Question

1) In a multivariable regression, the p-value for the test on the coefficient of a variable is equal to 0.0102. What does this tell us about the coefficient of that variable?

A) It is statistically different from 0 at 1% significance level

B) None of these are correct

C) It is statistically equal to 0 at 5% significance level

D) It is statistically different from 0 at 10% significance level

2) Which of the following is correct?

A) With Perfect multicollinearity the regression is computable but might be inconsistent

B) With Imperfect multicollinearity the regression is computable but it is inconsistent

C) With Perfect multicollinearity the regression is computable but might be biased

D) With Imperfect multicollinearity the regression is computable but might have large estimate error

Answer 1

Solution(1) : Option(D) is correct

Explanation:

The p-value for the test on the coefficient of a variable is equal to 0.0102

p-value=0.0102

let us define hypothesis for this variable

H0:β=0   ;not significant different from zero.

H1:β≠0   ;significant different from zero.

Criteria :

if p-value is less than given significance level then it is regarded as significant variable and we have to reject H0 and conclude that it is statistically significant different from zero at given level of significance.

if p-value is greater than given significance level then it is regarded as not significant variable and we have fail to reject H0 and conclude that it is statistically equal to zero at given level of significance.

Now, come to options:

A) It is statistically different from 0 at 1% significance level

Option (A) is wrong.

Explanation:

Significance level=1%=0.01

p-value =0.0102

p-value is greater than significance level, so we fail to reject H0 and conclude that it is statistically equal to zero at 1% level of significance.

C) It is statistically equal to 0 at 5% significance level

Option (C) is wrong.

Explanation:

Significance level=5%=0.05

p-value =0.0102

p-value is less than significance level, so we reject H0 and conclude that it is statistically different from zero at 5% level of significance.

D) It is statistically different from 0 at 10% significance level

Option(D) is correct .

Explanation:

Significance level=10%=0.10

p-value =0.0102

p-value is less than significance level, so we reject H0 and conclude that it is statistically different from zero at 10% level of significance.