• Japan Built a Wall… and a Forest

    After the devastating 2011 tsunami, Japan didn’t just rebuild—they went fortress mode.

    Stretching an unbelievable 395 km, the Great Tsunami Wall is a beast of engineering. In some spots, it’s taller than a 4-story building (14.7 meters), with foundations plunging 25 meters deep to hold back the ocean’s fury.

    But here’s the twist—Japan didn’t stop at concrete. They also planted 9 million trees along the coast, creating the “Great Forest Wall.” This living barrier slows incoming waves and traps dangerous debris before it can be dragged back to sea.

    It’s part man-made muscle, part Mother Nature magic—and it’s one of the boldest disaster defenses on Earth.
    🌊 Japan Built a Wall… and a Forest After the devastating 2011 tsunami, Japan didn’t just rebuild—they went fortress mode. Stretching an unbelievable 395 km, the Great Tsunami Wall is a beast of engineering. In some spots, it’s taller than a 4-story building (14.7 meters), with foundations plunging 25 meters deep to hold back the ocean’s fury. But here’s the twist—Japan didn’t stop at concrete. They also planted 9 million trees along the coast, creating the “Great Forest Wall.” This living barrier slows incoming waves and traps dangerous debris before it can be dragged back to sea. It’s part man-made muscle, part Mother Nature magic—and it’s one of the boldest disaster defenses on Earth. đŸ‡¯đŸ‡ĩ
    0 Comments 0 Shares 611 Views
  • #槍戰​#抗æ—Ĩ​#抗戰​#æˆ°čĄ“â€‹#功å¤Ģ大å¸Ģ​#中國功å¤Ģ​
    #Gunfight​, #Anti​-Japanese War, #Anti​-Japanese War,#Tactics​, #Kung​ Fu Master#Chinese​ Kongfu
    #槍戰​#抗æ—Ĩ​#抗戰​#æˆ°čĄ“â€‹#功å¤Ģ大å¸Ģ​#中國功å¤Ģ​ #Gunfight​, #Anti​-Japanese War, #Anti​-Japanese War,#Tactics​, #Kung​ Fu Master#Chinese​ Kongfu
    0 Comments 0 Shares 489 Views
  • University of Tokyo’s DRAGON Lab developed the world’s first flapping-wing drone capable of safe human contact, inspired by a falcon.

    The bird-like drone uses soft, flexible wings instead of propellers, making it quieter and safer for close interaction.

    It responds to simple hand gestures: bent arm signals “stay,” extended arm means “approach and land.”

    Eight motion-capture cameras track user movements, enabling precise flight planning that maintains 0.3-meter chest distance and approaches from predictable angles.
    The drone’s sophisticated algorithm adjusts velocity based on human motion perception, potentially enabling package delivery and accessibility applications in crowded urban environments.

    Š Fossbytes

    #drone #tech #bird #japan
    University of Tokyo’s DRAGON Lab developed the world’s first flapping-wing drone capable of safe human contact, inspired by a falcon. The bird-like drone uses soft, flexible wings instead of propellers, making it quieter and safer for close interaction. It responds to simple hand gestures: bent arm signals “stay,” extended arm means “approach and land.” Eight motion-capture cameras track user movements, enabling precise flight planning that maintains 0.3-meter chest distance and approaches from predictable angles. The drone’s sophisticated algorithm adjusts velocity based on human motion perception, potentially enabling package delivery and accessibility applications in crowded urban environments. © Fossbytes #drone #tech #bird #japan
    0 Comments 0 Shares 443 Views
  • China is building underwater data centers that use seawater for cooling and 97% wind energy for power to meet rising AI demand.

    A $223M facility six miles off Shanghai will hold up to 792 AI-capable servers and launch in September.

    It’s expected to train models like GPT-3.5 in a day while using 30% less electricity than land-based centers. Microsoft tested a similar idea with Project Natick in 2018 but shelved it.

    Meanwhile, China is scaling fast. Environmental concerns remain, but South Korea and Japan are already exploring similar offshore data solutions.
    China is building underwater data centers that use seawater for cooling and 97% wind energy for power to meet rising AI demand. A $223M facility six miles off Shanghai will hold up to 792 AI-capable servers and launch in September. It’s expected to train models like GPT-3.5 in a day while using 30% less electricity than land-based centers. Microsoft tested a similar idea with Project Natick in 2018 but shelved it. Meanwhile, China is scaling fast. Environmental concerns remain, but South Korea and Japan are already exploring similar offshore data solutions.
    0 Comments 0 Shares 288 Views
  • This House Literally Floats to Survive Powerful Earthquakes.

    Engineers in Japan are testing a futuristic earthquake defence system that could change how homes are built forever. In a country where tremors strike often and unpredictably, this groundbreaking technology could be the key to protecting lives, property, and peace of mind.

    Developed by Air Danshin Systems, the idea is as bold as it is brilliant. When an earthquake begins, high-speed sensors instantly detect the tremors. In less than a second, powerful air compressors activate, lifting the entire house a few centimetres off the ground using a cushion of compressed air. While the earth shakes beneath it, the home simply floats above the chaos. Once the shaking stops, the house gently returns to its original position, without damage, without stress.

    This technology is drastically different from traditional quake-resistant architecture, which relies on shock absorbers and flexible frames to handle seismic waves. Instead of fighting the movement, these floating homes rise above it entirely.

    The impact could be enormous. Every year, earthquakes cause billions in damage and displace thousands of families. This innovation has the potential to make homes safer, reduce insurance costs, and transform urban planning in quake-prone regions around the world.

    More than just an engineering achievement, this floating house represents a hopeful future where science defends us not only with strength but with grace. It’s a reminder that some of the most powerful solutions are also the most elegant.

    As global climate shifts increase the frequency of natural disasters, breakthroughs like this inspire a world where preparation and innovation walk hand in hand. The earth may move, but we don’t have to fall with it.

    #DiscoverTheUniverse #Discover #EarthquakeInnovation #FloatingHouse #DisasterTech
    This House Literally Floats to Survive Powerful Earthquakes. Engineers in Japan are testing a futuristic earthquake defence system that could change how homes are built forever. In a country where tremors strike often and unpredictably, this groundbreaking technology could be the key to protecting lives, property, and peace of mind. Developed by Air Danshin Systems, the idea is as bold as it is brilliant. When an earthquake begins, high-speed sensors instantly detect the tremors. In less than a second, powerful air compressors activate, lifting the entire house a few centimetres off the ground using a cushion of compressed air. While the earth shakes beneath it, the home simply floats above the chaos. Once the shaking stops, the house gently returns to its original position, without damage, without stress. This technology is drastically different from traditional quake-resistant architecture, which relies on shock absorbers and flexible frames to handle seismic waves. Instead of fighting the movement, these floating homes rise above it entirely. The impact could be enormous. Every year, earthquakes cause billions in damage and displace thousands of families. This innovation has the potential to make homes safer, reduce insurance costs, and transform urban planning in quake-prone regions around the world. More than just an engineering achievement, this floating house represents a hopeful future where science defends us not only with strength but with grace. It’s a reminder that some of the most powerful solutions are also the most elegant. As global climate shifts increase the frequency of natural disasters, breakthroughs like this inspire a world where preparation and innovation walk hand in hand. The earth may move, but we don’t have to fall with it. #DiscoverTheUniverse #Discover #EarthquakeInnovation #FloatingHouse #DisasterTech
    0 Comments 0 Shares 525 Views
  • 感čŦæ‚¨įš„æ”¯æŒīŧŒæ­ĄčŋŽč¨‚é–ąæˆ‘įš„é ģ道
    į˛žåŊŠåˆēæŋ€įš„æ§æˆ°åŠ‡æ­Ŗåœ¨æ›´æ–°ä¸­
    #抗æ—Ĩ​ #抗戰​ #čģæ—…​
    æˆ°įˆ­ | į‰šį¨Žå…ĩ | į‰šį¨Žéƒ¨éšŠ | čģæ—… | į‹™å‡ģ手 | 抗战 | 抗æ—Ĩ战äē‰ | 中å›Ŋ | martial arts | å…Ģ莝军 | martial arts fight | martial arts movie | Kung Fu | æ—Ĩ军 | fight | 动äŊœ | åŽ†å˛ | troops | Chinese television dramas | Chinese drama | 中å›Ŋį”ĩ视剧 | action | action movies | kung fu movie | eight route army | eight route army movie | 抗æ—ĨįĨžå‰§ | Second Sino-Japanese War | 战äē‰å‰§ | 战äē‰į‰‡ | 抗æ—Ĩį”ĩ视剧 | 抗æ—Ĩ剧 | 抗æ—Ĩ剧2023 | 抗æ—Ĩ战äē‰å‰§2023
    感čŦæ‚¨įš„æ”¯æŒīŧŒæ­ĄčŋŽč¨‚é–ąæˆ‘įš„é ģ道 į˛žåŊŠåˆēæŋ€įš„æ§æˆ°åŠ‡æ­Ŗåœ¨æ›´æ–°ä¸­ #抗æ—Ĩ​ #抗戰​ #čģæ—…​ æˆ°įˆ­ | į‰šį¨Žå…ĩ | į‰šį¨Žéƒ¨éšŠ | čģæ—… | į‹™å‡ģ手 | 抗战 | 抗æ—Ĩ战äē‰ | 中å›Ŋ | martial arts | å…Ģ莝军 | martial arts fight | martial arts movie | Kung Fu | æ—Ĩ军 | fight | 动äŊœ | åŽ†å˛ | troops | Chinese television dramas | Chinese drama | 中å›Ŋį”ĩ视剧 | action | action movies | kung fu movie | eight route army | eight route army movie | 抗æ—ĨįĨžå‰§ | Second Sino-Japanese War | 战äē‰å‰§ | 战äē‰į‰‡ | 抗æ—Ĩį”ĩ视剧 | 抗æ—Ĩ剧 | 抗æ—Ĩ剧2023 | 抗æ—Ĩ战äē‰å‰§2023
    0 Comments 0 Shares 279 Views
  • Action | The legendary Female Samurai challenges the Japanese Empire | Free Full Movie in English 4K
    đŸŽŦ Action | The legendary Female Samurai challenges the Japanese Empire | Free Full Movie in English 4K
    0 Comments 0 Shares 112 Views

  • Japan’s newest smart toilets are turning bathroom visits into high-tech health screenings! Equipped with AI, sensors, and urine analysis tools, they examine stool shape, color, and chemistry, then send a detailed health report directly to your phone. No more guesswork—just instant, personalized wellness insights, straight from your toilet. Welcome to the future of bathroom technology!
    Japan’s newest smart toilets are turning bathroom visits into high-tech health screenings! Equipped with AI, sensors, and urine analysis tools, they examine stool shape, color, and chemistry, then send a detailed health report directly to your phone. No more guesswork—just instant, personalized wellness insights, straight from your toilet. Welcome to the future of bathroom technology!
    0 Comments 0 Shares 163 Views
  • It’s one of the most dangerous places on Earth—and yet, many people may not have heard of it.

    The Ring of Fire is a horseshoe-shaped belt stretching over 40,000 kilometers around the Pacific Ocean, home to some of Earth’s most intense geological activity.

    This volatile region hosts about 75% of all active volcanoes and experiences nearly 90% of the world’s earthquakes. It runs through countries like Japan, Indonesia, the Philippines, New Zealand, the west coasts of North and South America, and even Antarctica.

    What makes the Ring of Fire so dangerous is the movement of tectonic plates. Here, massive plates of Earth’s crust collide, pull apart, or slide past each other in a slow but constant struggle. Subduction zones—where one plate dives beneath another—generate immense pressure, eventually unleashing it as powerful earthquakes or explosive volcanic eruptions.

