# Interpretation for R squared multiple regression

Call:
lm(formula = formal_engaged_replaced ~ setting_interest + setting_trust +
setting_contact + setting_confidence + setting_visibility +
network_close_network + network_help_neighbour + network_help_orgs +
personal_sex + poverty_replaced + personal_education, data = train_model)

Residuals:
Min      1Q  Median      3Q     Max
-0.6084 -0.3168 -0.1750  0.4730  0.9894

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept)             0.694967   0.172963   4.018 8.15e-05 ***
setting_interest        0.082989   0.036994   2.243   0.0259 *
setting_trust          -0.095590   0.039447  -2.423   0.0162 *
setting_contact         0.006969   0.040477   0.172   0.8635
setting_confidence      0.023480   0.041886   0.561   0.5757
setting_visibility      0.090994   0.040536   2.245   0.0258 *
network_close_network   0.001323   0.004591   0.288   0.7734
network_help_neighbour -0.008214   0.030320  -0.271   0.7867
network_help_orgs       0.032154   0.032971   0.975   0.3306
personal_sex            0.016613   0.059559   0.279   0.7806
poverty_replaced        0.017542   0.034989   0.501   0.6167
personal_education      0.035840   0.020845   1.719   0.0870 .
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.4294 on 212 degrees of freedom
Multiple R-squared:   0.11, Adjusted R-squared:  0.06385
F-statistic: 2.383 on 11 and 212 DF,  p-value: 0.008439



I'm very confused with interpreting the variable, as the Multiple R-squared: 0.11, does it mean that it's bad ?

Also when running the multiple regression is it recommended to check for the assumption as my data is categorical its doesn't meet any assumption. and I just coded for regression without any transformation, is there any way to do it?

• Do you mean check to see if your dependent variable meets the assumption that it’s normally distributed? Jan 21, 2023 at 16:02
• I mean, if i check for the data - it doesn't qualify any of the assumptions, is it necessary to check the assumptions, like independence, normal distribution etc in order to proceed with multivariate regression?
– none
Jan 22, 2023 at 17:18
• @none That question about checking for assumptions really warrants it’s own posted question, as it differs from the $R^2$ discussion.
– Dave
Jan 22, 2023 at 17:22

The context matters.

In general, it is difficult to assign labels like “good” and “bad” to any performance metric, be it $$R^2$$ or something else. Your value of $$0.11$$ is better than $$0.10$$ and worse than $$0.12$$. However, it is not reasonable to think of $$R^2$$ in terms of letter grades in school. It could be that your value is the best ever at a task like this, which sounds like an $$A$$-grade to me; or it could be than even $$R^2=0.9$$ is rather mediocre performance, when though such a number looks like an $$A$$-grade.

What your value of $$0.11$$ does tell you is that you have made an improvement upon naïvely predicting the overall mean of $$\bar y$$. While modelers might want to get much better predictions than such a naïve strategy would, you are doing something useful, rather than being outperformed by such a simple strategy.

If other work like yours is getting $$R^2$$ values around where you are, that should be encouraging. If other work is getting bigger values, that is less encouraging.

$$R^2$$ has some limitations, chiefly that it can be driven high by overfitting to the data. If you don’t want to do any kind of out-of-sample performance assessment, you might be interested in the adjusted $$R^2$$, which, loosely speaking, makes an attempt to penalize for overfitting, and I’ve given a more technical description here.

• Thankyou for the brief answer, for R2 the value should lie between 0 and 1, if i interpret my model is it the best fit for that with 0.11 %? and enough to say that the dependent variable made an improvement? also for the multivariate regression, is it necessary to check all the assumptions?
– none
Jan 22, 2023 at 17:21
• Your $R^2$ corresponds to explaining. $11\%$ of the variance, not $0.11\%$. // The inquiry about checking assumptions really warrants a separate posted question.
– Dave
Jan 22, 2023 at 17:23