In: Statistics and Probability
Consider the following regression model
Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i + ui
This model has been estimated by OLS. The Gretl output is below.
Model 1: OLS, using observations 1-59
coefficient | std. error | t-ratio | p-value | |
const | -0.1305 | 0.6856 | -0.1903 | 0.8498 |
X1 | 0.1702 | 0.1192 | 1.4275 | 0.1592 |
X2 | -0.2592 | 0.1860 | -1.3934 | 0.1692 |
X3 | 0.8661 | 0.1865 | 4.6432 | 0.0000 |
X4 | -0.8074 | 0.5488 | -1.4712 | 0.1470 |
Mean dependent var | -0.6338 | S.D. dependent var | 1.907 |
Sum squared resid | 143.74 | S.E. of regression | 1.6315 |
R-squared | 0.31849 | Adjusted R-squared | 0.26801 |
F(4, 54) | 6.309 | P-value(F) | 0.00031 |
Log-likelihood | -109.99 | Akaike criterion | 229.97 |
Schwarz criterion | 240.36 | Hannan-Quinn | 234.03 |
Construct a 99% confidence interval for β3β3.
Using the critical value method and a significance level of 5%, test H0:β1=1H0:β1=1 against H1:β1>1H1:β1>1.
Solution:
Given
n= 59 observation
P= Total number of parameters= 5
The 99% confidence interval for is
At
from t table
( 0.8661 - 0.497955, 0.8661+0.497955)
( 0.368145, 1.364055)
The 99% confidence interval for is
(0.368145, 1.364055)
To test the hypothesis
. Vs.
Test statistic
t = - 6.961409
Test statistic t = -6.961409
The t critical value at is
from t table
The t critical value = 1.674
Decision :
6.961409 > 1.674
Reject Ho
Conclusion : Reject Ho, there is sufficient evidence to conclude that has greater than 1