    Some of history’s most catastrophic natural disasters have emerged from this region, including the 2011 Japan earthquake and tsunami and the 2004 Indian Ocean tsunami. Yet, the Ring of Fire isn’t just a zone of destruction. Its geothermal energy supports local communities, its volcanic soils nourish rich ecosystems, and its landscapes—like Mount Fuji and Chile’s volcanic fields—are breathtakingly beautiful.

    The Ring of Fire is a dramatic reminder of how alive and dynamic our planet truly is.
    🌋 It’s one of the most dangerous places on Earth—and yet, many people may not have heard of it. The Ring of Fire is a horseshoe-shaped belt stretching over 40,000 kilometers around the Pacific Ocean, home to some of Earth’s most intense geological activity. This volatile region hosts about 75% of all active volcanoes and experiences nearly 90% of the world’s earthquakes. It runs through countries like Japan, Indonesia, the Philippines, New Zealand, the west coasts of North and South America, and even Antarctica. What makes the Ring of Fire so dangerous is the movement of tectonic plates. Here, massive plates of Earth’s crust collide, pull apart, or slide past each other in a slow but constant struggle. Subduction zones—where one plate dives beneath another—generate immense pressure, eventually unleashing it as powerful earthquakes or explosive volcanic eruptions. Some of history’s most catastrophic natural disasters have emerged from this region, including the 2011 Japan earthquake and tsunami and the 2004 Indian Ocean tsunami. Yet, the Ring of Fire isn’t just a zone of destruction. Its geothermal energy supports local communities, its volcanic soils nourish rich ecosystems, and its landscapes—like Mount Fuji and Chile’s volcanic fields—are breathtakingly beautiful. The Ring of Fire is a dramatic reminder of how alive and dynamic our planet truly is.
    0 Comments 0 Shares 200 Views
  • āφāĻĒāύāĻžāϰ āĻ—āĻŦ⧇āώāĻŖāĻž āĻĒāĻĻā§āϧāϤāĻŋāϰ āϏāĻžāϤāĻ•āĻžāĻšāύ: āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ
    (Linear Regression in Research methodology)

    āϧāϰ⧁āύ, āφāĻĒāύāĻŋ āĻ…āύ⧇āĻ•āϗ⧁āϞ⧋ āĻ•āĻžāρāϚāĻžāĻŽāĻžāϞ āĻœā§‹āĻ—āĻžā§œ āĻ•āϰ⧇āϛ⧇āύāĨ¤ āĻāĻ–āύ āϏ⧇āχ āĻ•āĻžāρāϚāĻžāĻŽāĻžāϞ āĻĻāĻŋā§Ÿā§‡ āϕ⧀ āĻŦāĻžāύāĻžāĻŦ⧇āύ, āϕ⧀āĻ­āĻžāĻŦ⧇ āĻŦāĻžāύāĻžāĻŦ⧇āύ, āϏ⧇āϟāĻžāχ āĻšāϞ⧋ āĻŦāĻŋāĻļā§āϞ⧇āώāϪ⧇āϰ āĻ•āĻžāϜāĨ¤ āφāϰ āĻāχ āĻŦāĻŋāĻļā§āϞ⧇āώāϪ⧇āϰ āĻĻ⧁āύāĻŋ⧟āĻžā§Ÿ āĻāĻ•āϟāĻž āĻĻāĻžāϰ⧁āĻŖ 'āĻŽā§āϝāĻžāϜāĻŋāĻ• āϟ⧁āϞ' āφāϛ⧇, āϝāĻžāϰ āύāĻžāĻŽ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύāĨ¤ āĻāϰ āύāĻžāĻŽāϟāĻž āĻāĻ•āϟ⧁ āϜāϟāĻŋāϞ āĻļā§‹āύāĻžāϞ⧇āĻ“, āĻāϰ āĻ•āĻžāϜāϟāĻž āĻ•āĻŋāĻ¨ā§āϤ⧁ āϖ⧁āĻŦāχ āϏāĻšāϜ āφāϰ āĻ•āĻžāĻœā§‡āϰāĨ¤ āϚāϞ⧁āύ, āφāϜ āφāĻŽāϰāĻž āĻāχ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ⧇āϰ āφāĻĻā§āϝ⧋āĻĒāĻžāĻ¨ā§āϤ āĻœā§‡āύ⧇ āύāĻŋāχ, āĻāĻ•āĻĻāĻŽ A2Z!

    āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āφāϏāϞ⧇ āϕ⧀? (What is Linear Regression?)
    āφāĻšā§āĻ›āĻž, āφāĻĒāύāĻŋ āĻ•āĻŋ āĻ•āĻ–āύ⧋ āϭ⧇āĻŦ⧇ āĻĻ⧇āϖ⧇āϛ⧇āύ, āĻāĻ•āϜāύ āĻļāĻŋāĻ•ā§āώāĻžāĻ°ā§āĻĨā§€ āϝāϤ āĻŦ⧇āĻļāĻŋ āϏāĻŽā§Ÿ āĻĒ⧜āĻžāĻļā§‹āύāĻž āĻ•āϰ⧇, āϤāĻžāϰ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ āϤāϤ āĻŦāĻžā§œā§‡ āϕ⧇āύ? āĻ…āĻĨāĻŦāĻž, āĻāĻ•āϟāĻŋ āĻĒāĻŖā§āϝ⧇āϰ āĻĻāĻžāĻŽ āĻŦāĻžā§œāϞ⧇ āϤāĻžāϰ āĻŦāĻŋāĻ•ā§āϰāĻŋ āĻ•āĻŽā§‡ āϝāĻžā§Ÿ āϕ⧇āύ? āĻāχ 'āϕ⧇āύ' āφāϰ 'āϕ⧀āĻ­āĻžāĻŦ⧇'āϰ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāĻžāϰ āϜāĻ¨ā§āϝāχ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύāϕ⧇ āφāĻŽāϰāĻž āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻŋāĨ¤

    āϏāĻšāϜ āĻ•āϰ⧇ āĻŦāϞāϞ⧇, āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻšāϞ⧋ āĻāĻŽāύ āĻāĻ•āϟāĻŋ āĻĒāϰāĻŋāϏāĻ‚āĻ–ā§āϝāĻžāύāĻ—āϤ āĻ•ā§ŒāĻļāϞ, āϝāĻž āĻĻ⧁āϟāĻŋ āĻŦāĻž āϤāĻžāϰ āĻŦ⧇āĻļāĻŋ āĻŦāĻŋāĻˇā§Ÿā§‡āϰ āĻŽāĻ§ā§āϝ⧇ āĻāĻ•āϟāĻž āϏāϰāϞāϰ⧇āĻ–āĻžāϰ āĻŽāϤ⧋ āϏāĻŽā§āĻĒāĻ°ā§āĻ• āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāϤ⧇ āϏāĻžāĻšāĻžāĻ¯ā§āϝ āĻ•āϰ⧇āĨ¤ āĻāϟāĻŋ āĻ…āύ⧇āĻ•āϟāĻž āĻāĻ•āϟāĻž āĻ…āĻĻ⧃āĻļā§āϝ āϏ⧁āϤ⧋ āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāĻžāϰ āĻŽāϤ⧋, āϝāĻž āĻĻ⧁āϟāĻŋ āϜāĻŋāύāĻŋāϏāϕ⧇ āĻāĻ•āϏāĻ™ā§āϗ⧇ āĻŦ⧇āρāϧ⧇ āϰāĻžāϖ⧇āĨ¤ āϝ⧇āĻŽāύ, āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿ āφāϰ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ⧇āϰ āĻŽāĻ§ā§āϝ⧇ āĻāĻ•āϟāĻž āϏāĻŽā§āĻĒāĻ°ā§āĻ• āφāϛ⧇, āϤāĻžāχ āύāĻž? āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āϏ⧇āχ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻžāϕ⧇ āĻāĻ•āϟāĻž āϏāϰāϞāϰ⧇āĻ–āĻž āĻĻāĻŋā§Ÿā§‡ āĻĒā§āϰāĻ•āĻžāĻļ āĻ•āϰ⧇āĨ¤

    āĻāĻ–āĻžāύ⧇ āĻĻ⧁āĻŸā§‹ āϗ⧁āϰ⧁āĻ¤ā§āĻŦāĻĒā§‚āĻ°ā§āĻŖ āϖ⧇āĻ˛ā§‹ā§ŸāĻžā§œ āφāϛ⧇, āϝāĻžāĻĻ⧇āϰāϕ⧇ āφāĻŽāϰāĻž 'āϚāϞāĻ•' (Variables) āĻŦāϞāĻŋ:

    ā§§āĨ¤ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• (Independent Variable): āĻāχ āĻšāϞ⧋ āϏ⧇āχ 'āĻ•āĻžāϰāĻŖ' āĻŦāĻž 'āχāύāĻĒ⧁āϟ'āĨ¤ āĻāϕ⧇ āφāĻĒāύāĻŋ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāύ āĻ•āϰāϤ⧇ āĻĒāĻžāϰ⧇āύ, āĻŦāĻž āĻāϟāĻŋ āύāĻŋāĻœā§‡ āύāĻŋāĻœā§‡āχ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāĻŋāϤ āĻšā§Ÿ āĻāĻŦāĻ‚ āĻ…āĻ¨ā§āϝ āϕ⧋āύ⧋ āĻ•āĻŋāϛ⧁āϕ⧇ āĻĒā§āϰāĻ­āĻžāĻŦāĻŋāϤ āĻ•āϰ⧇āĨ¤ āϝ⧇āĻŽāύ, āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿ, āĻŦāĻŋāĻœā§āĻžāĻžāĻĒāύ⧇āϰ āĻ–āϰāϚ, āĻŦāĻž āĻāĻ•āϟāĻŋ āĻŦāĻžā§œāĻŋāϰ āφāĻ•āĻžāϰāĨ¤ āĻ­āĻžāĻŦ⧁āύ āϤ⧋, āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿ āĻŦāĻžā§œāϞ⧇ āĻŦāĻž āĻ•āĻŽāϞ⧇ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ⧇āϰ āĻ“āĻĒāϰ āĻāĻ•āϟāĻž āĻĒā§āϰāĻ­āĻžāĻŦ āĻĒā§œā§‡, āϤāĻžāχ āύāĻž?

