# Statistics – Regression Intercept Confidence Interval

Regression Intercept Confidence Interval, is a way to determine closeness of two factors and is used to check the reliability of estimation.

## Formula

R=β0±t(1−α2,n−k−1)×SEβ0R=β0±t(1−α2,n−k−1)×SEβ0

Where −

·        β0β0 = Regression intercept.

·        kk = Number of Predictors.

·        nn = sample size.

·        SEβ0SEβ0 = Standard Error.

·        αα = Percentage of Confidence Interval.

·        tt = t-value.

### Example

Problem Statement:

Compute the Regression Intercept Confidence Interval of following data. Total number of predictors (k) are 1, regression intercept β0β0 as 5, sample size (n) as 10 and standard error SEβ0SEβ0 as 0.15.

Solution:

Let us consider the case of 99% Confidence Interval.

Step 1: Compute t-value where α=0.99α=0.99.

=t(1−α2,n−k−1)=t(1−0.992,10−1−1)=t(0.005,8)=3.3554=t(1−α2,n−k−1)=t(1−0.992,10−1−1)=t(0.005,8)=3.3554

Step 2: ≥≥Regression intercept:

=β0+t(1−α2,n−k−1)×SEβ0=5−(3.3554×0.15)=5−0.50331=4.49669=β0+t(1−α2,n−k−1)×SEβ0=5−(3.3554×0.15)=5−0.50331=4.49669

Step 3: ≤≤Regression intercept:

=β0−t(1−α2,n−k−1)×SEβ0=5+(3.3554×0.15)=5+0.50331=5.50331=β0−t(1−α2,n−k−1)×SEβ0=5+(3.3554×0.15)=5+0.50331=5.50331

As a result, Regression Intercept Confidence Interval is 4.496694.49669 or 5.503315.50331for 99% Confidence Interval.