#### Howdy, Stranger!

It looks like you're new here. If you want to get involved, click one of these buttons!

Supported by

# Linear regression analyses: Assumptions of linearity and normally distributed residuals

Hello everybody,

I have another question with regard to Bayesina linear regression analysis (I would like to conduct six regression analyses (6 DVs) with 4 IVs and 5 covariates.

1) Linearity: As recommended in the turorial on Bayesian regression of van den Bergh et al. (A tutorial on bayesian multi-model linear regression with BAS and JASP), assumptions of linearity should be checked first. I have attached my correlation plots (page 1). As my relations between the four IVs and the six DVs didn't look linear by eye, I log-transformed the IVs. However, I am not sure if the assumption of linearity is no longer violated because the plots do look a little bit strange (page 2).

2) Non-normally distributed residuals: Are there any indices indicating when the residuals are not normally distributed, by inspecting the plots residuals vs. fitted? Because I am not sure if my residuals are approx. normally distributed (I attached the plots, page 3/4), especially DV 2 and DV 3. Furthermore, I have no idea (based on theoretical knowledge) which term I should add to the analysis (e.g., interaction term).

And conerning both assumptions: I learned a long time ago that violations of linearity and non-normally distributed residuals can be "ignored" with larger samples sizes. My sample size is approx. 180. Still, I am wondering if I can ignore these assumptions?

Thank you so much for your help!

Alexa

----

As I was not able to upload my attachment (neither in word nor pdf): "Request failed with status code 413", I inserted the screenshots. I hope it works like this.

• Hello,

I already solved the issue of question 1. I commited a fallacy, as I simply do not have a linear relationship between some IV / DV. There is simply no logistic / quadratic relationship so I do not need to transform my variables. Concerning question 2, I am still curious if there are any indices telling me when the residulas are still accetably distrubted.

Thank you!

Alexa

• edited May 11

Regarding normality, a standard assumption-check is the Shapiro-Wilk test. While I'm not seeing that as an option in JASP's regression routines, you can find the test elsewhere, outside of JASP. You could put in a feature-request to have it included in JASP.

R

• Dear Alexa, I agree that it will be worthwhile to request the Shapiro-Wilk test. This being said, for now you can also use the residuals histogram with standardised residuals and the Q-Q plot of standardised residuals available under the plots tab in regression,

For more background, see, for example:

4 Normality | Regression Diagnostics with R (wisc.edu)

• JASP includes the Shapiro-Wilk test under "Descriptives" -> "Statistics" -> "Distributions". However, what is at issue here is whether the residuals are normally distributed. For this we offer QQ plots and plots of residuals vs fitted values.

EJ