    ⧍āĨ¤ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• (Dependent Variable): āφāϰ āĻāχ āĻšāϞ⧋ āϏ⧇āχ 'āĻĢāϞāĻžāĻĢāϞ' āĻŦāĻž 'āφāωāϟāĻĒ⧁āϟ', āϝāĻž āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāϕ⧇āϰ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāύ⧇āϰ āĻ•āĻžāϰāϪ⧇ āĻĒā§āϰāĻ­āĻžāĻŦāĻŋāϤ āĻšā§ŸāĨ¤ āϝ⧇āĻŽāύ, āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ, āĻĒāĻŖā§āϝ⧇āϰ āĻŦāĻŋāĻ•ā§āϰāĻŋ, āĻŦāĻž āĻŦāĻžā§œāĻŋāϰ āĻĻāĻžāĻŽāĨ¤ āĻāχ āϚāϞāĻ•āϟāĻŋ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāϕ⧇āϰ āωāĻĒāϰ 'āύāĻŋāĻ°ā§āĻ­āϰ' āĻ•āϰ⧇āĨ¤

    āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ⧇āϰ āĻŽā§‚āϞ āϞāĻ•ā§āĻˇā§āϝ āĻšāϞ⧋ āĻāχ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āĻ“ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāϕ⧇āϰ āĻŽāĻ§ā§āϝ⧇ āĻāĻ•āϟāĻž āĻ—āĻžāĻŖāĻŋāϤāĻŋāĻ• āϏāĻŽā§āĻĒāĻ°ā§āĻ• āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāĻž, āϝāĻž āĻĻ⧇āĻ–āϤ⧇ āĻāĻ•āϟāĻž āϏāϰāϞāϰ⧇āĻ–āĻžāϰ āĻŽāϤ⧋āĨ¤ āĻāχ āϰ⧇āĻ–āĻžāϰ āĻāĻ•āϟāĻž āϏāĻŽā§€āĻ•āϰāĻŖ āĻĨāĻžāϕ⧇: Y=a+bX

    āĻāĻ–āĻžāύ⧇: Y āĻšāϞ⧋ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• (āĻĢāϞāĻžāĻĢāϞ): āĻ…āĻ°ā§āĻĨāĻžā§Ž, āφāĻĒāύāĻŋ āϝ⧇ āϜāĻŋāύāĻŋāϏāϟāĻž āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāϤ⧇ āϚāĻžāύ āĻŦāĻž āϝāĻžāϰ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāύ āĻŽāĻžāĻĒāϤ⧇ āϚāĻžāύāĨ¤

    X āĻšāϞ⧋ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• (āĻ•āĻžāϰāĻŖ): āĻ…āĻ°ā§āĻĨāĻžā§Ž, āϝ⧇ āϜāĻŋāύāĻŋāϏāϟāĻž āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāύ⧇āϰ āĻ•āĻžāϰāĻŖ āĻšāĻŋāϏ⧇āĻŦ⧇ āĻ•āĻžāϜ āĻ•āϰāϛ⧇āĨ¤

    a āĻšāϞ⧋ āχāĻ¨ā§āϟāĻžāϰāϏ⧇āĻĒā§āϟ (Intercept): āĻāϟāĻŋ āĻ…āύ⧇āĻ•āϟāĻž āĻ—ā§āϰāĻžāĻĢ⧇āϰ Y-āĻ…āĻ•ā§āώāϕ⧇ āϰ⧇āĻ–āĻžāϟāĻŋ āϝ⧇āĻ–āĻžāύ⧇ āϛ⧇āĻĻ āĻ•āϰ⧇ āϏ⧇āχ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āĨ¤ āϏāĻšāϜ āĻ­āĻžāώāĻžā§Ÿ, āϝāĻ–āύ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• (X) āĻāϰ āĻŽāĻžāύ āĻļā§‚āĻ¨ā§āϝ āĻšā§Ÿ, āϤāĻ–āύ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• (Y) āĻāϰ āφāύ⧁āĻŽāĻžāύāĻŋāĻ• āĻŽāĻžāύ āĻ•āϤ āĻšāĻŦ⧇, āϏ⧇āϟāĻžāχ aāĨ¤ āϝ⧇āĻŽāύ, āϝāĻĻāĻŋ āφāĻĒāύāĻŋ āĻāĻ•āĻĻāĻŽāχ āĻĒ⧜āĻžāĻļā§‹āύāĻž āύāĻž āĻ•āϰ⧇āύ (X=0), āϤāĻžāĻšāϞ⧇ āφāĻĒāύāĻžāϰ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ āĻ•āϤ āĻšāϤ⧇ āĻĒāĻžāϰ⧇, āϤāĻžāϰ āĻāĻ•āϟāĻž āφāύ⧁āĻŽāĻžāύāĻŋāĻ• āϧāĻžāϰāĻŖāĻžāĨ¤

    b āĻšāϞ⧋ āĻ¸ā§āϞāĻĒ (Slope): āĻāϟāĻŋ āϰ⧇āĻ–āĻžāϰ āĻĸāĻžāϞ āĻŦāĻž āĻ–āĻžā§œāĻž āĻšāĻ“ā§ŸāĻžāϰ āĻĒāϰāĻŋāĻŽāĻžāĻŖ āύāĻŋāĻ°ā§āĻĻ⧇āĻļ āĻ•āϰ⧇āĨ¤ āĻāϟāĻŋ āĻĻ⧇āĻ–āĻžā§Ÿ, āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• (X) āĻāϰ āĻŽāĻžāύ āϝāĻ–āύ āĻāĻ• āχāωāύāĻŋāϟ āĻŦāĻžā§œā§‡, āϤāĻ–āύ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• (Y) āĻāϰ āĻŽāĻžāύ āĻ•āϤāϟ⧁āϕ⧁ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāύ āĻšā§ŸāĨ¤ āϝ⧇āĻŽāύ, āϝāĻĻāĻŋ b āĻāϰ āĻŽāĻžāύ ⧍ āĻšā§Ÿ, āϤāĻžāϰ āĻŽāĻžāύ⧇ āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿ āĻāĻ• āϘāĻŖā§āϟāĻž āĻŦāĻžā§œāĻžāϞ⧇ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ āφāύ⧁āĻŽāĻžāύāĻŋāĻ• ⧍ āĻŦāĻžā§œāĻŦ⧇āĨ¤

    āϕ⧇āύ āφāĻŽāϰāĻž āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻŋ? (Why Use It?)

    āĻāϰ āĻĒā§āϰāϧāĻžāύ āĻ•āĻžāϜ āĻĻ⧁āĻŸā§‹, āϝāĻž āĻ—āĻŦ⧇āώāĻŖāĻžā§Ÿ āĻĻāĻžāϰ⧁āĻŖ āĻ•āĻžāĻœā§‡ āφāϏ⧇:
    A) āϏāĻŽā§āĻĒāĻ°ā§āĻ• āĻŦā§‹āĻāĻž (Understanding Relationships): āĻāϟāĻŋ āφāĻĒāύāĻžāϕ⧇ āĻŦāϞ⧇ āĻĻ⧇āĻŦ⧇, āφāĻĒāύāĻžāϰ āϚāϞāĻ•āϗ⧁āϞ⧋āϰ āĻŽāĻ§ā§āϝ⧇ āφāĻĻ⧌ āϕ⧋āύ⧋ āϏāĻŽā§āĻĒāĻ°ā§āĻ• āφāϛ⧇ āĻ•āĻŋ āύāĻž, āĻāĻŦāĻ‚ āϏ⧇āχ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āĻ•āϤāϟāĻž āĻļāĻ•ā§āϤāĻŋāĻļāĻžāϞ⧀āĨ¤ āϧāϰ⧁āύ, āφāĻĒāύāĻŋ āϜāĻžāύāϤ⧇ āϚāĻžāύ, āĻŦāĻŋāĻœā§āĻžāĻžāĻĒāύ⧇ āĻ–āϰāϚ āĻŦāĻžā§œāĻžāϞ⧇ āĻĒāĻŖā§āϝ⧇āϰ āĻŦāĻŋāĻ•ā§āϰāĻŋ āĻ•āĻŋ āϏāĻ¤ā§āϝāĻŋāχ āĻŦāĻžā§œā§‡? āϝāĻĻāĻŋ āĻŦāĻžā§œā§‡, āϤāĻžāĻšāϞ⧇ āĻ•āϤāϟāĻž āĻŦāĻžā§œā§‡? āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āφāĻĒāύāĻžāϕ⧇ āĻāχ 'āĻ•āϤāϟāĻž'āϰ āĻāĻ•āϟāĻž āϏāĻ‚āĻ–ā§āϝāĻžāĻ—āϤ āĻĒāϰāĻŋāĻŽāĻžāĻĒ āĻĻ⧇āĻŦ⧇āĨ¤

    B) āĻ­āĻŦāĻŋāĻˇā§āĻ¯ā§Ž āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāĻž (Making Predictions): āĻāĻ•āĻŦāĻžāϰ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āĻŦ⧁āĻā§‡ āϗ⧇āϞ⧇, āφāĻŽāϰāĻž āĻ­āĻŦāĻŋāĻˇā§āĻ¯ā§Ž āϏāĻŽā§āĻĒāĻ°ā§āϕ⧇ āĻ•āĻŋāϛ⧁ āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāϤ⧇ āĻĒāĻžāϰāĻŋāĨ¤ āϧāϰ⧁āύ, āφāĻĒāύāĻŋ āĻĻ⧇āĻ–āϞ⧇āύ āϝ⧇, āϤāĻžāĻĒāĻŽāĻžāĻ¤ā§āϰāĻž āĻŦāĻžā§œāϞ⧇ āφāχāϏāĻ•ā§āϰāĻŋāĻŽā§‡āϰ āĻŦāĻŋāĻ•ā§āϰāĻŋ āĻŦāĻžā§œā§‡āĨ¤ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āφāĻĒāύāĻžāϕ⧇ āĻāĻ•āϟāĻŋ āĻŽāĻĄā§‡āϞ āĻĻ⧇āĻŦ⧇, āϝāĻžāϰ āĻŽāĻžāĻ§ā§āϝāĻŽā§‡ āφāĻĒāύāĻŋ āĻšā§ŸāϤ⧋ āĻŦāϞāϤ⧇ āĻĒāĻžāϰāĻŦ⧇āύ, āφāĻ—āĻžāĻŽā§€ āϏāĻĒā§āϤāĻžāĻšā§‡ āϤāĻžāĻĒāĻŽāĻžāĻ¤ā§āϰāĻž āϝāĻĻāĻŋ āφāϰāĻ“ āĻŦāĻžā§œā§‡, āϤāĻžāĻšāϞ⧇ āφāχāϏāĻ•ā§āϰāĻŋāĻŽā§‡āϰ āĻŦāĻŋāĻ•ā§āϰāĻŋ āϕ⧇āĻŽāύ āĻšāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤ āĻāϟāĻŋ āĻ…āύ⧇āĻ•āϟāĻž āφāĻŦāĻšāĻžāĻ“ā§ŸāĻžāϰ āĻĒā§‚āĻ°ā§āĻŦāĻžāĻ­āĻžāϏ āĻĻ⧇āĻ“ā§ŸāĻžāϰ āĻŽāϤ⧋, āϝ⧇āĻ–āĻžāύ⧇ āφāĻŽāϰāĻž āĻ…āϤ⧀āϤ⧇āϰ āĻĄā§‡āϟāĻž āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰ⧇ āĻ­āĻŦāĻŋāĻˇā§āϝāϤ⧇āϰ āĻāĻ•āϟāĻž āϧāĻžāϰāĻŖāĻž āĻĒāĻžāχāĨ¤

    āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āϕ⧀āĻ­āĻžāĻŦ⧇ āĻ•āĻžāϜ āĻ•āϰ⧇? (How Does It Work?)
    āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻ•āĻžāϜ āĻ•āϰ⧇ āĻāĻ•āϟāĻž āϏāϰāϞāϰ⧇āĻ–āĻž āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰ⧇āĨ¤ āĻ­āĻžāĻŦ⧁āύ, āφāĻĒāύāĻžāϰ āĻ•āĻžāϛ⧇ āĻ•āĻŋāϛ⧁ āĻĄā§‡āϟāĻž āĻĒā§Ÿā§‡āĻ¨ā§āϟ āφāϛ⧇, āϝ⧇āĻŽāύ āĻ—ā§āϰāĻžāĻĢ āĻĒ⧇āĻĒāĻžāϰ⧇ āĻ›ā§œāĻžāύ⧋ āĻ•āĻŋāϛ⧁ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āĨ¤ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ⧇āϰ āĻ•āĻžāϜ āĻšāϞ⧋ āĻāχ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āϗ⧁āϞ⧋āϰ āĻŽāĻžāĻāĻ–āĻžāύ āĻĻāĻŋā§Ÿā§‡ āĻāĻŽāύ āĻāĻ•āϟāĻž āϏāϰāϞāϰ⧇āĻ–āĻž āφāρāĻ•āĻž, āϝāĻž āϏāĻŦ āĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻĨ⧇āϕ⧇ 'āĻ—ā§œā§‡' āϏāĻŦāĻšā§‡ā§Ÿā§‡ āĻ•āĻŽ āĻĻā§‚āϰāĻ¤ā§āĻŦ⧇ āĻĨāĻžāϕ⧇āĨ¤ āĻāχ 'āϏāĻŦāĻšā§‡ā§Ÿā§‡ āĻ•āĻŽ āĻĻā§‚āϰāĻ¤ā§āĻŦ' āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāĻžāϰ āϜāĻ¨ā§āϝ āĻ•āĻŋāϛ⧁ āĻ—āĻžāĻŖāĻŋāϤāĻŋāĻ• āĻšāĻŋāϏāĻžāĻŦ-āύāĻŋāĻ•āĻžāĻļ āĻ•āϰāĻž āĻšā§Ÿ, āϝāĻžāϕ⧇ āφāĻŽāϰāĻž 'āĻāϰāϰ āĻŽāĻŋāύāĻŋāĻŽāĻžāχāĻœā§‡āĻļāύ' āĻŦāĻž 'āĻ…āĻŦāĻļāĻŋāĻˇā§āϟ āĻ•āĻŽāĻžāύ⧋' āĻŦāϞāĻŋāĨ¤ āĻ…āĻ°ā§āĻĨāĻžā§Ž, āĻĄā§‡āϟāĻž āĻĒā§Ÿā§‡āĻ¨ā§āϟāϗ⧁āϞ⧋ āĻĨ⧇āϕ⧇ āϰ⧇āĻ–āĻžāϰ āϝ⧇ āĻĻā§‚āϰāĻ¤ā§āĻŦ, āϏ⧇āχ āĻĻā§‚āϰāĻ¤ā§āĻŦāϗ⧁āϞ⧋āϕ⧇ āϝāϤāϟāĻž āϏāĻŽā§āĻ­āĻŦ āϛ⧋āϟ āĻ•āϰāĻž āĻšā§Ÿ, āϝāĻžāϤ⧇ āϰ⧇āĻ–āĻžāϟāĻŋ āĻĄā§‡āϟāĻžāϰ 'āĻĒā§āϰāĻŦāĻŖāϤāĻž' āĻŦāĻž 'āĻŸā§āϰ⧇āĻ¨ā§āĻĄ'āϕ⧇ āϏāĻŦāĻšā§‡ā§Ÿā§‡ āĻ­āĻžāϞ⧋āĻ­āĻžāĻŦ⧇ āĻĻ⧇āĻ–āĻžāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤ āĻāχ āϰ⧇āĻ–āĻžāϟāĻŋāχ āĻšāϞ⧋ āφāĻĒāύāĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āϞāĻžāχāύ, āϝāĻž āφāĻĒāύāĻžāϰ āĻĄā§‡āϟāĻžāϰ āĻ—āĻ˛ā§āĻĒāϟāĻž āĻŦāϞ⧇āĨ¤

    āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ⧇āϰ āĻĒā§āϰāĻ•āĻžāϰāϭ⧇āĻĻ (Types of Linear Regression)
    āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻŽā§‚āϞāϤ āĻĻ⧁āϟāĻŋ āĻĒā§āϰāϧāĻžāύ āϧāϰāύ⧇ āĻŦāĻŋāĻ­āĻ•ā§āϤ, āύāĻŋāĻ°ā§āĻ­āϰ āĻ•āϰ⧇ āφāĻĒāύāĻŋ āĻ•āϤāϗ⧁āϞ⧋ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāϛ⧇āύ āϤāĻžāϰ āωāĻĒāϰ:

    āϏāĻžāϧāĻžāϰāĻŖ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ (Simple Linear Regression): āĻāĻ–āĻžāύ⧇ āĻļ⧁āϧ⧁ āĻāĻ•āϟāĻŋ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• āĻāĻŦāĻ‚ āĻāĻ•āϟāĻŋ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• āĻĨāĻžāϕ⧇āĨ¤

    āωāĻĻāĻžāĻšāϰāĻŖ: āĻāĻ•āϜāύ āĻ›āĻžāĻ¤ā§āϰ⧇āϰ āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿā§‡āϰ (āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ•) āϏāĻžāĻĨ⧇ āϤāĻžāϰ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ⧇āϰ (āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ•) āϏāĻŽā§āĻĒāĻ°ā§āĻ•āĨ¤ āĻāĻ–āĻžāύ⧇ āφāĻĒāύāĻŋ āĻļ⧁āϧ⧁ āĻāĻ•āϟāĻŋ āĻ•āĻžāϰāĻŖ (āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿ) āĻĻāĻŋā§Ÿā§‡ āĻāĻ•āϟāĻŋ āĻĢāϞāĻžāĻĢāϞ (āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ) āĻŦā§‹āĻāĻžāϰ āĻšā§‡āĻˇā§āϟāĻž āĻ•āϰāϛ⧇āύāĨ¤

    āĻŽāĻžāĻ˛ā§āϟāĻŋāĻĒāϞ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ (Multiple Linear Regression): āĻāĻ–āĻžāύ⧇ āĻāĻ•āĻžāϧāĻŋāĻ• āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• āĻāĻŦāĻ‚ āĻāĻ•āϟāĻŋ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• āĻĨāĻžāϕ⧇āĨ¤

    āωāĻĻāĻžāĻšāϰāĻŖ: āĻāĻ•āϟāĻŋ āĻŦāĻžā§œāĻŋāϰ āĻĻāĻžāĻŽ (āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ•) āĻļ⧁āϧ⧁ āϤāĻžāϰ āφāĻ•āĻžāϰ⧇āϰ āωāĻĒāϰ āύāĻŋāĻ°ā§āĻ­āϰ āĻ•āϰ⧇ āύāĻž, āĻŦāϰāĻ‚ āĻāϞāĻžāĻ•āĻžāϰ āĻ…āĻŦāĻ¸ā§āĻĨāĻžāύ, āĻŦāĻžā§œāĻŋāϰ āĻŦ⧟āϏ, āϰ⧁āĻŽā§‡āϰ āϏāĻ‚āĻ–ā§āϝāĻž, āĻŦāĻžāĻĨāϰ⧁āĻŽā§‡āϰ āϏāĻ‚āĻ–ā§āϝāĻž – āĻāχ āϏāĻŦāĻ•āĻŋāϛ⧁āϰ āωāĻĒāϰ āύāĻŋāĻ°ā§āĻ­āϰ āĻ•āϰ⧇āĨ¤ āĻŽāĻžāĻ˛ā§āϟāĻŋāĻĒāϞ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻāχ āϏāĻŦ āĻ•āĻžāϰāĻŖ āĻāĻ•āϏāĻ™ā§āϗ⧇ āĻŦāĻŋāĻļā§āϞ⧇āώāĻŖ āĻ•āϰ⧇ āĻĻ⧇āĻ–āĻžā§Ÿ āϝ⧇, āϕ⧋āύ āĻ•āĻžāϰāĻŖāϟāĻŋ āĻŦāĻžā§œāĻŋāϰ āĻĻāĻžāĻŽā§‡āϰ āωāĻĒāϰ āĻ•āϤāϟāĻž āĻĒā§āϰāĻ­āĻžāĻŦ āĻĢ⧇āϞāϛ⧇āĨ¤ āĻāϟāĻŋ āĻ…āύ⧇āĻ•āϟāĻž āĻ…āύ⧇āĻ•āϗ⧁āϞ⧋ āĻ•āĻžāϰāĻŖ āĻāĻ•āϏāĻ™ā§āϗ⧇ āĻāĻ•āϟāĻŋ āĻĢāϞāĻžāĻĢāϞ⧇āϰ āωāĻĒāϰ āϕ⧀āĻ­āĻžāĻŦ⧇ āĻĒā§āϰāĻ­āĻžāĻŦ āĻĢ⧇āϞ⧇, āϤāĻž āĻĻ⧇āĻ–āĻžāϰ āĻŽāϤ⧋āĨ¤

    āĻ•āĻŋāϛ⧁ āϜāϰ⧁āϰāĻŋ āĻ•āĻĨāĻž (Key Concepts): āĻ…āĻŦāĻļāĻŋāĻˇā§āϟ (Residuals): āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āϰ⧇āĻ–āĻžāϟāĻŋ āϏāĻŦ āĻĄā§‡āϟāĻž āĻĒā§Ÿā§‡āĻ¨ā§āĻŸā§‡āϰ āωāĻĒāϰ āĻĻāĻŋā§Ÿā§‡ āϝāĻžā§Ÿ āύāĻž, āĻ•āĻŋāϛ⧁ āĻĒā§Ÿā§‡āĻ¨ā§āϟ āϰ⧇āĻ–āĻžāϰ āωāĻĒāϰ⧇ āĻŦāĻž āύāĻŋāĻšā§‡ āĻĨāĻžāϕ⧇āĨ¤ āĻāχ āĻĄā§‡āϟāĻž āĻĒā§Ÿā§‡āĻ¨ā§āϟ āĻāĻŦāĻ‚ āϰ⧇āĻ–āĻžāϰ āĻŽāĻ§ā§āϝ⧇ āϝ⧇ āĻĻā§‚āϰāĻ¤ā§āĻŦ, āϏ⧇āϟāĻŋāχ āĻšāϞ⧋ āĻ…āĻŦāĻļāĻŋāĻˇā§āϟ āĻŦāĻž āĻāϰāϰ (error)āĨ¤ āĻāϟāĻŋ āĻĻ⧇āĻ–āĻžā§Ÿ, āφāĻŽāĻžāĻĻ⧇āϰ āĻŽāĻĄā§‡āϞ āĻ•āϤāϟāĻž āύāĻŋāϖ⧁āρāϤāĻ­āĻžāĻŦ⧇ āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāϤ⧇ āĻĒāĻžāϰāϛ⧇āĨ¤ āϝāϤ āĻ•āĻŽ āĻ…āĻŦāĻļāĻŋāĻˇā§āϟ, āĻŽāĻĄā§‡āϞ āϤāϤ āĻ­āĻžāϞ⧋āĨ¤

    āϏāĻšāϏāĻŽā§āĻĒāĻ°ā§āĻ• (Correlation): āĻāϟāĻŋ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ⧇āϰ āϏāĻžāĻĨ⧇ āϜ⧜āĻŋāϤ āĻāĻ•āϟāĻŋ āϧāĻžāϰāĻŖāĻžāĨ¤ āϏāĻšāϏāĻŽā§āĻĒāĻ°ā§āĻ• (āϝ⧇āĻŽāύ āĻĒāĻŋāϝāĻŧāĻžāϰāϏāύ āϕ⧋āϰāĻŋāϞ⧇āĻļāύ āϕ⧋āĻāĻĢāĻŋāĻļāĻŋāϝāĻŧ⧇āĻ¨ā§āϟ) āĻĻ⧁āϟāĻŋ āϚāϞāϕ⧇āϰ āĻŽāĻ§ā§āϝ⧇ āϏāĻŽā§āĻĒāĻ°ā§āϕ⧇āϰ āĻļāĻ•ā§āϤāĻŋ āĻāĻŦāĻ‚ āĻĻāĻŋāĻ• (āχāϤāĻŋāĻŦāĻžāϚāĻ• āĻŦāĻž āύ⧇āϤāĻŋāĻŦāĻžāϚāĻ•) āĻĒāϰāĻŋāĻŽāĻžāĻĒ āĻ•āϰ⧇āĨ¤ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻāχ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϕ⧇ āĻāĻ•āϟāĻŋ āĻŽāĻĄā§‡āϞ⧇āϰ āĻŽāĻžāĻ§ā§āϝāĻŽā§‡ āĻŦā§āϝāĻžāĻ–ā§āϝāĻž āĻ•āϰ⧇āĨ¤ āϏāĻšāϏāĻŽā§āĻĒāĻ°ā§āĻ• āφāĻĒāύāĻžāϕ⧇ āĻŦāϞāĻŦ⧇ āϏāĻŽā§āĻĒāĻ°ā§āĻ• āφāϛ⧇ āĻ•āĻŋāύāĻž, āφāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āφāĻĒāύāĻžāϕ⧇ āĻŦāϞāĻŦ⧇ āϏ⧇āχ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āϕ⧇āĻŽāύ āĻāĻŦāĻ‚ āϕ⧀āĻ­āĻžāĻŦ⧇ āĻ•āĻžāϜ āĻ•āϰ⧇āĨ¤

