Is it possible to identify the following equations with any standard equation referred to in the discussion relating to two-variable linear regression?

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Econometrics Test Full mark  25.

1. Is it possible to identify the following equations with any standard equation referred to in the discussion relating to two-variable linear regression? If yes, write down the name of the equation. Otherwise, write no.

E (Y│X)= α + βX+e

Y= α+ βX+e

Y ̂= α ̂+βX

Y= α ̂+ β ̂ X+u

E(Y│X)= α ̂+ (β ) ̂X

Y= α ̂+ (β ) ̂X+u

(Y ) ̂= α ̂+ (β ) ̂X+e

Y= α+ βX+u (8)

2. For a two-variable linear regression equation, develop a procedure for testing the significance of the coefficient of the explanatory variable. A sample of size N is drawn from the population.

Answer with respect to the following points:

a. Null hypothesis

b. Alternative hypothesis

c. What is the sample statistic?

d. How to convert the sample statistic into test statistic?

e. What distribution is followed by the test statistic?

f. What is the degree of freedom associated with the test statistic?

g. What assumption is to be used to calculate the test statistic?

h. p value decided by the investigator

i. Actual p value

j. How does the test arrive the result? (10)

3. Can you find out regression equation of x on y from regression equation of y on x? Justify with special reference to principle of least squares. (4)

4. We already used X in explaining Z. Now, we want to test whether another variable Y may be used in explaining Z, over and above X.

Which test statistics need to be used?

What other test statistic one may use ?

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