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𝐀𝐬𝐬𝐚𝐥𝐚𝐚𝐦𝐮 𝐀𝐥𝐚𝐲𝐢𝐤𝐮𝐦 𝐖𝐨𝐫𝐚𝐡𝐦𝐚𝐭𝐮𝐥𝐥𝐚𝐚𝐡𝐢 𝐖𝐨𝐛𝐚𝐫𝐚𝐤𝐚𝐚𝐭𝐮𝐡𝐮𝐮

𝐎𝐝𝐮𝐮 𝐆𝐚𝐦𝐦𝐚𝐜𝐡𝐢𝐢𝐬𝐚𝐚 𝐀𝐤𝐤𝐚𝐦 𝐉𝐢𝐫𝐭𝐮 𝐌𝐚𝐚𝐭𝐢𝐢 𝐓𝐞𝐥𝐞𝐠𝐫𝐚𝐦 𝐌𝐚𝐫𝐭𝐢 𝐊𝐞𝐞𝐬𝐬𝐚𝐧𝐮𝐮 𝐂𝐡𝐚𝐧𝐧𝐞𝐥 𝐀𝐣𝐚𝐚'𝐢𝐛𝐚𝐚 𝐓𝐨𝐤𝐤𝐨 𝐈𝐬𝐢𝐧𝐢𝐢𝐟 𝐐𝐚𝐛𝐚𝐧𝐧𝐞𝐞 𝐃𝐡𝐮𝐟𝐧𝐞𝐞 𝐉𝐢𝐫𝐫𝐚𝐚 𝐌𝐚𝐚𝐫𝐫𝐞𝐞 𝐈𝐬𝐢𝐧𝐢𝐦𝐦𝐨𝐨 𝐉𝐨𝐢𝐧 𝐓𝐚𝐚𝐬𝐢𝐬𝐮𝐮𝐝𝐡𝐚𝐚 𝐍𝐮 𝐇𝐨𝐫𝐝𝐨𝐟𝐚𝐚!!

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𝐀𝐦𝐦𝐚𝐚𝐧 𝐃𝐮𝐫𝐚  𝐑𝐚𝐤𝐤𝐨𝐨 𝐓𝐞𝐤𝐧𝐨𝐨𝐥𝐨𝐨𝐣𝐢𝐢𝐭𝐢𝐢𝐧 𝐇𝐞𝐝𝐝𝐮𝐮 𝐑𝐚𝐤𝐤𝐚𝐭𝐭𝐞𝐞 𝐍𝐢 𝐁𝐞𝐞𝐤𝐭𝐚𝐚⁉️

𝑹𝒂𝒌𝒌𝒐𝒐𝒏 𝑲𝒂𝒏𝒂 𝑭𝒖𝒓𝒖𝒖𝒅𝒉𝒂𝒂𝒇 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐𝒕𝒊𝒊𝒏 𝑰𝒔𝒊𝒏 𝑻𝒂𝒋𝒂𝒂𝒋𝒊𝒍𝒖𝒖𝒅𝒉𝒂𝒂𝒇 𝑸𝒐𝒑𝒉𝒐𝒐𝒇𝒏𝒆𝒆 𝑫𝒉𝒖𝒇𝒏𝒆𝒆 𝑱𝒊𝒓𝒓𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑱𝒐𝒊𝒏 𝑮𝒐𝒄𝒉𝒖𝒖𝒅𝒉𝒂𝒂𝒏 𝑵𝒖 𝑯𝒐𝒓𝒅𝒐𝒇𝒂𝒂

✅ 𝐎𝐝𝐞𝐞𝐟𝐟𝐚𝐧𝐧𝐨𝐨 𝐓𝐞𝐤𝐧𝐨𝐨𝐥𝐨𝐨𝐣𝐢𝐢 𝐇𝐚𝐚𝐫𝐚𝐚 𝐟𝐢𝐢 𝐀𝐤𝐤𝐚𝐚𝐭𝐚𝐚 𝐈𝐭𝐭𝐢 𝐅𝐚𝐲𝐲𝐚𝐝𝐚𝐦𝐚 𝐈𝐬𝐚𝐚 𝐀𝐫𝐠𝐚𝐜𝐡𝐮𝐮𝐟 𝐂𝐡𝐚𝐧𝐧𝐞𝐥 𝐊𝐞𝐞𝐧𝐲𝐚 𝐇𝐨𝐫𝐝𝐨𝐟𝐚𝐚!!!

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𝐎𝐃𝐔𝐔 𝐆𝐀𝐌𝐌𝐀𝐂𝐇𝐈𝐈𝐒𝐀𝐀!!

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𝐎𝐃𝐔𝐔 𝐆𝐀𝐌𝐌𝐀𝐂𝐇𝐈𝐈𝐒𝐀𝐀!!

