Question

The table below is a correlation matrix from the multiple regression you want to run.

	x1	x2	x3	y
x1	1
x2	0.724724	1
x3	0.970725	0.794503	1
y	0.984868	0.611978	0.953998	1

A) Which independent variable has the strongest correlation to the dependent variable?

a. x2

b. The table does not contain enough information to answer that

c. x1

d. x3

B) What is the value of the correlation that indicates serious multicollinearity?

a. 1

b. 0.970725

c. 0.953998

d. 0.984868

C) Which two variables show an indication of serious multicollinearity/

a. y and x1

b. x2 and x3

c. x1 and x3

d. y and x3

D) Which of the variables would you drop?

a. y

b. x2

c. x1

d. x3

Answer 1

A.) The correct answer is (c.) x1

As we can see from the table, corr(x1, y) = .984868 is the highest

B.) The correct answer is (b.) .970725

As we see from the table, that corr(x1, x3) is very high, .970725 and is an indicator of multi-collinearity

C.) The correct answer is (c.) x1 and x3

As we see from the table, that corr(x1, x3) is very high, .970725 and is an indicator of multi-collinearity

D.) The correct answer is (d.) x3

As we see from the table, that corr(x1, x3) is very high, .970725 and is an indicator of multi-collinearity, so we can drop any of the variables among x1 and x3. But we see, corr(x1 , x2) < corr(x2, x3) so we prefer dropping x3.