+34 616 71 29 85 carsten@dataz4s.com

Residual plots

The residual plots can reveal conditions that are hard to see from the regression line. In a glimpse the residual plot can cast the overall picture of the errors in the model and thus if the conditions for inference seem to be met. The residual plots basically graph the conditions listed with the LINER model.

 

Key points on residual plots

  • Residual plots can, by a glimpse, reveal what is not so obvious viewing the regression line
  • Residual plots can give a visual cast of the overall error situation in a regression model
  • Residual plots enable visual assessment of the error scenario in a regression model
  • Residual plots graph the conditions described in the LINER model

 

 

Reflection on the residuals

As described in Regression line the true regression model can be denoted:

Residual plots_true line formula

where Y has the linear relationship with β0 + β1X and epsilon (ε) is the random error component which indicates that the observed datapoints have some variability in Y around the regression line. They are randomly distributed around the line.

The estimate of this line can be denoted:

Residual plots_estimated line formula

No epsilon (ε) is needed in the estimated regression model, because it is an estimated line and therefore, per definition, includes errors: Estimation is not the “exact thing”, it includes errors. So, the estimated regression line is composed by the estimated point, or, we can say that the estimated points are the line.

 

The errors in the estimated line are the distances from each observed datapoint to the regression line as I describe in Squared errors of line and can be denoted: ei = YiŶi.

 

Errors of line

 

  

Residual plots scenarios

In residual plots the errors are displayed around their mean of 0. The residuals sum up to zero: ∑ei = 0. The following examples display the two scenarios: 1) that inference is possible and 2) that inference is not possible:

Residual plots => inference possible

Residual plot 1: The variability for each observed X value is more or less equal and that there is linearity and thus no curvature. There is no indication of non-normality. So, this example indicates that the can be valid:

Residual plots

 

Residual plot 2: This residual plot also seems to be a ‘fairly reasonable’ as the variability in Y values seems to be approximately equal for all observed X values:

 

 

Residual plots

 

Residual plots => inference not possible

 

Residual plot 3: This residual plot would lead to the conclusion that inference is not possible as variability in the Y values differs for the observed X values. The greater X, the greater the variability in Y:

Residual plots

 

 

Residual plot 4: This residual plot shows a clear curvature:

 

Curvature

 

 

 

 

Residual plot 5: This residual plot shows a pattern of non-linearity and non-normality:

 

Residual plots_Non normality

 

 

Example: A model that complies with the conditions

Here is an example of a scatter plot with its estimated regression line that seemingly is ‘ok’ and seemingly allows for statistical inference:

 

Residual plots example

 

Our residual shows no ‘greater’ systematic variability nor curvature:

Glove size residual plot

 

The quantile-quantile plot can be applied to check for normality which also seems to be occurring as the datapoints indicate a “reasonable” fit to the line:

Quantile-quantile plot

 

So, for this model, we would accept the conditions and proceed with the statistical analysis for inference.

 

 

Example: “Revealed” by the residual plot

This example returns a regression line with a strong fit that also seemingly is ok, but where the residual plot reveals a different picture:

About the dataset

The following example is based on the dataset for Jankar hardness vs. density for 36 Austrialian trees. I’ve been inspired by the JBstatistics video for Checking Assumptions with Residual Plots and caught the dataset via the PASWR2 package for R statistical programming.

It shows 36 Australian trees for which density is relatively easy to measure and hardness is difficult to measure.

 

Regression line and r2

If we assess that the conditions for inference are met, we can predict the hardness by simply measuring the density. We can predict the values that are difficult to measure by observing the values that are easy to measure.

Based on the 36 datapoints the regression model gives a very strong fit with a coefficient of determination (r2) of some 95%:

 

Australian trees regression line

 

 

Visualizing the regression line, it seems reasonable to think that this model complies with the condition for statistical inference. However, the residual plot reveals a different picture:

Australian trees residual plot

 

 

It shows that there is both difference in the variability for each X value and that there is curvature:

Australian trees checking residual plot

 

And if we take an extra look at the regression line, we can maybe discern these conditions:

Australian trees hardness vs. density regression

 

So, what we initially, might not perceive from the scatter plot with the regression line was revealed by the residual plot.