𝐀𝐦𝐦𝐚𝐚𝐧 𝐃𝐮𝐫𝐚  𝐑𝐚𝐤𝐤𝐨𝐨 𝐓𝐞𝐤𝐧𝐨𝐨𝐥𝐨𝐨𝐣𝐢𝐢𝐭𝐢𝐢𝐧 𝐇𝐞𝐝𝐝𝐮𝐮 𝐑𝐚𝐤𝐤𝐚𝐭𝐭𝐞𝐞 𝐍𝐢 𝐁𝐞𝐞𝐤𝐭𝐚𝐚⁉️

𝑹𝒂𝒌𝒌𝒐𝒐𝒏 𝑲𝒂𝒏𝒂 𝑭𝒖𝒓𝒖𝒖𝒅𝒉𝒂𝒂𝒇 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐𝒕𝒊𝒊𝒏 𝑰𝒔𝒊𝒏 𝑻𝒂𝒋𝒂𝒂𝒋𝒊𝒍𝒖𝒖𝒅𝒉𝒂𝒂𝒇 𝑸𝒐𝒑𝒉𝒐𝒐𝒇𝒏𝒆𝒆 𝑫𝒉𝒖𝒇𝒏𝒆𝒆 𝑱𝒊𝒓𝒓𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑱𝒐𝒊𝒏 𝑮𝒐𝒄𝒉𝒖𝒖𝒅𝒉𝒂𝒂𝒏 𝑵𝒖 𝑯𝒐𝒓𝒅𝒐𝒇𝒂𝒂

✅ 𝐎𝐝𝐞𝐞𝐟𝐟𝐚𝐧𝐧𝐨𝐨 𝐓𝐞𝐤𝐧𝐨𝐨𝐥𝐨𝐨𝐣𝐢𝐢 𝐇𝐚𝐚𝐫𝐚𝐚 𝐟𝐢𝐢 𝐀𝐤𝐤𝐚𝐚𝐭𝐚𝐚 𝐈𝐭𝐭𝐢 𝐅𝐚𝐲𝐲𝐚𝐝𝐚𝐦𝐚 𝐈𝐬𝐚𝐚 𝐀𝐫𝐠𝐚𝐜𝐡𝐮𝐮𝐟 𝐂𝐡𝐚𝐧𝐧𝐞𝐥 𝐊𝐞𝐞𝐧𝐲𝐚 𝐇𝐨𝐫𝐝𝐨𝐟𝐚𝐚!!!

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Waver: @Rafiqul_Islaam

   𝗛𝗢𝗣𝗘 𝗣𝗥𝗢𝗠𝗢𝗧𝗜𝗢𝗡
   𝐀𝐝𝐯𝐞𝐫𝐭𝐢𝐬𝐢𝐧𝐠 𝐓𝐞𝐥𝐞𝐠𝐫𝐚𝐦
     𝐂𝐡𝐚𝐧𝐧𝐞𝐥𝐬/𝐆𝐫𝐨𝐮𝐩𝐬
    @hope_promotions
        

𝐂𝐡𝐚𝐚𝐧𝐚𝐚𝐥𝐢𝐢 𝐚𝐤𝐤𝐚𝐦𝐢𝐢 𝐛𝐚𝐫𝐛𝐚𝐚𝐝𝐝𝐮𝐮?
What channels do you want?
ምን አይነት ቻናል ይፈልጋሉ?

𝑨𝒅𝒔:👇
https://t.me/+0puaGJwLzLgyY2U8
https://t.me/+zOTmz0fXj3pkMTk0

t.me/naviton_game_bot/app?startapp=33770
🚗 Join me in NaviTON - Your Electric Delivery Adventure! ⚡

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#NaviTON #PlayToEarn #GreenDelivery #CryptoGaming

Assalaamu alayikum worahmatullaahi wobarakaatuhuu

Chaanaalii Ajaa'ibaa kana isiniif qabannee dhufneerraa join gochuudhaan erga inni qabu akka irraa fayyadamnuu

https://t.me/+HzNEski01TRkN2Jk
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𝐇𝐨𝐰 𝐎𝐥𝐝 𝐀𝐫𝐞 𝐘𝐨𝐮?
𝐔𝐦𝐫𝐢𝐢𝐧 𝐊𝐞𝐞 𝐌𝐞𝐞𝐪𝐚𝐚?

𝐅.𝐖: @Rafiqul_Islaam

𝐎𝐃𝐔𝐔 𝐆𝐀𝐌𝐌𝐀𝐂𝐇𝐈𝐈𝐒𝐀𝐀!!

