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Regression Intercept Confidence Interval, is a way to determine closeness of two factors and is used to check the reliability of estimation.
Formula
${R = beta_0 pm t(1 – frac{alpha}{2}, n-k-1) times SE_{beta_0} }$
Where −
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${beta_0}$ = Regression intercept.
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${k}$ = Number of Predictors.
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${n}$ = sample size.
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${SE_{beta_0}}$ = Standard Error.
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${alpha}$ = Percentage of Confidence Interval.
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${t}$ = t-value.
Example
Problem Statement:
Compute the Regression Intercept Confidence Interval of following data. Total number of predictors (k) are 1, regression intercept ${beta_0}$ as 5, sample size (n) as 10 and standard error ${SE_{beta_0}}$ as 0.15.
Solution:
Let us consider the case of 99% Confidence Interval.
Step 1: Compute t-value where ${ alpha = 0.99}$.
${ = t(1 – frac{alpha}{2}, n-k-1) \[7pt]
= t(1 – frac{0.99}{2}, 10-1-1) \[7pt]
= t(0.005,8) \[7pt]
= 3.3554 }$
Step 2: ${ge} $Regression intercept:
${ = beta_0 + t(1 – frac{alpha}{2}, n-k-1) times SE_{beta_0} \[7pt]
= 5 – (3.3554 times 0.15) \[7pt]
= 5 – 0.50331 \[7pt]
= 4.49669 }$
Step 3: ${le} $Regression intercept:
${ = beta_0 – t(1 – frac{alpha}{2}, n-k-1) times SE_{beta_0} \[7pt]
= 5 + (3.3554 times 0.15) \[7pt]
= 5 + 0.50331 \[7pt]
= 5.50331 }$
As a result, Regression Intercept Confidence Interval is ${4.49669}$ or ${5.50331}$ for 99% Confidence Interval.
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