Scatter Plot, Linear Reg, Correlation & Residuals with TI-NSPIRE

แชร์
ฝัง
  • เผยแพร่เมื่อ 15 พ.ย. 2024

ความคิดเห็น • 179

  • @assassanationman
    @assassanationman 5 ปีที่แล้ว +14

    You posted this 8 years ago and just saved me in my elementary stats class in my first semester of college!! Thank you so much!!

    • @profrobbob
      @profrobbob  5 ปีที่แล้ว

      You are so welcome...thanks for tuning in!
      Please sub and share this free resource with your college professor and all your classmates...BAM!!!

    • @ReversePrimeOFFICIAL
      @ReversePrimeOFFICIAL 4 ปีที่แล้ว

      Elementary?

    • @profrobbob
      @profrobbob  4 ปีที่แล้ว

      @@ReversePrimeOFFICIAL Yes, AP Statistics is equivalent to Introduction to Statistics in college.

  • @jessicam.2382
    @jessicam.2382 8 ปีที่แล้ว +23

    I owe you a huge thank you! My ap stats class just learned how to plot residual plots on ti-84 calculators, but I own a ti nspire cx! No one else has one or knows how to use it, so I turned to TH-cam! Thank you very much!

    • @jessicam.2382
      @jessicam.2382 8 ปีที่แล้ว +2

      I'm going to share this video with my teacher so in the future he can share it with his fellow ti nspire students!

    • @profrobbob
      @profrobbob  8 ปีที่แล้ว +3

      You're welcome...that's AWESOME!!!
      Glad it helped too...we really appreciate the share with your teacher, and don't forget to throw in that I have another 579 math videos to go with it...BAM!!!

  • @1samc
    @1samc 4 ปีที่แล้ว +1

    "Enjoy your NSpires if you got'em". Oh yeah, these are the Ferraris of calculators! Only problem I have is I didn't find out about it 6 months ago and bought it then! Thanks Mr. Tarrou for the amazingly detailed and thorough video, it helped a lot _more_ than I expected!!! :D

    • @profrobbob
      @profrobbob  3 ปีที่แล้ว +1

      Glad to hear that you are happy with your new calculator and that I could help you with scatter plots and regression lines🙂👨‍🏫

  • @JacobHuber
    @JacobHuber 11 ปีที่แล้ว

    THANK YOU SO MUCH FOR THIS TUTORIAL. You will not believe how much easier you just made my Trig class. I thank you.

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    I am glad you found my videos helpful:)

  • @AnaSmith1723
    @AnaSmith1723 10 ปีที่แล้ว +1

    It has been a year and I still think you are a life saver! This video is exactly what I needed it !!

    • @profrobbob
      @profrobbob  10 ปีที่แล้ว +1

      BAM!!! Ana Smith ...I'm glad to hear that you can still count on #ProfRobBob for help whenever you need it:)...and thanks for your continued support!

  • @RouKas
    @RouKas 4 ปีที่แล้ว +1

    THANK YOU SOO MUCH!! I have a huge test coming up and I needed this video!! thanks!!

    • @profrobbob
      @profrobbob  4 ปีที่แล้ว

      You're welcome...thanks for watching and subbing!
      Now go pass that test like BAM!!! and p[lease be sure to share this free resource with EVERYONE:D

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว

    Add a calculator page, in the Menu go to Statistics then List Math then Sum of Elements. Once the sum command is up hit Vars and chose stat.resid. The final command is sum(stat.Resid^2)

  • @jairogutierrez5223
    @jairogutierrez5223 4 ปีที่แล้ว +1

    +ProfRobBob Hello! Greetings from Colombia, I had looked for a tutorial in Spanish as well as this one and I had not found it, thanks you helped me a lot.

    • @profrobbob
      @profrobbob  4 ปีที่แล้ว

      Greetings from Florida and thanks for giving us a try!
      ...did you use google translate to watch it with or do you speak enough english to understand?