In cases like this, where the model is not appropriate, we can improve the model by adding an x2 term that could help fit a curve through the datapoints, or in other ways transform data to achieve a linearity.

 

Residual plots in Excel

By ticking off the options under Residuals in Data >> Data Analysis >> Regression, the residual plots:

Residual plots in Excel

 

 

Learning resources

I find these learning resources helpful for learning on residual plots:

Carsten Grube

Carsten Grube

Freelance Data Analyst

115 Comments

  1. 안산출장샵

    안산출장샵
    Hi! I could have sworn I’ve visited this website before but after browsing through many of the posts I realized it’s new to me.
    Anyways, I’m certainly delighted I found it and I’ll be book-marking it
    and checking back often!가평출장샵 , https://jeonjutrip.club.

  2. 영양출장샵

    영양출장샵
    Hello would you mind stating which blog platform you’re using?
    I’m going to start my own blog soon but I’m having a tough
    time deciding between BlogEngine/Wordpress/B2evolution and
    Drupal. The reason I ask is because your design and style seems different then most blogs and I’m
    looking for something unique. P.S My apologies for getting off-topic but I had to ask!이천안마 , https://jecheonhorse.club.

  3. 천안출장샵

    천안출장샵
    Great post. I was checking constantly this weblog and I’m impressed!
    Extremely useful information specially the last part 🙂 I care for such information much.
    I used to be seeking this particular info
    for a very long time. Thank you and good luck. 구미출장안마 , https://gyeongjuswedish.site.

  4. 영천출장안마

    영천출장안마
    Right here is the perfect blog for everyone
    who wants to understand this topic. You know a whole lot its almost hard to argue
    with you (not that I personally would want to…HaHa).
    You certainly put a new spin on a subject which has been discussed for a long time.

    Excellent stuff, just great!수원출장샵 , https://chungjumassage.club.

  5. 전주안마

    전주안마
    Wow, superb weblog format! How lengthy have you ever been blogging for?

    you made blogging look easy. The whole look of your site is magnificent,
    let alone the content!
    광주출장안마 , https://ricewinenight.club.

  6. 충주출장안마

    충주출장안마
    Great work! That is the type of information that should be shared across the net.
    Shame on the seek engines for no longer positioning
    this put up higher! Come on over and seek advice from my website .
    Thank you =)포항출장안마 , https://pearlprostate.club.

  7. 영주안마

    영주안마
    Hi there, I discovered your blog by means of Google
    whilst looking for a related matter, your web site came up, it
    seems to be good. I have bookmarked it in my google bookmarks.

    Hello there, just changed into aware of your weblog through
    Google, and found that it is truly informative. I’m going to watch out for brussels.

    I will be grateful if you continue this in future. Numerous people shall be benefited out of your writing.
    Cheers!화천출장샵 , https://bucheonmassage.site.

  8. 수원출장샵

    수원출장샵
    Hey there just wanted to give you a quick heads up. The
    words in your content seem to be running off the screen in Opera.
    I’m not sure if this is a formatting issue or something to do with internet browser compatibility but I thought I’d post to let you know.
    The layout look great though! Hope you get the issue resolved soon. Thanks일산출장마사지 , https://gangwontrip.site.

  9. best everlast tig welder

    This is the right webpage for everyone who would like to understand this topic.
    You understand so much its almost hard to argue with you (not
    that I personally will need to…HaHa). You definitely put
    a brand new spin on a subject which has been discussed for
    decades. Great stuff, just wonderful!

  10. 포항안마

    포항안마
    I have been surfing online more than 2 hours today, yet I never found any interesting article like yours.
    It is pretty worth enough for me. In my view, if all site
    owners and bloggers made good content as you did, the web will be a
    lot more useful than ever before.아산안마 , https://gimcheonmassage.site.

  11. 강릉안마

    강릉안마
    Thanks for any other informative web site. Where else may just I get
    that kind of information written in such an ideal approach?
    I’ve a venture that I am simply now running on, and I have been on the look out for
    such info.영주안마 , https://nutritionbusiness.club.

  12. 시흥출장샵

    시흥출장샵
    I blog often and I really thank you for your information. This great article has
    truly peaked my interest. I am going to book mark your website and keep checking for
    new details about once per week. I opted in for your RSS
    feed as well.부천출장마사지 , https://pohangbutterfly.club.

