Question

A study considered a sample of 50 observations used to predict SALES. Included in the analysis were 9 predictors variables, ( Independent Variables).

1. Based on the correlation matrix shown below, is there any concern about Multicollinearity?

Correlations

	X 1	X 2	X 3	X 4	X 5	X 6	X 7	X 8	X 9
X 2	0.804
X 3	0.625	0.443
X 4	0.032	0.032	0.231
X 5	0.159	0.214	0.177	-0.194
X 6	0.319	0.373	0.308	0.054	0.293
X 7	-0.016	0.030	0.079	0.168	-0.309	0.067
X 8	-0.026	0.103	0.015	0.151	-0.311	0.059	0.912
X 9	0.169	-0.027	-0.104	0.017	-0.248	0.114	0.174	0.223
SALES	0.764	0.630	0.756	0.149	0.171	0.426	0.145	0.141	-0.068

• If YES, list all pairs of variables involved:

• What limit did you use?

• What action must be taken to eliminate multicollinearity?  Be very specific.  

• Which variable appears to have the weakest relationship with SALES?

Answer 1

1)yes data having multicollinearity,

if independent dependent to each other then we can say that data have multicollinearity ,,

2)now we observ above correlation matrix, pairs are:

(x1,x2)

(x1,x3)

this pair included in multicollinearity.

3)0.50 correlation limit we can check

4)Using Principal componunt analysis (PCA) we reduce multicollinearity

5) x9 is very less relation with sales ,correlation between them is 0.068

we assume less then 0.20 correlation value, we can say weak relation,

so x4, x5, x7, x8 also showing weak correlation.