Question

MULTICOLLINEARITY
- definition, what cause M, how to detect M, example, effect if ignored M

Answer 1

Multi-Collinearity - It can be defined as the degree of correlation between two or more than two variable they can be moderately or Highly correlated to each other. When there is an increase in the correlation between the independent variables the regression model becomes less reliable.The Independent variables can together explain the dependent variables as of MultiCollinearity the coefficients may be rejected.

The model can be accepted through ANOVA and the F-Test, and the individual coefficients can be rejected through T-test.

Multicillinearity doesn't reduce the accuracy of the predictive powers.

Multiple Correlation Coefficients - Correlation Coefficients between two variables T and Z. The case of Multiple regression equation is -

Z = a + b₁T₁ + b₂T₂

Z can be correlated to both T₁ and T_2. We have a coefficient of multiple regression which measures correlation between Z and Both T₁ & T₂.

Causes of Multicollianearity -

1. Inaccurate use of Dummy variables.
2. When we include a variable which is a resultant of other variables in a data set.
3. Repetition of same variable again and again.
4. Higher Correlation among the variables.

Detection of Multicollinearity -

1. With the addition or deletion of variable increases the estimation of regression Coefficients.
2. With the help of F-test we can detect Multiple regression hypothesis.
3. Variance Inflation factor is another method to detect multicollinearity.
4. We can use Farrar- Glauber test to detect multicollinearity.
5. Correlation Matrices are also helpful.
6. Properly evaluating the incorrect Coefficients.

For Example - The following is the matrix of Correlation Coefficients between 3 variables Y, X₁ and X₂.

	Y	X1	X2
Y	1	0.8	0.6
X1	0.8	1	0.7
X2	0.6	0.7	1

When we calculate R_1.23 = ((r₁₂² + r₁₃² - 2r₁₂r₂₃r₁₃) (1-r₂₃²))^1/2

= ((0.8² + 0.6² -2*0.8*0.7*0.61) (1 - 0.7²))^1/2

= (0.643)^1/2 = 0.802

Hence 64.3% of the variation in Y can be explained by the Multiple regression equation in terms of X₁ and X_2.

Effects Multicollinearity is Ignored -

• When Variance Inflation factor is high,and the Interest factor do not effect Variance Inflation Factor.
• When the powers and products of other variables are included the model.
• Unbiased and consistent estimates, Doesn't effect them at all.
• Standard Errors tends to be large.