Standard Error of the Slope Calculator

Formula

The formula to calculate the standard error of the slope is:

\[ SE_b = \frac{\sigma_e}{\sqrt{SS_x}} \]

Where:

\( SE_b \) is the standard error of the slope
\( \sigma_e \) is the standard deviation of residuals
\( SS_x \) is the sum of squares of X

What is the Standard Error of the Slope?

The standard error of the slope (SE_b) is a measure used in statistics to estimate the accuracy of the slope coefficient (b) in a linear regression model. It represents the standard deviation of the sampling distribution of the slope coefficient and is used to construct confidence intervals and perform hypothesis tests on the slope.

Example Calculation

Let's assume the following values:

Standard Deviation of Residuals (σ_e): 3
Sum of Squares of X (SS_x): 100

Step 1: Calculate the Standard Error of the Slope (SE_b):

\[ SE_b = \frac{3}{\sqrt{100}} = \frac{3}{10} = 0.3 \]

The standard error of the slope is 0.3.