  13. 속초출장샵

    속초출장샵
    You’re so awesome! I don’t think I’ve truly read anything
    like this before. So great to find somebody with some genuine thoughts on this subject matter.
    Really.. thank you for starting this up. This site is one
    thing that is required on the internet, someone with
    a bit of originality!여주안마 , https://jeonjuaroma.club.

  14. 김천출장샵

    김천출장샵
    My partner and I stumbled over here different website
    and thought I should check things out. I like what I see so now
    i’m following you. Look forward to exploring your web page for a second time.구리출장샵 , https://mass-productionbutterfly.club.

  15. 영양출장샵

    영양출장샵
    Thanks a lot for sharing this with all people you really recognise what
    you are speaking about! Bookmarked. Kindly also seek advice from my website =).
    We may have a hyperlink exchange agreement between us진주안마 , https://jeonjuswedish.club.

  16. 울산안마

    울산안마
    We are a group of volunteers and opening a new scheme in our community.
    Your site offered us with valuable information to
    work on. You’ve done an impressive job and our whole community will
    be grateful to you.여주출장마사지 , https://pearltrip.club.

  17. 진주출장샵

    진주출장샵
    Nice post. I learn something totally new and challenging on blogs
    I stumbleupon everyday. It’s always useful to read through content from other authors and use something from their web
    sites. 충주출장안마 , https://nutritiontrip.club.

  18. 안산출장안마

    안산출장안마
    I am curious to find out what blog platform you happen to be using?
    I’m experiencing some small security issues with my latest website
    and I’d like to find something more secure.

    Do you have any suggestions?부천출장안마 , https://changwonaroma.club.

  19. 구미안마

    구미안마
    This is very interesting, You are a very skilled blogger.
    I have joined your rss feed and look forward to seeking more
    of your great post. Also, I’ve shared your web site in my social networks!영천출장샵 ,
    https://jeonjutrip.club.

  20. 김해출장샵

    김해출장샵
    My brother suggested I might like this website. He was totally right.
    This post actually made my day. You can not imagine simply how much time I had spent for
    this information! Thanks!이천출장안마 , https://pyeongtaeknight.site.

  21. 이천안마

    이천안마
    Someone essentially help to make critically articles I would state.
    That is the very first time I frequented your website
    page and thus far? I amazed with the research you made to create this particular post extraordinary.
    Excellent task!경주출장안마 , https://mass-productionmassage.club.

  22. 영주출장안마

    영주출장안마
    Hello! I realize this is somewhat off-topic but I needed to ask.

    Does running a well-established blog such as yours take a lot of work?
    I am completely new to blogging but I do write in my journal everyday.

    I’d like to start a blog so I can share my experience and feelings online.
    Please let me know if you have any ideas or tips for brand new aspiring
    blog owners. Thankyou!시흥출장마사지 , https://hwacheontrip.site.

  23. 성남출장샵

    성남출장샵
    Link exchange is nothing else except it is simply
    placing the other person’s blog link on your page at appropriate place and
    other person will also do same in support of you.성남안마 , https://gimcheonhorse.site.

  24. 울산출장샵

    울산출장샵
    Hello There. I found your blog using msn. This is an extremely well written article.
    I will be sure to bookmark it and return to read more of your useful info.

    Thanks for the post. I’ll definitely comeback.일산출장마사지 , https://il-sannight.site.

  25. 용인안마

    용인안마
    This is a good tip especially to those fresh to the blogosphere.
    Simple but very precise information… Thank you for sharing this
    one. A must read post!영천출장샵 , https://gimcheonnight.club.

  26. 제천출장안마

    제천출장안마
    Greate article. Keep posting such kind of information on your site.
    Im really impressed by your blog.
    Hey there, You have performed a great job. I’ll definitely digg it and in my
    view recommend to my friends. I am confident they’ll be benefited from this
    website.보성출장샵 , https://copperhorse.site.

