Question

In: Statistics and Probability

Consider the following regression model Yi = β0 + β1X1i + β2X2i + β3X3i + β4X4i ...

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
  1. Construct a 99% confidence interval for β3β3.

  2. Using the critical value method and a significance level of 5%, test H0:β1=1H0:β1=1 against H1:β1>1H1:β1>1.

Solutions

Expert Solution

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


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