Enter the sum of squares of X and the standard deviation of residuals into the calculator to determine the standard error of the slope. This calculator helps in statistical analysis to estimate the precision of the slope coefficient in linear regression.

Standard Error Of Slope Formula

The following formula is used to calculate the standard error of the slope. 

SE<sub>b</sub> = σ<sub>e</sub> / √(SS<sub>x</sub>)

Variables:

  • SEb is the standard error of the slope
  • σe is the standard deviation of residuals
  • SSx is the sum of squares of X

To calculate the standard error of the slope, divide the standard deviation of residuals by the square root of the sum of squares of X.

What is the Standard Error of the Slope?

The standard error of the slope (SEb) 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.

How to Calculate Standard Error of the Slope?

The following steps outline how to calculate the Standard Error of the Slope.

  1. First, determine the sum of squares of X (SSx).
  2. Next, determine the standard deviation of residuals (σe).
  3. Next, gather the formula from above = SEb = σe / √(SSx).
  4. Finally, calculate the Standard Error of the Slope (SEb).
  5. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Sum of squares of X (SSx) = 250

Standard deviation of residuals (σe) = 15