0
$\begingroup$

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?
$\endgroup$
1
  • $\begingroup$ What kind of model did you fit? $\endgroup$
    – Noah
    Aug 23, 2022 at 15:26

1 Answer 1

3
$\begingroup$

The standard errors are "high" because they are on the scale of the outcome variable. If you had measured income in 100s of thousands of dollars, the coefficients and standard errors would be rescaled accordingly. Qualifiers like "high" and "low" ned to be understood with respect to the scale of the variables they are measuring. 10 could be low if the variable was dollars and extremely high if the variable was millions of dollars. The same is true of your standard errors.

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()).

You don't need to interpret the deviance; those are used in model comparison and it is their relative value that is relevant, not their absolute value. Deviance is usually not relevant to linear regression models, which are typically fit using ordinary least squares. Several of these outputs are reported for generalized linear models fit with maximum likelihood, which is overkill for the simple model you are fitting.

$\endgroup$
9
  • $\begingroup$ In "10 could be low if the variable was dollars and extremely high if the variable was millions of dollars.", I think you might have switched "high" and "low". $\endgroup$
    – dipetkov
    Aug 23, 2022 at 21:12
  • $\begingroup$ Just so I understand correctly- if the range of income was 1-10, then the standard errors in my model would be ‘high’. However, my incomes rands from 1-180000. This is why I have such high standard errors? $\endgroup$
    – Rnovice
    Aug 24, 2022 at 0:30
  • $\begingroup$ Could you also explain why I’d use an identity like here? What is the purpose? $\endgroup$
    – Rnovice
    Aug 24, 2022 at 0:43
  • $\begingroup$ Finally, how would you interpret and report this model? I have never worked with a categorical predictor with multiple factor levels before- my interpretation is that members of segment 1 have significantly higher sales than segment 2. Is that accurate? $\endgroup$
    – Rnovice
    Aug 24, 2022 at 0:46
  • $\begingroup$ To answer your above comment, I used glm(). Let me run this using lm() and see what results I get $\endgroup$
    – Rnovice
    Aug 24, 2022 at 0:52

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.