  • @jessicalane9557
    @jessicalane9557 5 ปีที่แล้ว +2

    I owe you my life!!! THANK YOU FOR BEING SO SO HELPFUL

    • @profrobbob
      @profrobbob  5 ปีที่แล้ว +2

      No life necessary...just sub and spread the word about this free resource and Thanks for watching!

  • @leopardtate
    @leopardtate 12 ปีที่แล้ว

    was taking a quiz the other day, and could not for the life of me figure out how to do this on mine! Finally got it thanks to this tutorial :D

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว

    Happy to be able to help, that's what I'm here for! Thanks for subscribing and I hope you will enjoy learning from Tarrou's Chalk Talk and tell all your friends where to find me:) Now go get that A and pass that test like BAM!!!

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    Your'e welcome..thanks for choosing my video to watch:)

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    and I did it all without a life preserver...so glad I could help! Thanks for watching and supporting:)

  • @morgan_kinnaman
    @morgan_kinnaman 11 ปีที่แล้ว

    I purchased my TI-nspire for class so that I could use it in higher mathematics and save documents, but I fell behind for two days because of the learning curb to it... Thank you for helping me get over that curb, I'm now blazing through the problems and I'm sure I'll get an A tomorrow in my test :)

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    I hope you did good on your quiz. Glad I could help.

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    YOU ARE SO WELCOME:)) !!!!!! Thanks for watching too.

  • @THE31M0
    @THE31M0 13 ปีที่แล้ว

    thank you for posting this...my teacher has the whole class using ti 83 plus but i bought my own ti nspire cx and we are doing lin reg and i couldnt figure out how to do it. Thank you so much!

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    You need the lists and spreadsheets page to enter all the data required to make this graph.

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    You may want to pass this on to your teacher. I am sure you are not the only student with a TI-NSPIRE. I hope you do great in your class.

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    Happy to be able to send you a life-ring:)) Keep watching and sharing my channel with your friends:D...and have a happy turkey day!

  • @VictimOfFat3
    @VictimOfFat3 12 ปีที่แล้ว

    Thank you so much, was also wondering how to do a residual analysis but looking at this jogged my memory.

  • @profrobbob
    @profrobbob  13 ปีที่แล้ว

    @THE31M0 You are welcome. Glad I could help. Let me know if there is anything on this calculator you need to know how to do.

  • @atsedearagaw2695
    @atsedearagaw2695 9 ปีที่แล้ว +1

    U R A LIFESAVER!! My teacher doesn't teach anything correctly

    • @profrobbob
      @profrobbob  9 ปีที่แล้ว

      Atsede Aragaw thanks for watching and please share my channel with the rest of your class and your teacher as an additional study reference:D

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว

    And THANK YOU for your support!

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    There is a big learning curve for the NSPIRE over the ti-84, or at least I found there was. However, once you get used to the NSPIRE I believe you will love it. The NSPIRE does not take longer to do calculations and for a lot of statistics it will save you time. Get the color if you can afford it...it is much much easier to read. Thank you for the nice words and watching:)

  • @ReViizHD
    @ReViizHD 10 ปีที่แล้ว +2

    Thank you so much for this video. I'm in algebra 2 and my teacher was super confused with my calculator. You made a hell of a lot easier for me now.

    • @profrobbob
      @profrobbob  10 ปีที่แล้ว

      You're welcome ReViiz HD ...sounds like this would be a great time to share my channel with your teacher and your class as an after school study reference...and remind them it's important to like and SUBSCRIBE to support my channel growth!
      I'm sure they would all appreciate the help...BAM!!!

    • @benjamin-p
      @benjamin-p 10 ปีที่แล้ว +1

      Exactly the same thing happened to me. Everyone else in my class has ti-84s. my teacher was actually kind of angry with me because i didn't know how to use it. THANKS!

    • @profrobbob
      @profrobbob  10 ปีที่แล้ว

      Ben Paruzynski you're welcome and thanks for watching!

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    Once again, another survivor, seems I have single-handedly rescued another one with my log distance life-ring!...LOLhahaha:)) Glad to help and glad you found my channel, keep watching and sharing, thanks.