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𝐅𝐫𝐞𝐞 𝐖𝐚𝐯𝐞: @Rafiqul_Islaam

https://www.bybit.com/invite?ref=BLRJA92

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Waver: @Rafiqul_Islaam

   𝗛𝗢𝗣𝗘 𝗣𝗥𝗢𝗠𝗢𝗧𝗜𝗢𝗡
   𝐀𝐝𝐯𝐞𝐫𝐭𝐢𝐬𝐢𝐧𝐠 𝐓𝐞𝐥𝐞𝐠𝐫𝐚𝐦
     𝐂𝐡𝐚𝐧𝐧𝐞𝐥𝐬/𝐆𝐫𝐨𝐮𝐩𝐬
    @hope_promotions
        

Abdii hin kutatin. Furtuuwan (qulfiiwan) bayyeedhan Balbala Banuuf Yaalii Gootus, Garuu Furtuuwan hunda keessaa kan dhumaa irratti Hafe sun akka Balbala sif Banu Beekii.
#Nevergiveup
Share and join 👇👇
@kanajib

𝐎𝐃𝐔𝐔 𝐆𝐀𝐌𝐌𝐀𝐂𝐇𝐈𝐈𝐒𝐀𝐀

𝑪𝒉𝒂𝒂𝒏𝒂𝒂𝒍𝒐𝒕𝒂 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐𝒕𝒊𝒊𝒏 𝑩𝒂𝒓𝒔𝒊𝒊𝒔𝒐𝒐𝒇𝒊𝒊 𝑩𝒂𝒔𝒉𝒂𝒏𝒏𝒂𝒏𝒔𝒊𝒊𝒔𝒐𝒐 𝑻𝒂'𝒂𝒏 𝑰𝒔𝒊𝒏𝒊𝒊𝒇 𝑸𝒂𝒃𝒂𝒏𝒏𝒆𝒆 𝑫𝒉𝒖𝒇𝒏𝒆𝒆𝒓𝒓𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑪𝒉𝒂𝒂𝒏𝒂𝒂𝒍𝒐𝒕𝒂 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐𝒕𝒊𝒊𝒏 𝑩𝒂𝒓𝒔𝒊𝒊𝒔𝒂𝒏 𝑰𝒔𝒊𝒏𝒊𝒊𝒇 𝑸𝒂𝒃𝒂𝒏𝒏𝒆𝒆 𝑫𝒉𝒖𝒇𝒏𝒆𝒆𝒓𝒓𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑱𝒐𝒊𝒏 𝑮𝒐𝒅𝒉𝒖𝒖𝒅𝒉𝒂𝒂𝒏 𝑵𝒖 𝑯𝒐𝒓𝒅𝒐𝒇𝒂𝒂.

𝐇𝐮𝐛𝐚𝐜𝐡𝐢𝐢𝐬𝐚: 𝑪𝒉𝒂𝒂𝒏𝒂𝒂𝒍𝒊𝒊 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐 𝑻𝒂'𝒂𝒏 3𝑲 𝒇𝒊 𝑰𝒔𝒂𝒂 𝑾𝒐𝒍𝒊𝒊𝒏 𝑲𝒂𝒏 𝑯𝒐𝒋𝒋𝒂𝒏𝒏𝒖 𝑻𝒂'𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑵𝒂𝒎𝒏𝒊 𝑵𝒖𝒕𝒕𝒊 𝑫𝒂𝒃𝒂𝒍𝒂𝒎𝒖𝒖 𝑭𝒆𝒆𝒕𝒂𝒏 𝑨𝒔𝒊𝒊𝒏 𝑵𝒖 𝑸𝒖𝒏𝒏𝒂𝒎𝒂𝒂

𝐂𝐡𝐚𝐧𝐧𝐞𝐥 𝐀𝐟𝐚𝐚𝐧 𝐎𝐫𝐨𝐦𝐨𝐨 𝐐𝐨𝐟𝐚 3𝐊+
𝐅𝐫𝐞𝐞 𝐏𝐫𝐨𝐦𝐨𝐭𝐞𝐫: @Rafiiqul_Islaam2

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𝐅𝐫𝐞𝐞 𝐖𝐚𝐯𝐞𝐫: @Rafiqul_Islaam

https://t.me/jetbibot/app?startapp=4140404447

Up or Down. 15s Rounds. Play to Earn.
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          𝑨𝑫𝑽𝑬𝑹𝑻𝑰𝑺𝑰𝑵𝑮 𝑻𝑬𝑳𝑬𝑮𝑹𝑨𝑴
             𝑪𝑯𝑨𝑵𝑵𝑬𝑳𝑺/𝑮𝑹𝑶𝑼𝑷𝑺
 
       ➕ 𝑨𝑫𝑫 𝒀𝑶𝑼𝑹 𝑪𝑯𝑨𝑵𝑵𝑬𝑳➕

Assalaamu alayikum worahmatullaahi wobarakaatuhuu

Chaanaalii Ajaa'ibaa kana isiniif qabannee dhufneerraa join gochuudhaan erga inni qabu akka irraa fayyadamnuu

https://t.me/+HzNEski01TRkN2Jk
https://t.me/+zOTmz0fXj3pkMTk0

𝐂𝐡𝐚𝐚𝐧𝐚𝐚𝐥𝐢𝐢 𝐚𝐤𝐤𝐚𝐦𝐢𝐢 𝐛𝐚𝐫𝐛𝐚𝐚𝐝𝐝𝐮𝐮?
What channels do you want?
ምን አይነት ቻናል ይፈልጋሉ?

