Econometrics - confidence intervals

**J13** · September 1st 2009, 10:12 AM

this is quite a common question in the exam papers,

it says obtain a 95% confidence intervals for B2 (Beta(subscript 2)).....

you are give the coefficient itself, R squared (the coefficient of determination) and the standard error. I was just wondering what the formula was to calculate this (its not one particular question im stuck on, just this type)

Thankyou in advance for any help

**Robb** · September 1st 2009, 06:37 PM

Hi,

So I take it you have ran a regression such as $y=\beta_{1}+\beta_{2}x+u$ where $u$ is some unobservable error term, and obtained estimators for the coefficients(often called beta hat - $\hat{\beta_{2}}$ , as well as the standard errors of the coefficents $se(\hat{\beta_{2}})$

The 95% confidence interval will be $\hat{\beta_{2}}\pm t_{n-k,0.025}\cdot se(\hat{\beta_{2}})=[\hat{\beta_{2}}-t_{n-k,0.025}\cdot se(\hat{\beta_{2}}),\hat{\beta_{2}}+t_{n-k,0.025}\cdot se(\hat{\beta_{2}})]$

Where $t_{n-k,0.025}$ is the t-stat value at the 2.5% level of significance for however many degrees of freedom in the regression. So if you had n=100 observations, and the model above with a constant and one explanatory variable you would have k=2, so you would need a t-stat of $t_{98,0.025}$

**J13** · September 2nd 2009, 11:45 AM

Hi Robb,

Thats exactly what I meant, thankyou for explaining it

much appreciated

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