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=Î²0Â±t(1âˆ’Î±2,nâˆ’okâˆ’1)Ã—SEÎ²0R=Î²0Â±t(1âˆ’Î±2,nâˆ’okâˆ’1)Ã—SEÎ²0

The place âˆ’

• Î²0Î²0Â = Regression intercept.
• okokÂ = Variety of Predictors.
• nnÂ = pattern dimension.
• SEÎ²0SEÎ²0Â = Customary Error.
• Î±Î±Â = Share of Confidence Interval.
• ttÂ = t-value.

### Instance

Drawback Assertion:

Compute the Regression Intercept Confidence Interval of following information. Whole variety of predictors (ok) are 1, regression interceptÂ Î²0Î²0Â as 5, pattern dimension (n) as 10 and customary errorÂ SEÎ²0SEÎ²0Â as 0.15.

Resolution:

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

Step 1: Compute t-value the placeÂ Î±=0.99Î±=0.99.

=t(1âˆ’Î±2,nâˆ’okâˆ’1)=t(1âˆ’0.992,10âˆ’1âˆ’1)=t(0.005,8)=3.3554=t(1âˆ’Î±2,nâˆ’okâˆ’1)=t(1âˆ’0.992,10âˆ’1âˆ’1)=t(0.005,8)=3.3554

Step 2:Â â‰¥â‰¥Regression intercept:

=Î²0+t(1âˆ’Î±2,nâˆ’okâˆ’1)Ã—SEÎ²0=5âˆ’(3.3554Ã—0.15)=5âˆ’0.50331=4.49669=Î²0+t(1âˆ’Î±2,nâˆ’okâˆ’1)Ã—SEÎ²0=5âˆ’(3.3554Ã—0.15)=5âˆ’0.50331=4.49669

Step 3:Â â‰¤â‰¤Regression intercept:

=Î²0âˆ’t(1âˆ’Î±2,nâˆ’okâˆ’1)Ã—SEÎ²0=5+(3.3554Ã—0.15)=5+0.50331=5.50331=Î²0âˆ’t(1âˆ’Î±2,nâˆ’okâˆ’1)Ã—SEÎ²0=5+(3.3554Ã—0.15)=5+0.50331=5.50331

Because of this, Regression Intercept Confidence Interval isÂ 4.496694.49669Â orÂ 5.503315.50331Â for 99% Confidence Interval.