𝑨𝒅𝒔:👇
https://t.me/+0puaGJwLzLgyY2U8
https://t.me/+zOTmz0fXj3pkMTk0

Yeroo tokko tokko, filannoowwan dogoggoraa bakka sirrii ta’etti nu geessa.

✦Join @kanajib
✦Join @kanajib
✦Join @kanajib

✨ Qubee maqaan keessan ittiin eegalu irratti gadi tuquudhaan  Affeerraa isiniif qophaa'e argadhaa! ✨


⚜🄰⚜       ⚜🄱⚜       ⚜🄲⚜

⚜🄳⚜       ⚜🄴⚜       ⚜🄵⚜

⚜🄶⚜       ⚜🄷⚜       ⚜🄸⚜

⚜🄹⚜       ⚜🄺⚜       ⚜🄻⚜

⚜🄼⚜       ⚜🄽⚜       ⚜🄾⚜

⚜🄿⚜       ⚜🅀⚜       ⚜🅁⚜

⚜🅂⚜       ⚜🅃⚜       ⚜🅄⚜

⚜⚜          ⚜🅆⚜       ⚜🅇⚜
      
            ⚜🅈⚜       ⚜🅉⚜

     𝐀𝐟𝐟𝐞𝐞𝐫𝐫𝐚𝐚 𝐆𝐚𝐚𝐫𝐢𝐢!!

𝐅𝐫𝐞𝐞 𝐖𝐚𝐯𝐞: @Rafiqul_Islaam

𝐇𝐨𝐰 𝐎𝐥𝐝 𝐀𝐫𝐞 𝐘𝐨𝐮?
𝐔𝐦𝐫𝐢𝐢𝐧 𝐊𝐞𝐞 𝐌𝐞𝐞𝐪𝐚𝐚?

𝐅.𝐖: @Rafiqul_Islaam

𝐂𝐡𝐚𝐚𝐧𝐚𝐚𝐥𝐢𝐢 𝐚𝐤𝐤𝐚𝐦𝐢𝐢 𝐛𝐚𝐫𝐛𝐚𝐚𝐝𝐝𝐮𝐮?
What channels do you want?
ምን አይነት ቻናል ይፈልጋሉ?

𝑨𝒅𝒔:👇
https://t.me/+0puaGJwLzLgyY2U8
https://t.me/+zOTmz0fXj3pkMTk0

✨ Qubee maqaan keessan ittiin eegalu irratti gadi tuquudhaan  Affeerraa isiniif qophaa'e argadhaa! ✨


⚜🄰⚜       ⚜🄱⚜       ⚜🄲⚜

⚜🄳⚜       ⚜🄴⚜       ⚜🄵⚜

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The difference between multivariate probit and multinomial logistic regression models with its properties

Multivariate probit and multinomial logistic regression are both statistical models used to analyze categorical outcome variables, but they differ in their underlying assumptions, estimation methods, and applications. Here are the key differences and properties of each:

▎Multivariate Probit Model

▎Definition:

• The multivariate probit model is used for modeling multiple binary outcomes that may be correlated. It allows for the analysis of situations where there are multiple dependent binary variables.

▎Properties:

1. Outcome Variables: The model handles multiple binary (0/1) dependent variables simultaneously.

2. Correlation: It accounts for the correlation between the different binary outcomes, which is particularly useful when the outcomes may influence each other.

3. Normal Distribution: The errors in the model are assumed to follow a multivariate normal distribution.

4. Estimation Method: Estimation is typically done using maximum likelihood estimation (MLE), often requiring numerical methods due to the complexity of the multivariate normal distribution.

5. Interpretation: Coefficients represent the change in the latent variable associated with a unit change in the predictor variables, but interpreting these coefficients can be less straightforward compared to logistic regression.

6. Non-linearity: The relationship between predictors and the probability of outcomes is non-linear due to the cumulative distribution function (CDF) of the normal distribution.

▎Multinomial Logistic Regression

▎Definition:

• Multinomial logistic regression (also known as multinomial logit) is used when the dependent variable is categorical with more than two levels (outcomes). It models the probabilities of different outcomes based on one or more predictor variables.

▎Properties:

1. Outcome Variables: It can handle a single nominal dependent variable with multiple categories (more than two).

2. Independence of Irrelevant Alternatives (IIA): One of the key assumptions is that the odds of choosing one category over another do not depend on the presence of other categories.

3. Logistic Function: The model uses the logistic function to model the probabilities of each category, which means it inherently assumes a specific functional form for the relationship between predictors and outcomes.