  • @nimalchitrasena1693
    @nimalchitrasena1693 2 ปีที่แล้ว

    Great video with very clear instructions. Thanks

    • @profrobbob
      @profrobbob  2 ปีที่แล้ว

      You're welcome and thanks for watching!
      Don't forget to spread the word about this channel to everyone and remember to like, sub and support the channels that help you...BAM!!!

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว

    I know you can use one set of data for the x axis and add a second set of y axis data...like for matched pairs settings. I do not know how to graph two independent sets of data on the same screen unfortunately.

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว

    Thanks for "grabbing hold" of my videos!!

  • @BaoNguyen00
    @BaoNguyen00 11 ปีที่แล้ว +1

    Can you make a video, or at least explain to me how to predict value using regression line? For example, if I have a regression line, and I want to know what the value of Y is when I have a specific value of X, that type of question. Thank you very much.

  • @profrobbob
    @profrobbob  13 ปีที่แล้ว

    @jalene150 I do most calculations about density curves in my class by hand. What specifically about density curves would you like to know about? I can show you how to do something like a z-score test calculation as an example.

  • @SupremeKingKennedy
    @SupremeKingKennedy 12 ปีที่แล้ว

    to get residuals in there own column, once having entered 4 1 4, move across to empty select the grey or shaded box under the the first white box, click control menu (in grey box) variable, link to, resid,
    hope this helps

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    Your very welcome. I am glad I could help:)

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    Look...I see you have watched more of my videos already!!! Thank you so very much for telling viewers to watch my holiday greeting:D (our barking dogs in the background are one of the few drawbacks of filming at home...LOL...maybe we will feature them on their own video one day)...and a very merry christmas break to you:)

  • @firstgold
    @firstgold 11 ปีที่แล้ว +3

    Thanks for the help! I can finally use the darn thing for something useful!

    • @profrobbob
      @profrobbob  11 ปีที่แล้ว

      You're welcome!…and please check out the rest of my channel:)

  • @g3wb
    @g3wb 5 ปีที่แล้ว +5

    word around the streets is that you still reply to comments on this video to this very day !

    • @profrobbob
      @profrobbob  5 ปีที่แล้ว +3

      It's all TA-RROU (true:)
      Don't forget to like, sub, share on social medias and with your friends, classmates and especially your teachers to help us keep growing and remain free for everyone and continue to reply to our loyal subscribers...BAM!!!

  • @isabellaoconnor680
    @isabellaoconnor680 12 ปีที่แล้ว +1

    Thankyou so much!!! This helped me heaps with my maths assignment :)

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว

    Just plug the value of x you are given into the equation of your regression line and do the arithmetic to figure out y. I would just do this by hand/basic calculator usage.

  • @crshrdstryr
    @crshrdstryr 13 ปีที่แล้ว

    thanks so much. just know you're helping someone out there.

  • @sachitadahal2166
    @sachitadahal2166 5 ปีที่แล้ว +1

    youre an actual legend thank u

    • @profrobbob
      @profrobbob  5 ปีที่แล้ว

      ...not until I go viral and have a million subscribers...lol
      Thanks for the compliment and in the mean time please keep spreading the word...BAM!!!

  • @StoneKongStudios
    @StoneKongStudios 11 ปีที่แล้ว

    YES. THANK YOU. GOOD THINGS ARE IN YOUR FUTURE!

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    Sounds like I need to do an additional video:). Thanks for the tips!

  • @merlenerobinson4365
    @merlenerobinson4365 8 ปีที่แล้ว

    Mom and daughter's favorite site!

    • @profrobbob
      @profrobbob  8 ปีที่แล้ว +1

      That's AWESOME...the family who learns together...grows together!
      Thanks for subbing and supporting...BAM!!!

