Econ 299 Chapter4b - 4.3 Confidence Intervals for Simple...

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Unformatted text preview: 4.3 Confidence Intervals for Simple Economic Models As covered previously, ordinary least squares estimation derives POINT ESTIMATES for our coefficients (b 1 and b 2 ).-These are unlikely to be perfectly accurate. Alternately, Confidence Intervals provide for us an estimate of a range for our coefficients.-We are reasonably certain that our value lies within that range. 4.3.1 Deriving a Confidence Interval Step 1: Recall Distribution We know that: (b 1 hat-b 1 )/se(b 1 hat) has a t distribution with N-2 degrees of freedom (b 2 hat-b 2 )/se(b 2 hat) has a t distribution with N-2 degrees of freedom This was derived under hypothesis testing using central limit theorems. 4.3.1 Deriving a Confidence Interval Step 2: Establish Probability: Using t-tables with N-2 degrees of freedom, we find t* such that: P(-t*<t<t*)=1- Note that t* cuts off /2 of each tail. Ie: if N=25 and =0.10, t*=1.71 4.3.1 Deriving a Confidence Interval Step 3: Express t Steps 1 and 2 combine to give us: P(-t*<(b 1 hat-b 1 )/se(b 1 hat) <t*)=1- And P(-t*<(b 2 hat-b 2 )/se(b 2 hat) <t*)=1- 4.3.1 Deriving a Confidence 4....
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Econ 299 Chapter4b - 4.3 Confidence Intervals for Simple...

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