  27. 서산출장샵

    서산출장샵
    Unquestionably believe that that you stated. Your favourite justification appeared to be on the net the simplest thing to keep in mind of.
    I say to you, I certainly get irked while other folks think about concerns
    that they plainly do not realize about. You
    controlled to hit the nail upon the highest as neatly as outlined out the whole thing with no need side effect ,
    other folks could take a signal. Will probably be back to get more.
    Thanks아산출장샵 , https://gapyeongprostate.site.

  28. 평택출장안마

    평택출장안마
    I was very pleased to find this page. I need to to thank you for your time
    due to this fantastic read!! I definitely enjoyed every little bit of it and i also have you saved to fav to look
    at new things in your web site.양산안마 ,
    https://haeundaebutterfly.club.

  29. 가평출장샵

    가평출장샵
    I have been browsing on-line more than 3 hours nowadays, yet I by no means discovered
    any attention-grabbing article like yours.
    It’s beautiful price sufficient for me. In my view, if all
    web owners and bloggers made just right content as you did, the internet might be much more useful than ever before.안산안마 ,
    https://hwacheonprostate.site.

  30. 공주출장마사지

    공주출장마사지
    hey there and thank you for your info – I’ve definitely picked up something new from
    right here. I did however expertise a few technical points using this
    website, as I experienced to reload the web site lots of times previous to I could get it to load correctly.

    I had been wondering if your web hosting is OK? Not that
    I am complaining, but slow loading instances times will sometimes affect your placement
    in google and could damage your quality score if advertising and marketing
    with Adwords. Anyway I am adding this RSS to my e-mail and could look out for much more of your respective interesting
    content. Ensure that you update this again very soon.이천출장마사지 , https://ansanaroma.site.

  31. 서산안마

    서산안마
    An outstanding share! I have just forwarded this onto a friend
    who was conducting a little research on this.
    And he actually bought me dinner due to the fact
    that I stumbled upon it for him… lol. So allow me to reword this….
    Thank YOU for the meal!! But yeah, thanx for spending some time to talk
    about this matter here on your site.김천출장안마
    , https://seong-namhorse.site.

  32. 수원출장샵

    수원출장샵
    What’s up everyone, it’s my first pay a quick
    visit at this web site, and article is in fact fruitful in support of me, keep up posting such articles
    or reviews.공주출장샵 , https://siheungnight.site.

  33. 여주출장샵

    여주출장샵
    This is really fascinating, You are an overly professional blogger.
    I’ve joined your feed and sit up for seeking extra of your great post.
    Also, I’ve shared your website in my social networks평택출장마사지 ,
    https://ulsanhorse.site.

  34. 창원출장안마

    창원출장안마
    I’m no longer sure where you are getting your information, but good topic.

    I needs to spend a while studying much more or figuring out more.

    Thank you for excellent info I was searching for this information for my mission.아산출장안마 , https://cheonanaroma.club.

  35. 충주출장안마

    충주출장안마
    We are a group of volunteers and starting a new scheme in our community.

    Your site offered us with valuable information to work on. You have done an impressive job and
    our entire community will be grateful to you.해운대안마 , https://chungjunight.club.

  36. 구미출장샵

    구미출장샵
    Somebody essentially lend a hand to make critically articles I might state.

    This is the very first time I frequented your
    web page and so far? I surprised with the research
    you made to make this actual put up extraordinary.
    Great job!양산출장안마 , https://gangnamaroma.club.

  37. 시흥출장마사지

    시흥출장마사지
    Hi my friend! I wish to say that this post is awesome,
    great written and include approximately all significant infos.
    I would like to see extra posts like this .양산출장안마
    , https://sejongaroma.site.

  38. 진주출장샵

    진주출장샵
    Aw, this was an extremely good post. Taking a few minutes and actual effort to produce a very good article… but what can I say… I
    hesitate a whole lot and don’t seem to get nearly anything done.강릉출장마사지 ,
    https://gangwontrip.site.

  39. coin master hacks

    I want to to thank you for this wonderful read!!
    I definitely loved every little bit of it. I’ve got you book-marked to look at new stuff you post…

  40. free like me tik tok song

    I like the helpful information you supply in your articles.
    I’ll bookmark your weblog and take a look at
    once more here frequently. I’m moderately certain I’ll
    be informed many new stuff right right here!
    Best of luck for the following!

