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Math Help - Econometrics - confidence intervals

  1. #1
    J13
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    Econometrics - confidence intervals

    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
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  2. #2
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    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}
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  3. #3
    J13
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    Hi Robb,

    Thats exactly what I meant, thankyou for explaining it

    much appreciated
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