The problem of multicolinearity is a persistent one, usually bringing devestation with it for analysts unable to detect/treat it. Perform a preliminary search of cases in which multicolinearity presents an issue for researchers/analysts, and explain potential sources of the multicolinearity.

Now consider the below patient-satisfaction data. Analyze this data for near-linear dependence by using Equation 9.3 to compute the variance inflation factor. Does this data exhibit multicollinearity?

SatisfactionAgeSeverityAnxiety

6855502.1

7746242.8

9630463.8

8035484.5

4359582

4461655.1

2674605.5

8839423.2

7582423.1

5727502.4

5651382.2

8853302.1

8841311.9

10237343.1

8824303

7027484.2

8250614.6

4358715.3

Equation 9.3 (Image attached)

When there are more than two regressor variables, multicollinearity produces similar effects. It can be shown that the diagonal elements of the C = (X'X)-1 matrix are Ci =1-R? j = 1, 2, ..., P (9.3) where R? is the coefficient of multiple determination from the regression of x; on the remaining p - 1 regressor variables. If there is strong multicollinearity between x; and any subset of the other p - 1, regressors, then the value of R? will be close to unity. Since the variance of B, is Var ( B; ) = C,jo? = (1-R; ) 62 , strong multicol- linearity implies that the variance of the least-squares estimate of the regression coefficient , is very large. Generally, the covariance of B; and B, will also be large if the regressors x; and x; are involved in a multicollinear relationship