  41. american dad apocalypse soon cheats 2020

    What i do not realize is actually how you’re no longer really a lot more well-appreciated than you may
    be right now. You are very intelligent. You already know therefore considerably in the case of this matter, made me
    personally imagine it from numerous various angles. Its like
    men and women don’t seem to be involved unless it is something to do
    with Woman gaga! Your personal stuffs outstanding.
    Always maintain it up!

  42. free tiktok likes without email

    Write more, thats all I have to say. Literally, it seems as though you relied on the
    video to make your point. You obviously know what youre talking
    about, why throw away your intelligence on just posting videos to your weblog when you could be giving us something enlightening to read?

  43. badoo premium hack android

    I know this if off topic but I’m looking into starting my own blog and was curious what all is required to get set up?
    I’m assuming having a blog like yours would cost a pretty penny?
    I’m not very web smart so I’m not 100% positive.
    Any recommendations or advice would be greatly appreciated.
    Thanks

  44. visor de perfil privado de instagram xda

    Hello there! I know this is somewhat off topic but I was wondering if you knew where I could get a captcha plugin for my comment form?

    I’m using the same blog platform as yours and I’m having
    trouble finding one? Thanks a lot!

  45. Robbie

    Wonderful blog! Do you have any tips for aspiring
    writers? I’m hoping to start my own site soon but I’m a little lost on everything.
    Would you recommend starting with a free platform like WordPress or go
    for a paid option? There are so many choices out there that I’m totally confused ..
    Any recommendations? Cheers!

  46. tiktok gratuit comme

    I think that what you posted was very reasonable. However, what about this?
    suppose you added a little content? I ain’t suggesting your information isn’t good, but suppose you added a post title to
    maybe grab folk’s attention? I mean Residual Plots –
    Statistical Data Analysis. Freelance Consultant is kinda boring.
    You could look at Yahoo’s front page and note how they create news titles to get people to click.
    You might add a related video or a related
    pic or two to grab people interested about everything’ve written. Just my opinion, it would bring your website a little bit more interesting.

  47. badoo premium free 2020

    Thanks for your personal marvelous posting! I really enjoyed
    reading it, you might be a great author. I will make sure to bookmark your blog and will come back someday.
    I want to encourage continue your great work, have a
    nice weekend!

  48. treadmill reviews 2020 budget

    Do you have a spam issue on this blog; I also am a
    blogger, and I was curious about your situation; we have created some nice procedures and we are looking to exchange solutions with other
    folks, why not shoot me an email if interested.

  49. fifa 20 hack coin generator

    After looking over a number of the articles on your blog,
    I really appreciate your technique of blogging.

    I bookmarked it to my bookmark site list and will be checking back soon. Please check out my website too and tell me what
    you think.

  50. fifa 18 coin generator without human verification

    Woah! I’m really enjoying the template/theme of this site.
    It’s simple, yet effective. A lot of times it’s very hard to get that “perfect balance” between usability and visual
    appeal. I must say that you’ve done a great job with this.

    In addition, the blog loads very quick for me on Opera.

    Superb Blog!

  51. free tiktok followers and like

    I was recommended this web site by means of my cousin. I am not certain whether or not this submit is written by way
    of him as no one else realize such exact
    approximately my trouble. You are incredible! Thanks!

  52. badoo mobile free download

    What’s up i am kavin, its my first time to commenting anywhere,
    when i read this post i thought i could also create
    comment due to this sensible paragraph.

  53. cách hack badoo premium

    Hi! This post couldn’t be written any better! Reading
    this post reminds me of my old room mate! He always kept chatting
    about this. I will forward this article to him. Pretty sure he will have a good read.
    Many thanks for sharing!

  54. Générateur de code de carte cadeau Steam 2020

    Woah! I’m really digging the template/theme of this
    site. It’s simple, yet effective. A lot of times it’s
    difficult to get that “perfect balance” between user friendliness and visual appeal.
    I must say you have done a very good job with this.
    Also, the blog loads super quick for me on Safari.
    Exceptional Blog!

  55. relógio instagram privado

    Hi my friend! I want to say that this article is awesome, great written and come with almost all significant infos.
    I’d like to look more posts like this .