  • @drewnleonard
    @drewnleonard 12 ปีที่แล้ว

    This videos are amazing! I go to East Lake High, and I'm so glad you posted videos about statistics with this calculator. Quick question: do you have an opinion on using this calculator for the AP exam in May? I've been using a ti-84 for a couple years now, but the screen is dying so I may get the ti-nspire, but I'm hesitant because it seems as though it'd take to much time to use on the exam.

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    I would have to learn that first. I will look into it:)

  • @MsCyraR
    @MsCyraR 13 ปีที่แล้ว

    This was VERY helpful! Perhaps more importantly, you actually got me excited about stats - the same way I was about Calc!
    Thank you!

  • @victoriaalex318
    @victoriaalex318 9 ปีที่แล้ว +2

    thank you so much for this it was exactly what I needed help on and now I could finish the homework without pulling out my hair due to frustration

    • @profrobbob
      @profrobbob  9 ปีที่แล้ว

      +Victoria Alex BAM!!!...another bad hair day saved by my math skills:)
      Thanks for taking the time to study with #ProfRobBob !

    • @victoriaalex318
      @victoriaalex318 9 ปีที่แล้ว +1

      +ProfRobBob you have no idea :)

    • @profrobbob
      @profrobbob  9 ปีที่แล้ว

      +Victoria Alex next thing you know, you'll be shouting BAM!!! out loud:)

    • @victoriaalex318
      @victoriaalex318 9 ปีที่แล้ว +1

      +ProfRobBob lol true. I am going to show the people in my class about this because the teacher we have doesn't teach right so this will help everyone!

    • @profrobbob
      @profrobbob  9 ปีที่แล้ว

      +Victoria Alex that would be awesome!
      Don't forget to remind them all to like, subscribe, support the ads, like and share on all social medias, and with "their" friends too...because that's what helps us groW! (and our goal is 100,000 subscribers before the end of the year:)

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว

    You're welcome...That's what I like to hear!

  • @profrobbob
    @profrobbob  13 ปีที่แล้ว

    @TheYORR
    Thank you for watching. I started putting "push pins" on a world map today to see where my videos are being watched, liked, and to see where my subscribers are. It is quite amazing after just seven weeks how many people have watched my new videos and in how many countries. I am thrilled I could help. You keep me inspired to keep doing these videos.

  • @anzatzi
    @anzatzi 12 ปีที่แล้ว

    I advise everyone to visit the channel page for the most awesome holiday blackboard ever!
    Also it obvious your dog still prefers his t--89. merry christmas

  • @asmaaa5750
    @asmaaa5750 9 ปีที่แล้ว +1

    OMFG THANK YOU SO MUCH YOU JUST SAVED MY LIFE!!

    • @profrobbob
      @profrobbob  9 ปีที่แล้ว

      Asmaa Abdelzahet BAM!!!
      Thanks for taking the time to learn:)

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว

    You have to use the negative key, not the minus key.

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว

    You're welcome...And thanks for watching! I hope you will check out more of my teaching videos:)

  • @LuisCruz-gm1ym
    @LuisCruz-gm1ym 4 ปีที่แล้ว

    Thank you! Did you ever find out how to list the residuals on a separate column??

    • @profrobbob
      @profrobbob  4 ปีที่แล้ว

      No, sorry. I am using this calculator less and less in my classroom as the years go on.

  • @TheGreatBenjie
    @TheGreatBenjie 11 ปีที่แล้ว

    Is there a way to do this in scratchpad, or does it have to be a document each time?

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    You're very welcome! Thank for watching:)

  • @jalene150
    @jalene150 13 ปีที่แล้ว

    @profrobbob wow that's extremely helpful and thoughtful of you thanks and you have a new sub

  • @MrGregggleziii
    @MrGregggleziii 12 ปีที่แล้ว

    I see, just got done with your vid, thanks for the viddy man. I got midterms tomorrow, and thanks to you I expect to destroy this part on my exams.

  • @profrobbob
    @profrobbob  13 ปีที่แล้ว

    @jalene150 I will make that happen for you...but it will be a few days before I am able to do so.