    āĻ…āύ⧁āĻŽāĻžāύ (Assumptions): āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻ•āĻŋāϛ⧁ āύāĻŋāĻ°ā§āĻĻāĻŋāĻˇā§āϟ āĻļāĻ°ā§āϤ⧇āϰ āωāĻĒāϰ āĻ­āĻŋāĻ¤ā§āϤāĻŋ āĻ•āϰ⧇ āĻ•āĻžāϜ āĻ•āϰ⧇āĨ¤ āϝ⧇āĻŽāύ, āϚāϞāĻ•āϗ⧁āϞ⧋āϰ āĻŽāĻ§ā§āϝ⧇ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āϝ⧇āύ āϏāĻ¤ā§āϝāĻŋāχ āϏāϰāϞāϰ⧈āĻ–āĻŋāĻ• āĻšā§Ÿ, āĻĄā§‡āϟāĻž āĻĒā§Ÿā§‡āĻ¨ā§āϟāϗ⧁āϞ⧋ āϝ⧇āύ āϖ⧁āĻŦ āĻŦ⧇āĻļāĻŋ āĻ›ā§œāĻžāύ⧋-āĻ›āĻŋāϟāĻžāύ⧋ āύāĻž āĻĨāĻžāϕ⧇ (āφāωāϟāϞāĻžā§ŸāĻžāϰ āύāĻž āĻĨāĻžāϕ⧇), āĻāĻŦāĻ‚ āĻāϰāϰāϗ⧁āϞ⧋ āϝ⧇āύ āĻāϞ⧋āĻŽā§‡āϞ⧋āĻ­āĻžāĻŦ⧇ āĻ›ā§œāĻžāύ⧋ āĻĨāĻžāϕ⧇āĨ¤ āĻāχ āĻļāĻ°ā§āϤāϗ⧁āϞ⧋ āĻĒā§‚āϰāĻŖ āĻšāϞ⧇ āĻŽāĻĄā§‡āϞ⧇āϰ āĻĢāϞāĻžāĻĢāϞ āφāϰāĻ“ āύāĻŋāĻ°ā§āĻ­āϰāϝ⧋āĻ—ā§āϝ āĻšā§ŸāĨ¤

    āĻ•āĻ–āύ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻŦ⧇āύ, āĻ•āĻ–āύ āĻ•āϰāĻŦ⧇āύ āύāĻž? (When to Use, When Not to Use?)

    āĻ•āĻ–āύ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻŦ⧇āύ?: āϝāĻ–āύ āφāĻĒāύāĻŋ āĻĻ⧁āϟāĻŋ āĻŦāĻž āϤāĻžāϰ āĻŦ⧇āĻļāĻŋ āϚāϞāϕ⧇āϰ āĻŽāĻ§ā§āϝ⧇ āĻāĻ•āϟāĻŋ āϏāϰāϞāϰ⧈āĻ–āĻŋāĻ• āϏāĻŽā§āĻĒāĻ°ā§āĻ• āφāϛ⧇ āĻŦāϞ⧇ āĻŽāύ⧇ āĻ•āϰ⧇āύ āĻāĻŦāĻ‚ āϏ⧇āχ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āĻŦ⧁āĻāϤ⧇ āϚāĻžāύāĨ¤ āϝāĻ–āύ āφāĻĒāύāĻŋ āĻāĻ•āϟāĻŋ āϚāϞāϕ⧇āϰ āĻŽāĻžāύ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰ⧇ āĻ…āĻ¨ā§āϝ āĻāĻ•āϟāĻŋ āϚāϞāϕ⧇āϰ āĻŽāĻžāύ āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāϤ⧇ āϚāĻžāύāĨ¤

    āϝāĻ–āύ āφāĻĒāύāĻŋ āϜāĻžāύāϤ⧇ āϚāĻžāύ, āϕ⧋āύ āĻ•āĻžāϰāĻŖāϗ⧁āϞ⧋ (āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ•) āĻāĻ•āϟāĻŋ āύāĻŋāĻ°ā§āĻĻāĻŋāĻˇā§āϟ āĻĢāϞāĻžāĻĢāϞ⧇āϰ (āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ•) āωāĻĒāϰ āϏāĻŦāĻšā§‡ā§Ÿā§‡ āĻŦ⧇āĻļāĻŋ āĻĒā§āϰāĻ­āĻžāĻŦ āĻĢ⧇āϞāϛ⧇āĨ¤ āϝāĻ–āύ āφāĻĒāύāĻŋ āϕ⧋āύ⧋ āϧāĻžāϰāĻžāĻŦāĻžāĻšāĻŋāĻ• āĻĢāϞāĻžāĻĢāϞ (continuous outcome) āϝ⧇āĻŽāύ, āϤāĻžāĻĒāĻŽāĻžāĻ¤ā§āϰāĻž, āĻŦāĻŋāĻ•ā§āϰāĻŋ, āύāĻŽā§āĻŦāϰ āχāĻ¤ā§āϝāĻžāĻĻāĻŋ āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāϤ⧇ āϚāĻžāύāĨ¤

    āĻ•āĻ–āύ āĻ•āϰāĻŦ⧇āύ āύāĻž?
    āϝāĻĻāĻŋ āϚāϞāĻ•āϗ⧁āϞ⧋āϰ āĻŽāĻ§ā§āϝ⧇ āϕ⧋āύ⧋ āϏāϰāϞāϰ⧈āĻ–āĻŋāĻ• āϏāĻŽā§āĻĒāĻ°ā§āĻ• āύāĻž āĻĨāĻžāϕ⧇ (āϝ⧇āĻŽāύ, āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻŋ āĻŦāĻ•ā§āϰāϰ⧇āĻ–āĻžāϰ āĻŽāϤ⧋ āĻŦāĻž āĻāϞ⧋āĻŽā§‡āϞ⧋)āĨ¤ āĻāĻ•ā§āώ⧇āĻ¤ā§āϰ⧇ āĻ…āĻ¨ā§āϝ āϧāϰāύ⧇āϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻŽāĻĄā§‡āϞ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāϤ⧇ āĻšāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤ āϝāĻĻāĻŋ āφāĻĒāύāĻžāϰ āĻĄā§‡āϟāĻžā§Ÿ āĻ…āύ⧇āĻ• āĻŦ⧇āĻļāĻŋ āĻ…āĻ¸ā§āĻŦāĻžāĻ­āĻžāĻŦāĻŋāĻ• āĻŦāĻž āϭ⧁āϞ āĻĄā§‡āϟāĻž (outliers) āĻĨāĻžāϕ⧇, āϝāĻž āϰ⧇āĻ–āĻžāϟāĻŋāϕ⧇ āϭ⧁āϞāĻ­āĻžāĻŦ⧇ āĻĒā§āϰāĻ­āĻžāĻŦāĻŋāϤ āĻ•āϰāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤ āĻāχ 'āφāωāϟāϞāĻžā§ŸāĻžāϰ'āϗ⧁āϞ⧋ āĻĢāϞāĻžāĻĢāϞāϕ⧇ āϭ⧁āϞ āĻĒāĻĨ⧇ āϚāĻžāϞāĻŋāϤ āĻ•āϰāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤

    āϝāĻĻāĻŋ āφāĻĒāύāĻžāϰ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ•āϗ⧁āϞ⧋ āĻāϕ⧇ āĻ…āĻĒāϰ⧇āϰ āϏāĻžāĻĨ⧇ āϖ⧁āĻŦ āĻŦ⧇āĻļāĻŋ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āĻŋāϤ āĻšā§Ÿ (multicollinearity), āϤāĻžāĻšāϞ⧇ āĻŽāĻžāĻ˛ā§āϟāĻŋāĻĒāϞ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻž āĻ•āĻ āĻŋāύ āĻšāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤ āĻāϟāĻŋ āĻ…āύ⧇āĻ•āϟāĻž āĻāĻŽāύ āϝ⧇, āĻĻ⧁āϟāĻŋ āĻ•āĻžāϰāĻŖ āĻāĻ•āχ āϰāĻ•āĻŽ āĻĒā§āϰāĻ­āĻžāĻŦ āĻĢ⧇āϞāϛ⧇, āϤāĻ–āύ āĻŦā§‹āĻāĻž āĻ•āĻ āĻŋāύ āĻšā§Ÿā§‡ āϝāĻžā§Ÿ āϕ⧋āύāϟāĻŋ āφāϏāϞ āĻĒā§āϰāĻ­āĻžāĻŦāĻ•āĨ¤

    āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻšāϞ⧋ āĻĄā§‡āϟāĻž āĻŦāĻŋāĻļā§āϞ⧇āώāϪ⧇āϰ āĻāĻ• āĻĻāĻžāϰ⧁āĻŖ āĻšāĻžāϤāĻŋ⧟āĻžāϰ, āϝāĻž āφāĻĒāύāĻžāϕ⧇ āĻĄā§‡āϟāĻžāϰ āϭ⧇āϤāϰ⧇āϰ āϞ⧁āĻ•āĻžāύ⧋ āĻ—āĻ˛ā§āĻĒāϗ⧁āϞ⧋ āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāϤ⧇ āϏāĻžāĻšāĻžāĻ¯ā§āϝ āĻ•āϰāĻŦ⧇āĨ¤ āĻāϟāĻŋ āĻļ⧁āϧ⧁ āϏāĻ‚āĻ–ā§āϝāĻž āύ⧟, āĻŦāϰāĻ‚ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āĻĒ⧇āĻ›āύ⧇āϰ āĻ•āĻžāϰāĻŖ āĻ“ āĻĒā§āϰāĻ­āĻžāĻŦāϕ⧇ āĻŦ⧁āĻāϤ⧇ āĻļ⧇āĻ–āĻžā§ŸāĨ¤ āφāĻļāĻž āĻ•āϰāĻŋ, āĻāχ āĻŦāĻŋāĻ¸ā§āϤāĻžāϰāĻŋāϤ āφāϞ⧋āϚāύāĻž āφāĻĒāύāĻžāϰ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āϏāĻŽā§āĻĒāĻ°ā§āϕ⧇ āϧāĻžāϰāĻŖāĻž āφāϰāĻ“ āĻĒāϰāĻŋāĻˇā§āĻ•āĻžāϰ āĻ•āϰ⧇āϛ⧇āĨ¤ āφāĻĒāύāĻžāϰ āϝāĻĻāĻŋ āφāϰāĻ“ āĻ•āĻŋāϛ⧁ āϜāĻžāύāĻžāϰ āĻĨāĻžāϕ⧇, āϤāĻžāĻšāϞ⧇ āφāĻŽāĻžāϕ⧇ āϜāĻžāύāĻžāϤ⧇ āĻĒāĻžāϰ⧇āύ!