  56. abonnés tiktok gratuits kostenlos

    Excellent post. I used to be checking constantly this blog and I am impressed!
    Very helpful information specially the closing part :
    ) I maintain such info much. I used to be seeking this certain info for a very long time.
    Thank you and good luck.

  57. Antony

    This is my first time visit at here and i am really impressed
    to read all at single place.

  58. Code d'activation du générateur de cartes-cadeaux Steam

    Have you ever considered publishing an e-book or guest authoring on other websites?
    I have a blog based upon on the same ideas you discuss and would love to have
    you share some stories/information. I know my audience would
    value your work. If you’re even remotely interested, feel free to shoot me an e mail.

  59. generator key for fifa 16

    Hi there! I know this is somewhat off topic
    but I was wondering which blog platform are you using for this site?

    I’m getting tired of WordPress because I’ve had problems with
    hackers and I’m looking at options for another platform.
    I would be great if you could point me in the direction of a good platform.

  60. fifa 20 generator coins

    Wow that was unusual. I just wrote an incredibly long comment but after I clicked submit my
    comment didn’t appear. Grrrr… well I’m not writing all that over again. Anyhow, just wanted to say superb blog!

  61. free dating sites uk badoo

    We’re a bunch of volunteers and opening a brand new scheme in our community.
    Your web site provided us with valuable info to work on. You’ve performed an impressive task
    and our whole community will be grateful to you.

  62. badoo premium free cydia

    What’s Taking place i’m new to this, I stumbled upon this I’ve discovered It positively useful and it has aided me
    out loads. I hope to give a contribution & assist other customers
    like its aided me. Good job.

  63. visor de perfil privado de instagram en línea sin verificación humana

    hello there and thank you for your info – I have definitely picked up something new from right here.
    I did however expertise a few technical issues using this website, since I experienced to reload the web site
    a lot of times previous to I could get it to load correctly.
    I had been wondering if your web host is OK?
    Not that I’m complaining, but sluggish loading instances times
    will very frequently affect your placement in google and could damage your high-quality score if ads and marketing with Adwords.
    Well I am adding this RSS to my e-mail and could look out
    for a lot more of your respective interesting content.
    Make sure you update this again soon.

  64. aplicación de visor de instagram privado 2020

    Simply want to say your article is as astonishing.

    The clearness in your post is just spectacular and i can assume you are an expert on this subject.

    Fine with your permission allow me to grab your feed to keep up to date with forthcoming post.
    Thanks a million and please carry on the gratifying work.

  65. software de visualización de instagram privado

    A fascinating discussion is definitely worth comment.
    I do believe that you need to write more about this subject matter, it may not be a taboo subject but
    generally folks don’t talk about these topics.
    To the next! Best wishes!!

  66. tiktok gratuit aime le piratage

    Wow! This blog looks just like my old one! It’s on a
    completely different subject but it has pretty much the same layout and design. Superb choice
    of colors!

  67. visor de perfil privado de instagram sin verificación o encuesta humana

    Hey there! I realize this is kind of off-topic however I had to ask.
    Does operating a well-established website like yours require a
    lot of work? I am completely new to running a blog however I do write in my diary daily.

    I’d like to start a blog so I will be able to share
    my own experience and feelings online. Please let me know if you have
    any ideas or tips for brand new aspiring blog owners.
    Thankyou!

  68. Race Kings cash

    Fantastic beat ! I would like to apprentice while you amend your website, how
    could i subscribe for a weblog website? The account aided me a appropriate deal.

    I were tiny bit familiar of this your broadcast provided bright clear idea

  69. Ngan

    Admiring the commitment you put into your blog and detailed information you provide.
    It’s awesome to come across a blog every once in a while that isn’t the same unwanted rehashed information. Excellent read!
    I’ve saved your site and I’m adding your RSS feeds to my Google account.

Submit a Comment

+34 616 71 29 85

Call me

Spain: Ctra. 404, km 2, 29100 Coín, Malaga

...........

Denmark: c/o Musvitvej 4, 3660 Stenløse

Drop me a line

What are you working on just now? Can I help you, and can you help me? 

About me

Learning statistics. Doing statistics. Freelance since 2005. Dane. Living in Spain. With my Spanish wife and two children. 

What they say

20 years in sales, analysis, journalism and startups. See what my customers and partners say about me.