I ran a linear regression with one variable predicting the dependent variable. I got two sets of results with different Std.Errors with one being under model summary and another being under coefficients sections. Which one should I rely on?
This annotated SPSS output may be useful: https://stats.idre.ucla.edu/spss/output/regression-analysis/
Your regression coefficient estimates are in the coefficient table. Your betas/slopes and y-intercept are here.
The model summary table gives you information as to how well your independent variable(s) is/are related to the dependent variable. The standard error of the estimate is the square root of the mean square residual in the ANOVA table.
Hello Hooman,
In the case of a regression model that has a single predictor (yours here is "age"), the test of the overall regression model is exactly the same as testing whether the correlation between the lone IV and the DV is significantly different from zero.
Note that the ANOVA table summarizes the test of the explanatory power of the regression model (e.g., testing that R = 0). The "Coefficients" table gives a t-test for whether the regression coefficient for age = 0. If you square the t-statistic (-14.093), you get the F-ratio from the ANOVA table (198.62; any discrepancy is due to SPSS not reporting all the decimal places). So, the tests are identical (again, in the case of a single predictor).
Finally, the standard error of estimate (given as 0.405) is the estimated standard deviation of the residuals, and if you square it, should equal the variance error (MSE) from the ANOVA table (.405^2 =.164), so these two statistics are congruent, as you would expect. [Technical note: I believe that SPSS uses the adjusted R-squared to compute SEE, so there can be times in which the SEE is actually larger than the square root of MSE.]
The standard error for the regression coefficient of age (given as 0.002) is not the estimated standard deviation of the residuals (as is SEE or the square root of MSE). It is the estimated SD of the presumed distribution of unstandardized coefficient values for age (given your sample size and observed r). So, this is a statistic that is distinct from SEE.
Good luck with your work.
Hi Hooman,
In this case, the regression results are presented in the coefficients section. However I expect that the significance level of ANOVA and slope of the model (at coefficients table) would be equal.
Hooman -
I'd say that the estimated unstandardized coefficients, and here their estimated standard errors, are important, but what may be concerning here, I think, is that the model consists of only a positive intercept from which one predictor, age, chips away. I don't know your application, and situations vary, but that sounds like (1) you may only have linearity in a limited range, and/or (2) there may be one or more additional predictors that are missing, or others you should use instead of age. Regarding (2), you don't want to overfit, but you don't want to underfit either. (A "graphical residual analysis" can be used to check fit, and "cross-validation" to check for overfitting to your data set.)
Cheers - Jim
This can be useful https://www.reneshbedre.com/blog/linear-regression.html
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