    Md. Rony Masud
    BBA, MBA (DU), MS (Japan)
    āφāĻĒāύāĻžāϰ āĻ—āĻŦ⧇āώāĻŖāĻž āĻĒāĻĻā§āϧāϤāĻŋāϰ āϏāĻžāϤāĻ•āĻžāĻšāύ: āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ (Linear Regression in Research methodology) āϧāϰ⧁āύ, āφāĻĒāύāĻŋ āĻ…āύ⧇āĻ•āϗ⧁āϞ⧋ āĻ•āĻžāρāϚāĻžāĻŽāĻžāϞ āĻœā§‹āĻ—āĻžā§œ āĻ•āϰ⧇āϛ⧇āύāĨ¤ āĻāĻ–āύ āϏ⧇āχ āĻ•āĻžāρāϚāĻžāĻŽāĻžāϞ āĻĻāĻŋā§Ÿā§‡ āϕ⧀ āĻŦāĻžāύāĻžāĻŦ⧇āύ, āϕ⧀āĻ­āĻžāĻŦ⧇ āĻŦāĻžāύāĻžāĻŦ⧇āύ, āϏ⧇āϟāĻžāχ āĻšāϞ⧋ āĻŦāĻŋāĻļā§āϞ⧇āώāϪ⧇āϰ āĻ•āĻžāϜāĨ¤ āφāϰ āĻāχ āĻŦāĻŋāĻļā§āϞ⧇āώāϪ⧇āϰ āĻĻ⧁āύāĻŋ⧟āĻžā§Ÿ āĻāĻ•āϟāĻž āĻĻāĻžāϰ⧁āĻŖ 'āĻŽā§āϝāĻžāϜāĻŋāĻ• āϟ⧁āϞ' āφāϛ⧇, āϝāĻžāϰ āύāĻžāĻŽ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύāĨ¤ āĻāϰ āύāĻžāĻŽāϟāĻž āĻāĻ•āϟ⧁ āϜāϟāĻŋāϞ āĻļā§‹āύāĻžāϞ⧇āĻ“, āĻāϰ āĻ•āĻžāϜāϟāĻž āĻ•āĻŋāĻ¨ā§āϤ⧁ āϖ⧁āĻŦāχ āϏāĻšāϜ āφāϰ āĻ•āĻžāĻœā§‡āϰāĨ¤ āϚāϞ⧁āύ, āφāϜ āφāĻŽāϰāĻž āĻāχ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ⧇āϰ āφāĻĻā§āϝ⧋āĻĒāĻžāĻ¨ā§āϤ āĻœā§‡āύ⧇ āύāĻŋāχ, āĻāĻ•āĻĻāĻŽ A2Z! āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āφāϏāϞ⧇ āϕ⧀? (What is Linear Regression?) āφāĻšā§āĻ›āĻž, āφāĻĒāύāĻŋ āĻ•āĻŋ āĻ•āĻ–āύ⧋ āϭ⧇āĻŦ⧇ āĻĻ⧇āϖ⧇āϛ⧇āύ, āĻāĻ•āϜāύ āĻļāĻŋāĻ•ā§āώāĻžāĻ°ā§āĻĨā§€ āϝāϤ āĻŦ⧇āĻļāĻŋ āϏāĻŽā§Ÿ āĻĒ⧜āĻžāĻļā§‹āύāĻž āĻ•āϰ⧇, āϤāĻžāϰ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ āϤāϤ āĻŦāĻžā§œā§‡ āϕ⧇āύ? āĻ…āĻĨāĻŦāĻž, āĻāĻ•āϟāĻŋ āĻĒāĻŖā§āϝ⧇āϰ āĻĻāĻžāĻŽ āĻŦāĻžā§œāϞ⧇ āϤāĻžāϰ āĻŦāĻŋāĻ•ā§āϰāĻŋ āĻ•āĻŽā§‡ āϝāĻžā§Ÿ āϕ⧇āύ? āĻāχ 'āϕ⧇āύ' āφāϰ 'āϕ⧀āĻ­āĻžāĻŦ⧇'āϰ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāĻžāϰ āϜāĻ¨ā§āϝāχ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύāϕ⧇ āφāĻŽāϰāĻž āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻŋāĨ¤ āϏāĻšāϜ āĻ•āϰ⧇ āĻŦāϞāϞ⧇, āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻšāϞ⧋ āĻāĻŽāύ āĻāĻ•āϟāĻŋ āĻĒāϰāĻŋāϏāĻ‚āĻ–ā§āϝāĻžāύāĻ—āϤ āĻ•ā§ŒāĻļāϞ, āϝāĻž āĻĻ⧁āϟāĻŋ āĻŦāĻž āϤāĻžāϰ āĻŦ⧇āĻļāĻŋ āĻŦāĻŋāĻˇā§Ÿā§‡āϰ āĻŽāĻ§ā§āϝ⧇ āĻāĻ•āϟāĻž āϏāϰāϞāϰ⧇āĻ–āĻžāϰ āĻŽāϤ⧋ āϏāĻŽā§āĻĒāĻ°ā§āĻ• āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāϤ⧇ āϏāĻžāĻšāĻžāĻ¯ā§āϝ āĻ•āϰ⧇āĨ¤ āĻāϟāĻŋ āĻ…āύ⧇āĻ•āϟāĻž āĻāĻ•āϟāĻž āĻ…āĻĻ⧃āĻļā§āϝ āϏ⧁āϤ⧋ āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāĻžāϰ āĻŽāϤ⧋, āϝāĻž āĻĻ⧁āϟāĻŋ āϜāĻŋāύāĻŋāϏāϕ⧇ āĻāĻ•āϏāĻ™ā§āϗ⧇ āĻŦ⧇āρāϧ⧇ āϰāĻžāϖ⧇āĨ¤ āϝ⧇āĻŽāύ, āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿ āφāϰ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ⧇āϰ āĻŽāĻ§ā§āϝ⧇ āĻāĻ•āϟāĻž āϏāĻŽā§āĻĒāĻ°ā§āĻ• āφāϛ⧇, āϤāĻžāχ āύāĻž? āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āϏ⧇āχ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻžāϕ⧇ āĻāĻ•āϟāĻž āϏāϰāϞāϰ⧇āĻ–āĻž āĻĻāĻŋā§Ÿā§‡ āĻĒā§āϰāĻ•āĻžāĻļ āĻ•āϰ⧇āĨ¤ āĻāĻ–āĻžāύ⧇ āĻĻ⧁āĻŸā§‹ āϗ⧁āϰ⧁āĻ¤ā§āĻŦāĻĒā§‚āĻ°ā§āĻŖ āϖ⧇āĻ˛ā§‹ā§ŸāĻžā§œ āφāϛ⧇, āϝāĻžāĻĻ⧇āϰāϕ⧇ āφāĻŽāϰāĻž 'āϚāϞāĻ•' (Variables) āĻŦāϞāĻŋ: ā§§āĨ¤ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• (Independent Variable): āĻāχ āĻšāϞ⧋ āϏ⧇āχ 'āĻ•āĻžāϰāĻŖ' āĻŦāĻž 'āχāύāĻĒ⧁āϟ'āĨ¤ āĻāϕ⧇ āφāĻĒāύāĻŋ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāύ āĻ•āϰāϤ⧇ āĻĒāĻžāϰ⧇āύ, āĻŦāĻž āĻāϟāĻŋ āύāĻŋāĻœā§‡ āύāĻŋāĻœā§‡āχ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāĻŋāϤ āĻšā§Ÿ āĻāĻŦāĻ‚ āĻ…āĻ¨ā§āϝ āϕ⧋āύ⧋ āĻ•āĻŋāϛ⧁āϕ⧇ āĻĒā§āϰāĻ­āĻžāĻŦāĻŋāϤ āĻ•āϰ⧇āĨ¤ āϝ⧇āĻŽāύ, āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿ, āĻŦāĻŋāĻœā§āĻžāĻžāĻĒāύ⧇āϰ āĻ–āϰāϚ, āĻŦāĻž āĻāĻ•āϟāĻŋ āĻŦāĻžā§œāĻŋāϰ āφāĻ•āĻžāϰāĨ¤ āĻ­āĻžāĻŦ⧁āύ āϤ⧋, āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿ āĻŦāĻžā§œāϞ⧇ āĻŦāĻž āĻ•āĻŽāϞ⧇ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ⧇āϰ āĻ“āĻĒāϰ āĻāĻ•āϟāĻž āĻĒā§āϰāĻ­āĻžāĻŦ āĻĒā§œā§‡, āϤāĻžāχ āύāĻž? ⧍āĨ¤ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• (Dependent Variable): āφāϰ āĻāχ āĻšāϞ⧋ āϏ⧇āχ 'āĻĢāϞāĻžāĻĢāϞ' āĻŦāĻž 'āφāωāϟāĻĒ⧁āϟ', āϝāĻž āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāϕ⧇āϰ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāύ⧇āϰ āĻ•āĻžāϰāϪ⧇ āĻĒā§āϰāĻ­āĻžāĻŦāĻŋāϤ āĻšā§ŸāĨ¤ āϝ⧇āĻŽāύ, āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ, āĻĒāĻŖā§āϝ⧇āϰ āĻŦāĻŋāĻ•ā§āϰāĻŋ, āĻŦāĻž āĻŦāĻžā§œāĻŋāϰ āĻĻāĻžāĻŽāĨ¤ āĻāχ āϚāϞāĻ•āϟāĻŋ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāϕ⧇āϰ āωāĻĒāϰ 'āύāĻŋāĻ°ā§āĻ­āϰ' āĻ•āϰ⧇āĨ¤ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ⧇āϰ āĻŽā§‚āϞ āϞāĻ•ā§āĻˇā§āϝ āĻšāϞ⧋ āĻāχ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āĻ“ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāϕ⧇āϰ āĻŽāĻ§ā§āϝ⧇ āĻāĻ•āϟāĻž āĻ—āĻžāĻŖāĻŋāϤāĻŋāĻ• āϏāĻŽā§āĻĒāĻ°ā§āĻ• āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāĻž, āϝāĻž āĻĻ⧇āĻ–āϤ⧇ āĻāĻ•āϟāĻž āϏāϰāϞāϰ⧇āĻ–āĻžāϰ āĻŽāϤ⧋āĨ¤ āĻāχ āϰ⧇āĻ–āĻžāϰ āĻāĻ•āϟāĻž āϏāĻŽā§€āĻ•āϰāĻŖ āĻĨāĻžāϕ⧇: Y=a+bX āĻāĻ–āĻžāύ⧇: Y āĻšāϞ⧋ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• (āĻĢāϞāĻžāĻĢāϞ): āĻ…āĻ°ā§āĻĨāĻžā§Ž, āφāĻĒāύāĻŋ āϝ⧇ āϜāĻŋāύāĻŋāϏāϟāĻž āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāϤ⧇ āϚāĻžāύ āĻŦāĻž āϝāĻžāϰ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāύ āĻŽāĻžāĻĒāϤ⧇ āϚāĻžāύāĨ¤ X āĻšāϞ⧋ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• (āĻ•āĻžāϰāĻŖ): āĻ…āĻ°ā§āĻĨāĻžā§Ž, āϝ⧇ āϜāĻŋāύāĻŋāϏāϟāĻž āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāύ⧇āϰ āĻ•āĻžāϰāĻŖ āĻšāĻŋāϏ⧇āĻŦ⧇ āĻ•āĻžāϜ āĻ•āϰāϛ⧇āĨ¤ a āĻšāϞ⧋ āχāĻ¨ā§āϟāĻžāϰāϏ⧇āĻĒā§āϟ (Intercept): āĻāϟāĻŋ āĻ…āύ⧇āĻ•āϟāĻž āĻ—ā§āϰāĻžāĻĢ⧇āϰ Y-āĻ…āĻ•ā§āώāϕ⧇ āϰ⧇āĻ–āĻžāϟāĻŋ āϝ⧇āĻ–āĻžāύ⧇ āϛ⧇āĻĻ āĻ•āϰ⧇ āϏ⧇āχ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āĨ¤ āϏāĻšāϜ āĻ­āĻžāώāĻžā§Ÿ, āϝāĻ–āύ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• (X) āĻāϰ āĻŽāĻžāύ āĻļā§‚āĻ¨ā§āϝ āĻšā§Ÿ, āϤāĻ–āύ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• (Y) āĻāϰ āφāύ⧁āĻŽāĻžāύāĻŋāĻ• āĻŽāĻžāύ āĻ•āϤ āĻšāĻŦ⧇, āϏ⧇āϟāĻžāχ aāĨ¤ āϝ⧇āĻŽāύ, āϝāĻĻāĻŋ āφāĻĒāύāĻŋ āĻāĻ•āĻĻāĻŽāχ āĻĒ⧜āĻžāĻļā§‹āύāĻž āύāĻž āĻ•āϰ⧇āύ (X=0), āϤāĻžāĻšāϞ⧇ āφāĻĒāύāĻžāϰ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ āĻ•āϤ āĻšāϤ⧇ āĻĒāĻžāϰ⧇, āϤāĻžāϰ āĻāĻ•āϟāĻž āφāύ⧁āĻŽāĻžāύāĻŋāĻ• āϧāĻžāϰāĻŖāĻžāĨ¤ b āĻšāϞ⧋ āĻ¸ā§āϞāĻĒ (Slope): āĻāϟāĻŋ āϰ⧇āĻ–āĻžāϰ āĻĸāĻžāϞ āĻŦāĻž āĻ–āĻžā§œāĻž āĻšāĻ“ā§ŸāĻžāϰ āĻĒāϰāĻŋāĻŽāĻžāĻŖ āύāĻŋāĻ°ā§āĻĻ⧇āĻļ āĻ•āϰ⧇āĨ¤ āĻāϟāĻŋ āĻĻ⧇āĻ–āĻžā§Ÿ, āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• (X) āĻāϰ āĻŽāĻžāύ āϝāĻ–āύ āĻāĻ• āχāωāύāĻŋāϟ āĻŦāĻžā§œā§‡, āϤāĻ–āύ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• (Y) āĻāϰ āĻŽāĻžāύ āĻ•āϤāϟ⧁āϕ⧁ āĻĒāϰāĻŋāĻŦāĻ°ā§āϤāύ āĻšā§ŸāĨ¤ āϝ⧇āĻŽāύ, āϝāĻĻāĻŋ b āĻāϰ āĻŽāĻžāύ ⧍ āĻšā§Ÿ, āϤāĻžāϰ āĻŽāĻžāύ⧇ āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿ āĻāĻ• āϘāĻŖā§āϟāĻž āĻŦāĻžā§œāĻžāϞ⧇ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ āφāύ⧁āĻŽāĻžāύāĻŋāĻ• ⧍ āĻŦāĻžā§œāĻŦ⧇āĨ¤ āϕ⧇āύ āφāĻŽāϰāĻž āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻŋ? (Why Use It?) āĻāϰ āĻĒā§āϰāϧāĻžāύ āĻ•āĻžāϜ āĻĻ⧁āĻŸā§‹, āϝāĻž āĻ—āĻŦ⧇āώāĻŖāĻžā§Ÿ āĻĻāĻžāϰ⧁āĻŖ āĻ•āĻžāĻœā§‡ āφāϏ⧇: A) āϏāĻŽā§āĻĒāĻ°ā§āĻ• āĻŦā§‹āĻāĻž (Understanding Relationships): āĻāϟāĻŋ āφāĻĒāύāĻžāϕ⧇ āĻŦāϞ⧇ āĻĻ⧇āĻŦ⧇, āφāĻĒāύāĻžāϰ āϚāϞāĻ•āϗ⧁āϞ⧋āϰ āĻŽāĻ§ā§āϝ⧇ āφāĻĻ⧌ āϕ⧋āύ⧋ āϏāĻŽā§āĻĒāĻ°ā§āĻ• āφāϛ⧇ āĻ•āĻŋ āύāĻž, āĻāĻŦāĻ‚ āϏ⧇āχ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āĻ•āϤāϟāĻž āĻļāĻ•ā§āϤāĻŋāĻļāĻžāϞ⧀āĨ¤ āϧāϰ⧁āύ, āφāĻĒāύāĻŋ āϜāĻžāύāϤ⧇ āϚāĻžāύ, āĻŦāĻŋāĻœā§āĻžāĻžāĻĒāύ⧇ āĻ–āϰāϚ āĻŦāĻžā§œāĻžāϞ⧇ āĻĒāĻŖā§āϝ⧇āϰ āĻŦāĻŋāĻ•ā§āϰāĻŋ āĻ•āĻŋ āϏāĻ¤ā§āϝāĻŋāχ āĻŦāĻžā§œā§‡? āϝāĻĻāĻŋ āĻŦāĻžā§œā§‡, āϤāĻžāĻšāϞ⧇ āĻ•āϤāϟāĻž āĻŦāĻžā§œā§‡? āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āφāĻĒāύāĻžāϕ⧇ āĻāχ 'āĻ•āϤāϟāĻž'āϰ āĻāĻ•āϟāĻž āϏāĻ‚āĻ–ā§āϝāĻžāĻ—āϤ āĻĒāϰāĻŋāĻŽāĻžāĻĒ āĻĻ⧇āĻŦ⧇āĨ¤ B) āĻ­āĻŦāĻŋāĻˇā§āĻ¯ā§Ž āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāĻž (Making Predictions): āĻāĻ•āĻŦāĻžāϰ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āĻŦ⧁āĻā§‡ āϗ⧇āϞ⧇, āφāĻŽāϰāĻž āĻ­āĻŦāĻŋāĻˇā§āĻ¯ā§Ž āϏāĻŽā§āĻĒāĻ°ā§āϕ⧇ āĻ•āĻŋāϛ⧁ āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāϤ⧇ āĻĒāĻžāϰāĻŋāĨ¤ āϧāϰ⧁āύ, āφāĻĒāύāĻŋ āĻĻ⧇āĻ–āϞ⧇āύ āϝ⧇, āϤāĻžāĻĒāĻŽāĻžāĻ¤ā§āϰāĻž āĻŦāĻžā§œāϞ⧇ āφāχāϏāĻ•ā§āϰāĻŋāĻŽā§‡āϰ āĻŦāĻŋāĻ•ā§āϰāĻŋ āĻŦāĻžā§œā§‡āĨ¤ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āφāĻĒāύāĻžāϕ⧇ āĻāĻ•āϟāĻŋ āĻŽāĻĄā§‡āϞ āĻĻ⧇āĻŦ⧇, āϝāĻžāϰ āĻŽāĻžāĻ§ā§āϝāĻŽā§‡ āφāĻĒāύāĻŋ āĻšā§ŸāϤ⧋ āĻŦāϞāϤ⧇ āĻĒāĻžāϰāĻŦ⧇āύ, āφāĻ—āĻžāĻŽā§€ āϏāĻĒā§āϤāĻžāĻšā§‡ āϤāĻžāĻĒāĻŽāĻžāĻ¤ā§āϰāĻž āϝāĻĻāĻŋ āφāϰāĻ“ āĻŦāĻžā§œā§‡, āϤāĻžāĻšāϞ⧇ āφāχāϏāĻ•ā§āϰāĻŋāĻŽā§‡āϰ āĻŦāĻŋāĻ•ā§āϰāĻŋ āϕ⧇āĻŽāύ āĻšāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤ āĻāϟāĻŋ āĻ…āύ⧇āĻ•āϟāĻž āφāĻŦāĻšāĻžāĻ“ā§ŸāĻžāϰ āĻĒā§‚āĻ°ā§āĻŦāĻžāĻ­āĻžāϏ āĻĻ⧇āĻ“ā§ŸāĻžāϰ āĻŽāϤ⧋, āϝ⧇āĻ–āĻžāύ⧇ āφāĻŽāϰāĻž āĻ…āϤ⧀āϤ⧇āϰ āĻĄā§‡āϟāĻž āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰ⧇ āĻ­āĻŦāĻŋāĻˇā§āϝāϤ⧇āϰ āĻāĻ•āϟāĻž āϧāĻžāϰāĻŖāĻž āĻĒāĻžāχāĨ¤ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āϕ⧀āĻ­āĻžāĻŦ⧇ āĻ•āĻžāϜ āĻ•āϰ⧇? (How Does It Work?) āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻ•āĻžāϜ āĻ•āϰ⧇ āĻāĻ•āϟāĻž āϏāϰāϞāϰ⧇āĻ–āĻž āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰ⧇āĨ¤ āĻ­āĻžāĻŦ⧁āύ, āφāĻĒāύāĻžāϰ āĻ•āĻžāϛ⧇ āĻ•āĻŋāϛ⧁ āĻĄā§‡āϟāĻž āĻĒā§Ÿā§‡āĻ¨ā§āϟ āφāϛ⧇, āϝ⧇āĻŽāύ āĻ—ā§āϰāĻžāĻĢ āĻĒ⧇āĻĒāĻžāϰ⧇ āĻ›ā§œāĻžāύ⧋ āĻ•āĻŋāϛ⧁ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āĨ¤ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ⧇āϰ āĻ•āĻžāϜ āĻšāϞ⧋ āĻāχ āĻŦāĻŋāĻ¨ā§āĻĻ⧁āϗ⧁āϞ⧋āϰ āĻŽāĻžāĻāĻ–āĻžāύ āĻĻāĻŋā§Ÿā§‡ āĻāĻŽāύ āĻāĻ•āϟāĻž āϏāϰāϞāϰ⧇āĻ–āĻž āφāρāĻ•āĻž, āϝāĻž āϏāĻŦ āĻŦāĻŋāĻ¨ā§āĻĻ⧁ āĻĨ⧇āϕ⧇ 'āĻ—ā§œā§‡' āϏāĻŦāĻšā§‡ā§Ÿā§‡ āĻ•āĻŽ āĻĻā§‚āϰāĻ¤ā§āĻŦ⧇ āĻĨāĻžāϕ⧇āĨ¤ āĻāχ 'āϏāĻŦāĻšā§‡ā§Ÿā§‡ āĻ•āĻŽ āĻĻā§‚āϰāĻ¤ā§āĻŦ' āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāĻžāϰ āϜāĻ¨ā§āϝ āĻ•āĻŋāϛ⧁ āĻ—āĻžāĻŖāĻŋāϤāĻŋāĻ• āĻšāĻŋāϏāĻžāĻŦ-āύāĻŋāĻ•āĻžāĻļ āĻ•āϰāĻž āĻšā§Ÿ, āϝāĻžāϕ⧇ āφāĻŽāϰāĻž 'āĻāϰāϰ āĻŽāĻŋāύāĻŋāĻŽāĻžāχāĻœā§‡āĻļāύ' āĻŦāĻž 'āĻ…āĻŦāĻļāĻŋāĻˇā§āϟ āĻ•āĻŽāĻžāύ⧋' āĻŦāϞāĻŋāĨ¤ āĻ…āĻ°ā§āĻĨāĻžā§Ž, āĻĄā§‡āϟāĻž āĻĒā§Ÿā§‡āĻ¨ā§āϟāϗ⧁āϞ⧋ āĻĨ⧇āϕ⧇ āϰ⧇āĻ–āĻžāϰ āϝ⧇ āĻĻā§‚āϰāĻ¤ā§āĻŦ, āϏ⧇āχ āĻĻā§‚āϰāĻ¤ā§āĻŦāϗ⧁āϞ⧋āϕ⧇ āϝāϤāϟāĻž āϏāĻŽā§āĻ­āĻŦ āϛ⧋āϟ āĻ•āϰāĻž āĻšā§Ÿ, āϝāĻžāϤ⧇ āϰ⧇āĻ–āĻžāϟāĻŋ āĻĄā§‡āϟāĻžāϰ 'āĻĒā§āϰāĻŦāĻŖāϤāĻž' āĻŦāĻž 'āĻŸā§āϰ⧇āĻ¨ā§āĻĄ'āϕ⧇ āϏāĻŦāĻšā§‡ā§Ÿā§‡ āĻ­āĻžāϞ⧋āĻ­āĻžāĻŦ⧇ āĻĻ⧇āĻ–āĻžāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤ āĻāχ āϰ⧇āĻ–āĻžāϟāĻŋāχ āĻšāϞ⧋ āφāĻĒāύāĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āϞāĻžāχāύ, āϝāĻž āφāĻĒāύāĻžāϰ āĻĄā§‡āϟāĻžāϰ āĻ—āĻ˛ā§āĻĒāϟāĻž āĻŦāϞ⧇āĨ¤ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ⧇āϰ āĻĒā§āϰāĻ•āĻžāϰāϭ⧇āĻĻ (Types of Linear Regression) āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻŽā§‚āϞāϤ āĻĻ⧁āϟāĻŋ āĻĒā§āϰāϧāĻžāύ āϧāϰāύ⧇ āĻŦāĻŋāĻ­āĻ•ā§āϤ, āύāĻŋāĻ°ā§āĻ­āϰ āĻ•āϰ⧇ āφāĻĒāύāĻŋ āĻ•āϤāϗ⧁āϞ⧋ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāϛ⧇āύ āϤāĻžāϰ āωāĻĒāϰ: āϏāĻžāϧāĻžāϰāĻŖ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ (Simple Linear Regression): āĻāĻ–āĻžāύ⧇ āĻļ⧁āϧ⧁ āĻāĻ•āϟāĻŋ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• āĻāĻŦāĻ‚ āĻāĻ•āϟāĻŋ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• āĻĨāĻžāϕ⧇āĨ¤ āωāĻĻāĻžāĻšāϰāĻŖ: āĻāĻ•āϜāύ āĻ›āĻžāĻ¤ā§āϰ⧇āϰ āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿā§‡āϰ (āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ•) āϏāĻžāĻĨ⧇ āϤāĻžāϰ āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ⧇āϰ (āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ•) āϏāĻŽā§āĻĒāĻ°ā§āĻ•āĨ¤ āĻāĻ–āĻžāύ⧇ āφāĻĒāύāĻŋ āĻļ⧁āϧ⧁ āĻāĻ•āϟāĻŋ āĻ•āĻžāϰāĻŖ (āĻĒ⧜āĻžāĻļā§‹āύāĻžāϰ āϏāĻŽā§Ÿ) āĻĻāĻŋā§Ÿā§‡ āĻāĻ•āϟāĻŋ āĻĢāϞāĻžāĻĢāϞ (āĻĒāϰ⧀āĻ•ā§āώāĻžāϰ āύāĻŽā§āĻŦāϰ) āĻŦā§‹āĻāĻžāϰ āĻšā§‡āĻˇā§āϟāĻž āĻ•āϰāϛ⧇āύāĨ¤ āĻŽāĻžāĻ˛ā§āϟāĻŋāĻĒāϞ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ (Multiple Linear Regression): āĻāĻ–āĻžāύ⧇ āĻāĻ•āĻžāϧāĻŋāĻ• āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ• āĻāĻŦāĻ‚ āĻāĻ•āϟāĻŋ āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ• āĻĨāĻžāϕ⧇āĨ¤ āωāĻĻāĻžāĻšāϰāĻŖ: āĻāĻ•āϟāĻŋ āĻŦāĻžā§œāĻŋāϰ āĻĻāĻžāĻŽ (āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ•) āĻļ⧁āϧ⧁ āϤāĻžāϰ āφāĻ•āĻžāϰ⧇āϰ āωāĻĒāϰ āύāĻŋāĻ°ā§āĻ­āϰ āĻ•āϰ⧇ āύāĻž, āĻŦāϰāĻ‚ āĻāϞāĻžāĻ•āĻžāϰ āĻ…āĻŦāĻ¸ā§āĻĨāĻžāύ, āĻŦāĻžā§œāĻŋāϰ āĻŦ⧟āϏ, āϰ⧁āĻŽā§‡āϰ āϏāĻ‚āĻ–ā§āϝāĻž, āĻŦāĻžāĻĨāϰ⧁āĻŽā§‡āϰ āϏāĻ‚āĻ–ā§āϝāĻž – āĻāχ āϏāĻŦāĻ•āĻŋāϛ⧁āϰ āωāĻĒāϰ āύāĻŋāĻ°ā§āĻ­āϰ āĻ•āϰ⧇āĨ¤ āĻŽāĻžāĻ˛ā§āϟāĻŋāĻĒāϞ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻāχ āϏāĻŦ āĻ•āĻžāϰāĻŖ āĻāĻ•āϏāĻ™ā§āϗ⧇ āĻŦāĻŋāĻļā§āϞ⧇āώāĻŖ āĻ•āϰ⧇ āĻĻ⧇āĻ–āĻžā§Ÿ āϝ⧇, āϕ⧋āύ āĻ•āĻžāϰāĻŖāϟāĻŋ āĻŦāĻžā§œāĻŋāϰ āĻĻāĻžāĻŽā§‡āϰ āωāĻĒāϰ āĻ•āϤāϟāĻž āĻĒā§āϰāĻ­āĻžāĻŦ āĻĢ⧇āϞāϛ⧇āĨ¤ āĻāϟāĻŋ āĻ…āύ⧇āĻ•āϟāĻž āĻ…āύ⧇āĻ•āϗ⧁āϞ⧋ āĻ•āĻžāϰāĻŖ āĻāĻ•āϏāĻ™ā§āϗ⧇ āĻāĻ•āϟāĻŋ āĻĢāϞāĻžāĻĢāϞ⧇āϰ āωāĻĒāϰ āϕ⧀āĻ­āĻžāĻŦ⧇ āĻĒā§āϰāĻ­āĻžāĻŦ āĻĢ⧇āϞ⧇, āϤāĻž āĻĻ⧇āĻ–āĻžāϰ āĻŽāϤ⧋āĨ¤ āĻ•āĻŋāϛ⧁ āϜāϰ⧁āϰāĻŋ āĻ•āĻĨāĻž (Key Concepts): āĻ…āĻŦāĻļāĻŋāĻˇā§āϟ (Residuals): āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āϰ⧇āĻ–āĻžāϟāĻŋ āϏāĻŦ āĻĄā§‡āϟāĻž āĻĒā§Ÿā§‡āĻ¨ā§āĻŸā§‡āϰ āωāĻĒāϰ āĻĻāĻŋā§Ÿā§‡ āϝāĻžā§Ÿ āύāĻž, āĻ•āĻŋāϛ⧁ āĻĒā§Ÿā§‡āĻ¨ā§āϟ āϰ⧇āĻ–āĻžāϰ āωāĻĒāϰ⧇ āĻŦāĻž āύāĻŋāĻšā§‡ āĻĨāĻžāϕ⧇āĨ¤ āĻāχ āĻĄā§‡āϟāĻž āĻĒā§Ÿā§‡āĻ¨ā§āϟ āĻāĻŦāĻ‚ āϰ⧇āĻ–āĻžāϰ āĻŽāĻ§ā§āϝ⧇ āϝ⧇ āĻĻā§‚āϰāĻ¤ā§āĻŦ, āϏ⧇āϟāĻŋāχ āĻšāϞ⧋ āĻ…āĻŦāĻļāĻŋāĻˇā§āϟ āĻŦāĻž āĻāϰāϰ (error)āĨ¤ āĻāϟāĻŋ āĻĻ⧇āĻ–āĻžā§Ÿ, āφāĻŽāĻžāĻĻ⧇āϰ āĻŽāĻĄā§‡āϞ āĻ•āϤāϟāĻž āύāĻŋāϖ⧁āρāϤāĻ­āĻžāĻŦ⧇ āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāϤ⧇ āĻĒāĻžāϰāϛ⧇āĨ¤ āϝāϤ āĻ•āĻŽ āĻ…āĻŦāĻļāĻŋāĻˇā§āϟ, āĻŽāĻĄā§‡āϞ āϤāϤ āĻ­āĻžāϞ⧋āĨ¤ āϏāĻšāϏāĻŽā§āĻĒāĻ°ā§āĻ• (Correlation): āĻāϟāĻŋ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ⧇āϰ āϏāĻžāĻĨ⧇ āϜ⧜āĻŋāϤ āĻāĻ•āϟāĻŋ āϧāĻžāϰāĻŖāĻžāĨ¤ āϏāĻšāϏāĻŽā§āĻĒāĻ°ā§āĻ• (āϝ⧇āĻŽāύ āĻĒāĻŋāϝāĻŧāĻžāϰāϏāύ āϕ⧋āϰāĻŋāϞ⧇āĻļāύ āϕ⧋āĻāĻĢāĻŋāĻļāĻŋāϝāĻŧ⧇āĻ¨ā§āϟ) āĻĻ⧁āϟāĻŋ āϚāϞāϕ⧇āϰ āĻŽāĻ§ā§āϝ⧇ āϏāĻŽā§āĻĒāĻ°ā§āϕ⧇āϰ āĻļāĻ•ā§āϤāĻŋ āĻāĻŦāĻ‚ āĻĻāĻŋāĻ• (āχāϤāĻŋāĻŦāĻžāϚāĻ• āĻŦāĻž āύ⧇āϤāĻŋāĻŦāĻžāϚāĻ•) āĻĒāϰāĻŋāĻŽāĻžāĻĒ āĻ•āϰ⧇āĨ¤ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻāχ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϕ⧇ āĻāĻ•āϟāĻŋ āĻŽāĻĄā§‡āϞ⧇āϰ āĻŽāĻžāĻ§ā§āϝāĻŽā§‡ āĻŦā§āϝāĻžāĻ–ā§āϝāĻž āĻ•āϰ⧇āĨ¤ āϏāĻšāϏāĻŽā§āĻĒāĻ°ā§āĻ• āφāĻĒāύāĻžāϕ⧇ āĻŦāϞāĻŦ⧇ āϏāĻŽā§āĻĒāĻ°ā§āĻ• āφāϛ⧇ āĻ•āĻŋāύāĻž, āφāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āφāĻĒāύāĻžāϕ⧇ āĻŦāϞāĻŦ⧇ āϏ⧇āχ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āϕ⧇āĻŽāύ āĻāĻŦāĻ‚ āϕ⧀āĻ­āĻžāĻŦ⧇ āĻ•āĻžāϜ āĻ•āϰ⧇āĨ¤ āĻ…āύ⧁āĻŽāĻžāύ (Assumptions): āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻ•āĻŋāϛ⧁ āύāĻŋāĻ°ā§āĻĻāĻŋāĻˇā§āϟ āĻļāĻ°ā§āϤ⧇āϰ āωāĻĒāϰ āĻ­āĻŋāĻ¤ā§āