multi-collinearity.

VIF value for independent variable price is 2.415, which is normal and there is no case of multi-collinearity.

VIF value for independent variable promotional exp is 1.047, which is normal and there is no case of multi-collinearity.

VIF value for independent variable quality is 10.387, which is not normal and there is a case of serious multi-collinearity.

So, only quality variable is showing a case of multi-collinearity because its VIF value is too high.

We can say that there is a problem with multi-collinearity among independent variables in the analysis.