4. Estimation Method: Like the multivariate probit, estimation is typically done using maximum likelihood estimation.

5. Interpretation: Coefficients can be interpreted as log-odds ratios, making it easier to understand the effect of predictors on the likelihood of each outcome.

6. Linear in Logits: The model is linear in terms of logits, meaning that it models the log-odds of each outcome as a linear combination of predictor variables.

▎Summary of Differences:

| Feature | Multivariate Probit | Multinomial Logistic Regression |
|-----------------------------|-----------------------------------------------|----------------------------------------------|
| Type of Outcome | Multiple binary outcomes | Single nominal outcome with multiple categories |
| Correlation Handling | Yes, accounts for correlation between outcomes| No, assumes independence among alternatives |
| Assumption on Errors | Multivariate normal distribution | No specific distribution assumption for errors |
| Estimation | Maximum likelihood (numerical methods needed) | Maximum likelihood |
| Interpretation | Coefficients relate to latent variables | Coefficients are interpreted as odds ratios |
| Functional Form | Non-linear (normal CDF) | Linear in log-odds |

▎Conclusion

The choice between multivariate probit and multinomial logistic regression depends on the nature of the data and research questions. If you have multiple correlated binary outcomes, a multivariate probit model is appropriate. If you have a single categorical outcome with more than two levels, multinomial logistic regression is suitable.

𝐎𝐃𝐔𝐔 𝐆𝐀𝐌𝐌𝐀𝐂𝐇𝐈𝐈𝐒𝐀𝐀!!

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𝑪𝒉𝒂𝒂𝒏𝒂𝒂𝒍𝒐𝒕𝒂 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐𝒕𝒊𝒊𝒏 𝑩𝒂𝒓𝒔𝒊𝒊𝒔𝒐𝒐𝒇𝒊𝒊 𝑩𝒂𝒔𝒉𝒂𝒏𝒏𝒂𝒏𝒔𝒊𝒊𝒔𝒐𝒐 𝑻𝒂'𝒂𝒏 𝑰𝒔𝒊𝒏𝒊𝒊𝒇 𝑸𝒂𝒃𝒂𝒏𝒏𝒆𝒆 𝑫𝒉𝒖𝒇𝒏𝒆𝒆𝒓𝒓𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑪𝒉𝒂𝒂𝒏𝒂𝒂𝒍𝒐𝒕𝒂 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐𝒕𝒊𝒊𝒏 𝑩𝒂𝒓𝒔𝒊𝒊𝒔𝒂𝒏 𝑰𝒔𝒊𝒏𝒊𝒊𝒇 𝑸𝒂𝒃𝒂𝒏𝒏𝒆𝒆 𝑫𝒉𝒖𝒇𝒏𝒆𝒆𝒓𝒓𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑱𝒐𝒊𝒏 𝑮𝒐𝒅𝒉𝒖𝒖𝒅𝒉𝒂𝒂𝒏 𝑵𝒖 𝑯𝒐𝒓𝒅𝒐𝒇𝒂𝒂.

𝐇𝐮𝐛𝐚𝐜𝐡𝐢𝐢𝐬𝐚: 𝑪𝒉𝒂𝒂𝒏𝒂𝒂𝒍𝒊𝒊 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐 𝑻𝒂'𝒂𝒏 3𝑲 𝒇𝒊 𝑰𝒔𝒂𝒂 𝑾𝒐𝒍𝒊𝒊𝒏 𝑲𝒂𝒏 𝑯𝒐𝒋𝒋𝒂𝒏𝒏𝒖 𝑻𝒂'𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑵𝒂𝒎𝒏𝒊 𝑵𝒖𝒕𝒕𝒊 𝑫𝒂𝒃𝒂𝒍𝒂𝒎𝒖𝒖 𝑭𝒆𝒆𝒕𝒂𝒏 𝑨𝒔𝒊𝒊𝒏 𝑵𝒖 𝑸𝒖𝒏𝒏𝒂𝒎𝒂𝒂

𝐂𝐡𝐚𝐧𝐧𝐞𝐥 𝐀𝐟𝐚𝐚𝐧 𝐎𝐫𝐨𝐦𝐨𝐨 𝐐𝐨𝐟𝐚 3𝐊+
𝐅𝐫𝐞𝐞 𝐏𝐫𝐨𝐦𝐨𝐭𝐞𝐫: @Rafiiqul_Islaam2

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𝐅𝐫𝐞𝐞 𝐖𝐚𝐯𝐞: @Rafiqul_Islaam

𝐎𝐃𝐔𝐔 𝐆𝐀𝐌𝐌𝐀𝐂𝐇𝐈𝐈𝐒𝐀𝐀!!

𝐀𝐦𝐦𝐚𝐚𝐧 𝐃𝐮𝐫𝐚  𝐑𝐚𝐤𝐤𝐨𝐨 𝐓𝐞𝐤𝐧𝐨𝐨𝐥𝐨𝐨𝐣𝐢𝐢𝐭𝐢𝐢𝐧 𝐇𝐞𝐝𝐝𝐮𝐮 𝐑𝐚𝐤𝐤𝐚𝐭𝐭𝐞𝐞 𝐍𝐢 𝐁𝐞𝐞𝐤𝐭𝐚𝐚⁉️

𝑹𝒂𝒌𝒌𝒐𝒐𝒏 𝑲𝒂𝒏𝒂 𝑭𝒖𝒓𝒖𝒖𝒅𝒉𝒂𝒂𝒇 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐𝒕𝒊𝒊𝒏 𝑰𝒔𝒊𝒏 𝑻𝒂𝒋𝒂𝒂𝒋𝒊𝒍𝒖𝒖𝒅𝒉𝒂𝒂𝒇 𝑸𝒐𝒑𝒉𝒐𝒐𝒇𝒏𝒆𝒆 𝑫𝒉𝒖𝒇𝒏𝒆𝒆 𝑱𝒊𝒓𝒓𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑱𝒐𝒊𝒏 𝑮𝒐𝒄𝒉𝒖𝒖𝒅𝒉𝒂𝒂𝒏 𝑵𝒖 𝑯𝒐𝒓𝒅𝒐𝒇𝒂𝒂

✅ 𝐎𝐝𝐞𝐞𝐟𝐟𝐚𝐧𝐧𝐨𝐨 𝐓𝐞𝐤𝐧𝐨𝐨𝐥𝐨𝐨𝐣𝐢𝐢 𝐇𝐚𝐚𝐫𝐚𝐚 𝐟𝐢𝐢 𝐀𝐤𝐤𝐚𝐚𝐭𝐚𝐚 𝐈𝐭𝐭𝐢 𝐅𝐚𝐲𝐲𝐚𝐝𝐚𝐦𝐚 𝐈𝐬𝐚𝐚 𝐀𝐫𝐠𝐚𝐜𝐡𝐮𝐮𝐟 𝐂𝐡𝐚𝐧𝐧𝐞𝐥 𝐊𝐞𝐞𝐧𝐲𝐚 𝐇𝐨𝐫𝐝𝐨𝐟𝐚𝐚!!!

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𝐂𝐡𝐚𝐚𝐧𝐚𝐚𝐥𝐢𝐢 𝐚𝐤𝐤𝐚𝐦𝐢𝐢 𝐛𝐚𝐫𝐛𝐚𝐚𝐝𝐝𝐮𝐮?
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𝐎𝐃𝐔𝐔 𝐆𝐀𝐌𝐌𝐀𝐂𝐇𝐈𝐈𝐒𝐀𝐀!!

𝐍𝐚𝐦𝐨𝐨𝐧𝐧𝐢 𝐈𝐝𝐝𝐨𝐨 𝐉𝐢𝐫𝐭𝐚𝐧 𝐓𝐞𝐞𝐬𝐬𝐚𝐧𝐢𝐢 𝐁𝐞𝐞𝐤𝐬𝐢𝐬𝐚𝐚𝐰𝐰𝐚𝐧 𝐆𝐚𝐫𝐚𝐚 𝐆𝐚𝐫𝐚𝐚 𝐇𝐨𝐫𝐝𝐨𝐟𝐮𝐮𝐧 𝐇𝐨𝐣𝐢𝐢 𝐀𝐫𝐠𝐚𝐜𝐡𝐮𝐮 𝐁𝐚𝐫𝐛𝐚𝐚𝐝𝐝𝐚𝐧 𝐂𝐡𝐚𝐧𝐧𝐞𝐥 𝐊𝐚𝐧𝐚 𝐈𝐫𝐫𝐚𝐭𝐭𝐢 𝐁𝐞𝐞𝐤𝐬𝐢𝐬𝐚 𝐆𝐮𝐲𝐲𝐚𝐚 𝐆𝐮𝐲𝐲𝐚𝐚𝐧 𝐁𝐚𝐡𝐮 𝐇𝐨𝐫𝐝𝐨𝐟𝐚𝐚

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𝐂𝐡𝐚𝐚𝐧𝐚𝐚𝐥𝐢𝐢 𝐚𝐤𝐤𝐚𝐦𝐢𝐢 𝐛𝐚𝐫𝐛𝐚𝐚𝐝𝐝𝐮𝐮?
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𝐇𝐨𝐰 𝐎𝐥𝐝 𝐀𝐫𝐞 𝐘𝐨𝐮?
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𝐀𝐦𝐦𝐚𝐚𝐧 𝐃𝐮𝐫𝐚  𝐑𝐚𝐤𝐤𝐨𝐨 𝐓𝐞𝐤𝐧𝐨𝐨𝐥𝐨𝐨𝐣𝐢𝐢𝐭𝐢𝐢𝐧 𝐇𝐞𝐝𝐝𝐮𝐮 𝐑𝐚𝐤𝐤𝐚𝐭𝐭𝐞𝐞 𝐍𝐢 𝐁𝐞𝐞𝐤𝐭𝐚𝐚⁉️

