The standard error of the coefficient estimates the variability between coefficient estimates that you would obtain if you took samples from the same population again and again. The calculation assumes that the sample size and the coefficients to estimate would remain the same if you sampled again and again.
Use the standard error of the coefficient to measure the precision of the estimate of the coefficient. The smaller the standard error, the more precise the estimate. Dividing the coefficient by its standard error calculates a t-value. If the p-value associated with this t-statistic is less than your significance level, you conclude that the coefficient is statistically significant.
For example, technicians estimate a model for insolation as part of a solar thermal energy test:
Regression Analysis: Insolation versus South, North, Time of Day
Term Coef SE Coef T-Value P-Value VIF
Constant 809 377 2.14 0.042
South 20.81 8.65 2.41 0.024 2.24
North -23.7 17.4 -1.36 0.186 2.17
Time of Day -30.2 10.8 -2.79 0.010 3.86
In this model, North and South measure the position of a focal point in inches. The coefficients for North and South are similar in magnitude. The standard error of the coefficient for South is smaller than the standard error of the coefficient for North. Therefore, the model is able to estimate the coefficient for South with greater precision.
The standard error of the North coefficient is nearly as large as the value of the coefficient itself. The resulting p-value is greater than common levels of the significance level, so you cannot conclude that the coefficient for North differs from 0.
While the coefficient for South is closer to 0 than the coefficient for North, the standard error of the coefficient for South is also smaller. The resulting p-value is smaller than common significance levels. Because the estimate of the coefficient for South is more precise, you can conclude that the coefficient for South differs from 0.
Statistical significance is one criterion you can use to reduce a model in multiple regression. For more information, go to Model reduction.