# Interpreting high standard errors

I am new to regression analysis. Some information about the data. Income is the dependent variable (continuous) and segments are predictors (nominal factors / categorical)

                  Estimate Std. Error t value     Pr(>|t|)
(Intercept)         79367      13510   5.874 0.0000000151 ***
segmentSegment2    -55827      20771  -2.688      0.00773 **
segmentSegment3    -32444      18073  -1.795      0.07397 .
segmentSegment4    -36729      19328  -1.900      0.05866 .
segmentSegment5    -30563      22062  -1.385      0.16732
segmentSegment6    -18841      22062  -0.854      0.39401
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

(Dispersion parameter for gaussian family taken to be 8213968357)

Null deviance: 1923983664930  on 231  degrees of freedom
Residual deviance: 1856356848731  on 226  degrees of freedom
AIC: 5962.7

Number of Fisher Scoring iterations: 2


Can someone explain to me:

1. Why are standard errors so high? Does it mean my data has many outliers?
2. What is the dispersion parameter and how do I interpret it?
3. How do I interpret such high null and residual deviance; again, how do I correct for this?
• What kind of model did you fit?
– Noah
Aug 23, 2022 at 15:26

Assuming you fit a linear regression model with a Gaussian family and identity link (which could have been fit using lm() for ordinary least squares instead of maximum likelihood), the dispersion parameter is the residual variance, the variance in the outcome not explained by the predictors. It's "high" because it is measured in square units. It has no useful interpretation on its own but is used to compute the standard errors and $$R^2$$ values (which would be reported if you used lm()).