  • @SmileyKylee1212
    @SmileyKylee1212 13 ปีที่แล้ว

    Thanks soooo much, you just helped me with a lot of homework!! :)

  • @Rebullx46
    @Rebullx46 8 ปีที่แล้ว

    do you prefer this way for making a scatter plot or the way by going through the graph page going over the function section and selecting scatter plot. does the difference matter?

  • @jonathanhoward5284
    @jonathanhoward5284 11 ปีที่แล้ว

    Thanks. Algebra just got easy

  • @jalene150
    @jalene150 13 ปีที่แล้ว

    You should do a tutorial on density curves on this calculator.

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว

    You're welcome...don't forget I'm here 24/7, whenever you need help:)

  • @PockyEater101
    @PockyEater101 11 ปีที่แล้ว

    Is there a way to plot two sets of data so that there's two lines of linear regression on one screen instead of having to switch back and forth between 1.2 and 1.3?

  • @willkerwin1999
    @willkerwin1999 12 ปีที่แล้ว

    THANK YOU SO MUCH FOR THIS VIDEO!!!!!

  • @Emadavid
    @Emadavid 12 ปีที่แล้ว

    very helpful, but I want to now if is possible to do it with multiple variables. I'm a student of industrial engineering, and the linear regression are not that simple in my course...

  • @profrobbob
    @profrobbob  13 ปีที่แล้ว

    @MsCyraR Well...it sounds like I have done my job:):):) Glad I could help!

  • @MrGregggleziii
    @MrGregggleziii 12 ปีที่แล้ว

    Question. Why cant I do this through the scrathpad graph that you pull up with the calculator button?

  • @LinLin009
    @LinLin009 11 ปีที่แล้ว

    can you find the Sum of the Squared Residuals on TI-NSPIRE?

  • @profrobbob
    @profrobbob  9 ปีที่แล้ว +3

    Now Closed Captioned

    • @isabellamarvel9400
      @isabellamarvel9400 9 ปีที่แล้ว

      THANK YOU

    • @profrobbob
      @profrobbob  9 ปีที่แล้ว

      You're welcome Isabella Marvel thanks for watching and learning!

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    Good luck. I hope you do awesome:)

  • @adelelouisa7883
    @adelelouisa7883 4 ปีที่แล้ว

    thank you!! i have a question. do you know how i can copy the equation from the stats plot to be able to plug in my own x values ?

  • @55Firestorm
    @55Firestorm 7 ปีที่แล้ว

    Is there anyway to calculate outliers on a residual plot within a ti-nspire?

  • @brandongehrke3711
    @brandongehrke3711 8 ปีที่แล้ว

    You saved my day thank you

    • @profrobbob
      @profrobbob  8 ปีที่แล้ว

      BAM!!!
      ...and you're welcome!
      Please like, subscribe and share this free educational channel with everyone:D

  • @jalene150
    @jalene150 13 ปีที่แล้ว

    @profrobbob that would be awesome review for me. If you have time I would greatly appreciate it.

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    You are very welcome. Please help me by spreading the word about my new math channel I am building:)

  • @AntonioMac3301
    @AntonioMac3301 5 ปีที่แล้ว +2

    OMG THANK YOU BEST VIDEO EVER

    • @profrobbob
      @profrobbob  5 ปีที่แล้ว

      THANKS!
      Don't forget to like. sub and share with everyone!

  • @arzey100
    @arzey100 11 ปีที่แล้ว

    How do I determine the q-correlation of a scatter graph that I've put on my calculator already.

  • @gregstiemsma3277
    @gregstiemsma3277 11 ปีที่แล้ว

    bailed me out for finals, thanks bro

  • @leopardtate
    @leopardtate 12 ปีที่แล้ว

    I did very well, thanks :D. I was trying to use the graph, instead of database/stats. wasn't working.

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว +2

    You're welcome...I'm going to hold you to that:)

  • @Penguino3544
    @Penguino3544 11 ปีที่แล้ว

    Subscribed. Thanks so much!

