Learn How to Calculate Regression Intercept Confidence Interval - Tutorial

Calculate Regression Intercept Confidence Interval - Definition, Formula and Example

Definition:

Regression Intercept Confidence interval is the method to discover the affinity between any two factors and is used to specify the reliability of estimation.

Formula:

Where,

β0 = Regression intercept k = Number of Predictors n = Sample Size SEβ0 = Standard Error α = Percentage of Confidence Interval t = t-Value

Example:

Assume that the total number of predictors (k) as 1, regression intercept (β0) as 5, sample size (n) as 10 and standard error (SEβ0) as 0.15. Calculate the Regression Intercept Confidence Interval.

Solution:
Given,

Number of Predictors (k) = 1 Regression intercept (β0) = 5 Sample Size (n) = 10 Standard Error (SEβ0) = 0.15

To Find,

Regression Intercept Confidence Interval

Case 1 : Calculation of 99% Confidence Interval

Calculate the t value from the given formula,

t(1-α/2,n-k-1)
α = 99 / 100 = 0.99
= t(1-0.99/2,10-1-1)
= t(0.005,8)
= 3.3554

Now substitute the t-value in the formula,

≤Regression intercept is = 5 - (3.3554 x 0.15)
= 5 - 0.50331
= 4.49669
≥Regression intercept is = 5 + (3.3554 x 0.15)
= 5 + 0.50331
= 5.50331
Case 2 : Calculation of 95% Confidence Interval

Calculate the t value from the given formula,

t(1-α/2,n-k-1)
α = 95 / 100 = 0.95
= t(1-0.95/2,10-1-1)
= t(0.025,8)
= 2.3060

Now substitute the t-value in the formula,

≤Regression intercept is = 5 - (2.3060 x 0.15)
= 5 - 0.3459
= 4.6541
≥Regression intercept is = 5 + (2.3060 x 0.15)
= 5 + 0.3459
= 5.3459
Case 3 : Calculation of 90% Confidence Interval

Calculate the t value from the given formula,

t(1-α/2,n-k-1)
α = 90 / 100 = 0.90
= t(1-0.90/2,10-1-1)
= t(0.05,8)
= 1.8595

Now substitute the t-value in the formula,

≤Regression intercept is = 5 - (1.8595 x 0.15)
= 5 - 0.278925
= 4.721075
≥Regression intercept is = 5 + (1.8595 x 0.15)
= 5 + 0.278925
= 5.278925

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