Regression Intercept Confidence interval is the method to discover the affinity between any two factors and is used to specify the reliability of estimation.
β0 = Regression intercept k = Number of Predictors n = Sample Size SEβ0 = Standard Error α = Percentage of Confidence Interval t = t-Value
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.
Number of Predictors (k) = 1 Regression intercept (β0) = 5 Sample Size (n) = 10 Standard Error (SEβ0) = 0.15
Regression Intercept 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 | |
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 | |
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 | |