  • @Preachingthechoirnow
    @Preachingthechoirnow 11 ปีที่แล้ว

    is it workk if you put a negative value in Y? mine does no work an error domain.

  • @Ms_Cherry_Bomb
    @Ms_Cherry_Bomb 8 ปีที่แล้ว

    Do you have to buy this software or does it come with the calculator?

    • @profrobbob
      @profrobbob  8 ปีที่แล้ว

      I got a teacher package so I am not sure if it would come with a this emulation software. I wish I could be more helpful.

    • @Ms_Cherry_Bomb
      @Ms_Cherry_Bomb 8 ปีที่แล้ว

      Its okay! Thank you for the info! ^-^

    • @totallyrandomLLAUREN
      @totallyrandomLLAUREN 8 ปีที่แล้ว

      I bought the calculator as a student. It does come with the software :)

  • @Fordguy1997
    @Fordguy1997 10 ปีที่แล้ว

    I'm taking AP Stats next year and I'm starting my summer work. I have an nspire CX CAS, which is an amazing calculator. My only problem is, my teacher made all of the instructions specific to the TI-84 and I have no idea how to use the nspire as a result. I'm doing my best to figure it out, but there are so many features that it's overwhelming.

    • @profrobbob
      @profrobbob  10 ปีที่แล้ว

      I have a playlist of lessons for the NSPIRE here th-cam.com/play/PLE38C0018292BE9D9.html , granted it could use a few more tutorials. It is a great calculator. Once you get used to it I am sure you will grow to love it. There is only a few minor quirks that rarely bother me. Like I set up a document just for doing trig work in degrees since it is not as easy as a TI-84 to switch back and forth between radians to degrees.

    • @Fordguy1997
      @Fordguy1997 10 ปีที่แล้ว +1

      ProfRobBob Thanks, I'll check it out!

  • @notmarcus17
    @notmarcus17 ปีที่แล้ว

    Thank you for this video

  • @profrobbob
    @profrobbob  13 ปีที่แล้ว

    @SmileyKylee1212
    You are welcome:)

  • @alangillette4699
    @alangillette4699 8 ปีที่แล้ว +1

    thank you for your videos

    • @profrobbob
      @profrobbob  8 ปีที่แล้ว

      +Alan Gillette you're welcome and thanks for choosing my channel to study with and sub to!
      Please share with everyone:D

  • @MehrdadIrani24
    @MehrdadIrani24 8 ปีที่แล้ว

    Thanks. could you let us know how to fit y=mx instead of y=mx+h, basically set the intercept to zero?

  • @profrobbob
    @profrobbob  12 ปีที่แล้ว

    Thanks for watching!

  • @christinakcover
    @christinakcover 9 ปีที่แล้ว +1

    Thank you!!! Once again!

    • @profrobbob
      @profrobbob  9 ปีที่แล้ว

      +Christina Cover another video already..BAM!!!

  • @BobTurnip123
    @BobTurnip123 12 ปีที่แล้ว

    THANKYOU SOOO MUCH!!

  • @profrobbob
    @profrobbob  11 ปีที่แล้ว

    I am sorry but I am not familiar with q-correlation.

  • @keerthanakumar8832
    @keerthanakumar8832 9 ปีที่แล้ว

    Thank you so much!

    • @profrobbob
      @profrobbob  9 ปีที่แล้ว

      +Keerthana Kumar you're welcome!

  • @samsunggalaxy4692
    @samsunggalaxy4692 5 ปีที่แล้ว

    is there anyway i can get rid of that stat.regeqn thing making new variables everytime its getting hard to find x and y

  • @Xxblackout332xX
    @Xxblackout332xX 10 ปีที่แล้ว +1

    After graphing the regression line of y on x, how can I graph the regression line of x on y while still keeping the first line?

    • @profrobbob
      @profrobbob  10 ปีที่แล้ว

      I am not sure, sorry.

  • @dnfnfndnd
    @dnfnfndnd 8 ปีที่แล้ว +1

    THANK YOU SO MUCH!