Statistics - Regression Intercept Confidence Interval

Statistics – Regression Intercept Confidence Interval

Regression Intercept Confidence Interval, is a method to decide closeness of two elements and is used to verify the reliability of estimation.

Method

R=β0±t(1α2,nok1)×SEβ0R=β0±t(1−α2,n−ok−1)×SEβ0

The place −

  • β0β0 = Regression intercept.
  • okok = Variety of Predictors.
  • nn = pattern dimension.
  • SEβ0SEβ0 = Customary Error.
  • αα = Share of Confidence Interval.
  • tt = t-value.

Instance

Drawback Assertion:

Compute the Regression Intercept Confidence Interval of following information. Whole variety of predictors (ok) are 1, regression intercept β0β0 as 5, pattern dimension (n) as 10 and customary error SEβ0SEβ0 as 0.15.

Resolution:

Allow us to think about the case of 99% Confidence Interval.

Step 1: Compute t-value the place α=0.99α=0.99.

=t(1α2,nok1)=t(10.992,1011)=t(0.005,8)=3.3554=t(1−α2,n−ok−1)=t(1−0.992,10−1−1)=t(0.005,8)=3.3554

Step 2: Regression intercept:

=β0+t(1α2,nok1)×SEβ0=5(3.3554×0.15)=50.50331=4.49669=β0+t(1−α2,n−ok−1)×SEβ0=5−(3.3554×0.15)=5−0.50331=4.49669

Step 3: Regression intercept:

=β0t(1α2,nok1)×SEβ0=5+(3.3554×0.15)=5+0.50331=5.50331=β0−t(1−α2,n−ok−1)×SEβ0=5+(3.3554×0.15)=5+0.50331=5.50331

Because of this, Regression Intercept Confidence Interval is 4.496694.49669 or 5.503315.50331 for 99% Confidence Interval.