Statistics 简明教程

Statistics - Regression Intercept Confidence Interval

回归截距置信区间是一种确定两个因素接近度的方法，用于检验估计的准确性。

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

Formula

其中——

Where −

${\beta_0}$ = Regression intercept.
${k}$ = Number of Predictors.
${n}$ = sample size.
${SE_{\beta_0}}$ = Standard Error.
${\alpha}$ = Percentage of Confidence Interval.
${t}$ = t-value.

Example

Problem Statement:

计算以下数据的回归截距置信区间。预测变量总数（k）为 1，回归截距 ${\beta_0}$ 为 5，样本量 (n) 为 10，标准误差 ${SE_{\beta_0}}$ 为 0.15。

Compute the Regression Intercept Confidence Interval of following data. Total number of predictors (k) are 1, regression intercept ${\beta_0}$ as 5, sample size (n) as 10 and standard error ${SE_{\beta_0}}$ as 0.15.

Solution:

Let us consider the case of 99% Confidence Interval.

步骤 1：计算 ${ \alpha = 0.99}$ 处的 t 值。

Step 1: Compute t-value where ${ \alpha = 0.99}$.

步骤 2：${\ge} $ 回归截距：

Step 2: ${\ge} $Regression intercept:

步骤 3：${\le} $ 回归截距：

Step 3: ${\le} $Regression intercept:

因此，对于 99% 置信区间，回归截距置信区间为 ${4.49669}$ 或 ${5.50331}$ 。

As a result, Regression Intercept Confidence Interval is ${4.49669}$ or ${5.50331}$ for 99% Confidence Interval.