Bayesian Linear Regression: A Distribution Over Lines

Fit a line through some data and ordinary regression hands you back a single answer: one slope, one intercept, the best fit. Bayesian linear regression asks a different question entirely. It starts before the data with a whole cloud of candidate lines, the prior, where every line you might believe gets a probability. Then Bayes' rule takes over: the posterior is proportional to the likelihood times the prior, so your new belief is just the evidence times your old belief. As the points arrive one by one, every observation reshapes that belief and the cloud tightens around the lines that actually explain the data. When it is time to predict you get a whole band, narrow where the data lives and honestly wider where it does not, with the single best line running right through the middle. The answer was never one line, it is a distribution over lines. #shorts *Follow Me* ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ 🐦 X: @datamlistic https://x.com/datamlistic 📸 Instagram: @datamlistic https://www.instagram.com/datamlistic 📱 TikTok: @datamlistic https://www.tiktok.com/@datamlistic 👔 Linkedin: https://www.linkedin.com/company/datamlistic *Channel Support* ▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬▬ The best way to support the channel is to share the content. ;) If you'd like to also support the channel financially, donating the price of a coffee is always warmly welcomed! (completely optional and voluntary) ► Patreon: https://www.patreon.com/datamlistic ► Bitcoin (BTC): 3C6Pkzyb5CjAUYrJxmpCaaNPVRgRVxxyTq ► Ethereum (ETH): 0x9Ac4eB94386C3e02b96599C05B7a8C71773c9281 ► Cardano (ADA): addr1v95rfxlslfzkvd8sr3exkh7st4qmgj4ywf5zcaxgqgdyunsj5juw5 ► Tether (USDT): 0xeC261d9b2EE4B6997a6a424067af165BAA4afE1a #shorts #machinelearning #bayesian