Question

For any of the independent variables, if the 95% confidence range was not given, how could you approximate it based on the other information in the table?

df

5 Residual

61 Regression

66 Total

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95%	Upper 95%
Intercept	1.4846	0.9086	1.6339	0.1074	-0.3323	3.3014	-0.3323	3.3014
Qtrly Close	0.0344	0.0310	1.1077	0.2723	-0.0277	0.0965	-0.0277	0.0965
Treasury (%)	0.4670	0.1735	2.6924	0.0091	0.1202	0.8138	0.1202	0.8138
M2 Supply	-0.7697	0.3085	-2.4953	0.0153	-1.3865	-0.1529	-1.3865	-0.1529
Unempl. Rate	-0.2017	0.0430	-4.6965	0.0000	-0.2876	-0.1158	-0.2876	-0.1158
Starts	0.0722	0.0315	2.2934	0.0253	0.0093	0.1352	0.0093	0.1352

Answer 1

Suppose we need to find the 95% CI for , the coefficient of the first independent variable.

It is known that ~t_n-k-1, where n= sample size, k= number of independent variables

Then 95% CI is  

Here, n=66+1, k=5, t_.025,61=1.99

For the first independent variable (Qrtrly close) , given that

Then the 95% CI is [.0344-1.9996*.031, .0344+1.9996*.031]=[-0.0277, 0.0965]

In a similar manner, the other CI's can also be obtained by replacing the respective estimates and SE.