𝑹𝒂𝒌𝒌𝒐𝒐𝒏 𝑲𝒂𝒏𝒂 𝑭𝒖𝒓𝒖𝒖𝒅𝒉𝒂𝒂𝒇 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐𝒕𝒊𝒊𝒏 𝑰𝒔𝒊𝒏 𝑻𝒂𝒋𝒂𝒂𝒋𝒊𝒍𝒖𝒖𝒅𝒉𝒂𝒂𝒇 𝑸𝒐𝒑𝒉𝒐𝒐𝒇𝒏𝒆𝒆 𝑫𝒉𝒖𝒇𝒏𝒆𝒆 𝑱𝒊𝒓𝒓𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑱𝒐𝒊𝒏 𝑮𝒐𝒄𝒉𝒖𝒖𝒅𝒉𝒂𝒂𝒏 𝑵𝒖 𝑯𝒐𝒓𝒅𝒐𝒇𝒂𝒂

✅ 𝐎𝐝𝐞𝐞𝐟𝐟𝐚𝐧𝐧𝐨𝐨 𝐓𝐞𝐤𝐧𝐨𝐨𝐥𝐨𝐨𝐣𝐢𝐢 𝐇𝐚𝐚𝐫𝐚𝐚 𝐟𝐢𝐢 𝐀𝐤𝐤𝐚𝐚𝐭𝐚𝐚 𝐈𝐭𝐭𝐢 𝐅𝐚𝐲𝐲𝐚𝐝𝐚𝐦𝐚 𝐈𝐬𝐚𝐚 𝐀𝐫𝐠𝐚𝐜𝐡𝐮𝐮𝐟 𝐂𝐡𝐚𝐧𝐧𝐞𝐥 𝐊𝐞𝐞𝐧𝐲𝐚 𝐇𝐨𝐫𝐝𝐨𝐟𝐚𝐚!!!

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𝑪𝒉𝒂𝒂𝒏𝒂𝒂𝒍𝒐𝒕𝒂 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐𝒕𝒊𝒊𝒏 𝑩𝒂𝒓𝒔𝒊𝒊𝒔𝒐𝒐𝒇𝒊𝒊 𝑩𝒂𝒔𝒉𝒂𝒏𝒏𝒂𝒏𝒔𝒊𝒊𝒔𝒐𝒐 𝑻𝒂'𝒂𝒏 𝑰𝒔𝒊𝒏𝒊𝒊𝒇 𝑸𝒂𝒃𝒂𝒏𝒏𝒆𝒆 𝑫𝒉𝒖𝒇𝒏𝒆𝒆𝒓𝒓𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑪𝒉𝒂𝒂𝒏𝒂𝒂𝒍𝒐𝒕𝒂 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐𝒕𝒊𝒊𝒏 𝑩𝒂𝒓𝒔𝒊𝒊𝒔𝒂𝒏 𝑰𝒔𝒊𝒏𝒊𝒊𝒇 𝑸𝒂𝒃𝒂𝒏𝒏𝒆𝒆 𝑫𝒉𝒖𝒇𝒏𝒆𝒆𝒓𝒓𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑱𝒐𝒊𝒏 𝑮𝒐𝒅𝒉𝒖𝒖𝒅𝒉𝒂𝒂𝒏 𝑵𝒖 𝑯𝒐𝒓𝒅𝒐𝒇𝒂𝒂.

𝐇𝐮𝐛𝐚𝐜𝐡𝐢𝐢𝐬𝐚: 𝑪𝒉𝒂𝒂𝒏𝒂𝒂𝒍𝒊𝒊 𝑨𝒇𝒂𝒂𝒏 𝑶𝒓𝒐𝒎𝒐𝒐 𝑻𝒂'𝒂𝒏 3𝑲 𝒇𝒊 𝑰𝒔𝒂𝒂 𝑾𝒐𝒍𝒊𝒊𝒏 𝑲𝒂𝒏 𝑯𝒐𝒋𝒋𝒂𝒏𝒏𝒖 𝑻𝒂'𝒂𝒂 𝑲𝒂𝒏𝒂𝒂𝒇𝒖𝒖 𝑵𝒂𝒎𝒏𝒊 𝑵𝒖𝒕𝒕𝒊 𝑫𝒂𝒃𝒂𝒍𝒂𝒎𝒖𝒖 𝑭𝒆𝒆𝒕𝒂𝒏 𝑨𝒔𝒊𝒊𝒏 𝑵𝒖 𝑸𝒖𝒏𝒏𝒂𝒎𝒂𝒂

𝐂𝐡𝐚𝐧𝐧𝐞𝐥 𝐀𝐟𝐚𝐚𝐧 𝐎𝐫𝐨𝐦𝐨𝐨 𝐐𝐨𝐟𝐚 3𝐊+
𝐅𝐫𝐞𝐞 𝐏𝐫𝐨𝐦𝐨𝐭𝐞𝐫: @Rafiiqul_Islaam2

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𝐂𝐡𝐚𝐚𝐧𝐚𝐚𝐥𝐢𝐢 𝐚𝐤𝐤𝐚𝐦𝐢𝐢 𝐛𝐚𝐫𝐛𝐚𝐚𝐝𝐝𝐮𝐮?
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𝐎𝐃𝐔𝐔 𝐆𝐀𝐌𝐌𝐀𝐂𝐇𝐈𝐈𝐒𝐀𝐀!!

