Question

Suppose you are estimating parameters of the following regression model:

Ŷt = 9941 + 0.25 X2t+ 15125 X3t

(6114) (0.121) (7349)

R²= 0.87, RSS = 10310

Answer 1

complete question:Suppose you are estimating parameters of the following regression model:

Ŷt = 9941 + 0.25 X2t+ 15125 X3t

(6114) (0.121) (7349)

R2= 0.87, RSS = 10310

(The figures in parentheses are the estimated standard errors. RSS are residual sum of squares.)(A) Using t-tests show whether individual coefficients are significantly different from zero at 5%

level of significance.(B) Test whether the coefficient of X2 is significantly different from 1 at 5% level ofsignificance.

solution

$A) \\ H0:β_0=0\space vs\space H1: β_0≠0\\T=\frac{β_0ˆ−β_0}{S.D.(β_0)}\\Under\space Null\space hypothesis\\T= \frac{9941}{6114} =1.626\\H0:β_1=0\space vs\space H1: β_1≠0\\T=\frac{\bar{β_1}−β_1}{S.D.(β_1)}\\Under\space Null\space hypothesis\\T= \frac{0.25}{0.121} =2.066\\ H0:β_2=0 \space vs \space H1: β_2≠0\\T=\frac{\bar{β_2}−β_2}{S.D.(β_2)}\\Under\space Null \space hypothesis\\T= \frac{15125}{7349} =2.058$

$H0:β_1=1 \space vs \space H1: β_1≠1\\T=\frac{\bar{β_1}−β_1}{S.D.(β_1)}\\Under\space Null\space hypothesis\\T=\frac{ 0.25−1}{0.121} =−6.19$

If T critical is less than the calculated value of T then we reject null hypothesis and conclude that there is significance of thecoefficient '