Question

In: Statistics and Probability

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

Consider the following regression model

Y_i = β₀ + β₁X_1i + β₂X_2i + β₃X_3i + β₄X_4i + u_i

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.

Solutions

Expert Solution

Solution:

Given

n= 59 observation

P= Total number of parameters= 5

The 99% confidence interval for is

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

orchestra answered 1 year ago

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