Question

Consider the following set of dependent and independent variables. Using? technology, check for the presence of multicollinearity. If multicollinearity is? present, take the necessary steps to eliminate it.

y x1 x2 x3

10 2 15 5

10 5 10 15

16 5 13 9

13 8 10 12

22 7 2 18

23 11 8 17

27 16 7 23

30 20 4 20

26 39 8 27

38 22 5 30

A. Eliminate the variable (x ?) which has a VIF of ( ). No more variables need to be eliminated.

B. Eliminate the variable (x ?) Which has a VIF of ( ). Then, eliminate the variable (x ?) which has a VIF of (?).

C.No variables need to be eliminated.

Answer 1

The Variance Inflation Factor detects multicollinearity between the predictor variables where VIF = 1 means no multicollinearity and VIF = 1 to 5 means moderately correlated while VIF > 5 means there is a high multicollinearity in the predictor variables.

The VIF is defined as,

Where SE is the standard error of predictor variable (Obtained through regression analysis), Std.dev is the standard deviation of predictor variable ( Obtained using the excel function =STDEV() ) and OSE is the Overall standard error of regression (Obtained through regression analysis).

The VIF are obtained from the regression analysis in excel by using following steps,

Step 1: Write the data values in excel.

Step 2: DATA > Data Analysis > Regression > OK. The screenshot is shown below,

Step 3: Select Input Y Range: Variable Y column, Input X Range: Varable X1 and X2 column. The screenshot is shown below,

The result is obtained. The screenshot is shown below,

Step 4 Calculate the standard deviation of each predictor variable X1 and X2. The screenshot is shown below,

Step 5: Calculate the VIF for each predictor variable using the formula stated above,

From the result summary,

	Coefficients	Standard Error	OSE	Std.dev
x1	0.027781282	0.305486205	5.258453793	11.18779
x2	-0.482216939	0.707387686	5.258453793	3.994441
x3	0.821671388	0.575124405	5.258453793	7.805981

Eliminate the variable (x 1) which has a VIF of ( 3.644795) then, eliminate the variable (x 3) which has a VIF of (2.552665)