1. In the following correlation matrix, variable 1 is the dependent variable 78
ID: 3313477 • Letter: 1
Question
1. In the following correlation matrix, variable 1 is the dependent variable 78 43 23 07 09 .87 -.87 78 23 2 43 .07 4 09 a) Are variables 2,3, and 4 good potential predictor variables? b) Will multicollinearity be a problem for any combination? c) Which variable(s) will be included in the final model? 2. In the following correlation matrix, variable 1 is the dependent variable 2 92 81 21 84 75 .21 a) Are variables 2,3, and 4 good potential predictor variables? 84 92 7S 81 b) Will multicollinearity be a problem for any combination? c) Which variable(s) will be included in the final model?Explanation / Answer
1.
a)From the correlation matrix we can see that cor(2,1) and cor(3,1) are moderately good but cor(4,1) is very bad.So,this should not be a predictor variable.
b)Multicollinearity wont be a problem here because none of the quantities cor(2,3),cor(2,4),cor(3,4) are significantly good.Hence,multicollinearity should not be a problem for this data.
c)Final model wont include 4,because neither it is signifcanlty effecting y,nor any predictors,hence it will not be included in the final model
2.
a)Each one of 2,3,4 is highly correlated to 1,hence all predictors are potentially good.
b)Multicollinearity is very likely to occur here,cor(2,3) and cor(2,4) are signicantly good,which means they are correlated with each other.
c)For final model,4 will always be included because it has maximum correlation with y.Now,among the other 2 variables 2 and 3,cor(2,3) is also very good(0.75).Hence,including one of them will complete the procedure.Now,which one to include? we include 3,because it has more correlation with 1 than 2,and also,it is almost uncorrelated with 4,so multicollinearity will not occur in the model.
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