𝐍𝐚𝐦𝐨𝐨𝐧𝐧𝐢 𝐈𝐝𝐝𝐨𝐨 𝐉𝐢𝐫𝐭𝐚𝐧 𝐓𝐞𝐞𝐬𝐬𝐚𝐧𝐢𝐢 𝐁𝐞𝐞𝐤𝐬𝐢𝐬𝐚𝐚𝐰𝐰𝐚𝐧 𝐆𝐚𝐫𝐚𝐚 𝐆𝐚𝐫𝐚𝐚 𝐇𝐨𝐫𝐝𝐨𝐟𝐮𝐮𝐧 𝐇𝐨𝐣𝐢𝐢 𝐀𝐫𝐠𝐚𝐜𝐡𝐮𝐮 𝐁𝐚𝐫𝐛𝐚𝐚𝐝𝐝𝐚𝐧 𝐂𝐡𝐚𝐧𝐧𝐞𝐥 𝐊𝐚𝐧𝐚 𝐈𝐫𝐫𝐚𝐭𝐭𝐢 𝐁𝐞𝐞𝐤𝐬𝐢𝐬𝐚 𝐆𝐮𝐲𝐲𝐚𝐚 𝐆𝐮𝐲𝐲𝐚𝐚𝐧 𝐁𝐚𝐡𝐮 𝐇𝐨𝐫𝐝𝐨𝐟𝐚𝐚

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Cause and consequences of violations assumptions of regression analysis with remedial measures

Violations of the assumptions of regression analysis can lead to misleading results and interpretations. Here are some common violations, their causes and consequences, along with remedial measures:

▎1. Linearity

• Cause: The relationship between the independent and dependent variables is not linear.

• Consequences: The model may underestimate or overestimate the effect of predictors, leading to biased coefficients.

• Remedial Measures:

• Transform variables (e.g., log, square root).

• Use polynomial regression or interaction terms.

• Consider non-linear models (e.g., generalized additive models).

▎2. Independence of Errors

• Cause: Errors are correlated (e.g., in time series data).

• Consequences: Underestimation of standard errors, leading to inflated t-statistics and false significance.

• Remedial Measures:

• Use time series methods (e.g., ARIMA).

• Add lagged variables to the model.

• Employ Generalized Least Squares (GLS) or robust standard errors.

▎3. Homoscedasticity

• Cause: Variance of errors is not constant across all levels of the independent variable(s).

• Consequences: Standard errors may be biased, affecting hypothesis tests and confidence intervals.

• Remedial Measures:

• Use weighted least squares (WLS).

• Transform the dependent variable.

• Check for outliers that may affect variance.

▎4. Normality of Errors

• Cause: Errors are not normally distributed, especially in small samples.

• Consequences: Violated assumptions can affect the validity of hypothesis tests and confidence intervals.

• Remedial Measures:

• Use transformations (e.g., log or Box-Cox).

• Consider robust regression techniques.

• Increase sample size if possible.

▎5. No Multicollinearity

• Cause: High correlation among independent variables.

• Consequences: Inflated standard errors, making it difficult to determine the effect of individual predictors.

• Remedial Measures:

• Remove or combine correlated predictors.

• Use ridge regression or principal component analysis (PCA).

• Center variables to reduce multicollinearity.

▎6. No Autocorrelation

• Cause: Errors are correlated across observations, often in time series data.

• Consequences: Underestimation of standard errors, leading to unreliable hypothesis tests.

• Remedial Measures:

• Use Durbin-Watson test to detect autocorrelation.

• Incorporate lagged variables.

• Use autoregressive models.

▎Conclusion

To ensure the validity of regression analysis, it's crucial to check for these assumptions before interpreting results. If violations are detected, appropriate remedial measures should be taken to improve the model's reliability and accuracy. Regular diagnostic checks and visualizations (like residual plots) can help identify potential issues early in the analysis process.

𝐂𝐡𝐚𝐚𝐧𝐚𝐚𝐥𝐢𝐢 𝐚𝐤𝐤𝐚𝐦𝐢𝐢 𝐛𝐚𝐫𝐛𝐚𝐚𝐝𝐝𝐮𝐮?
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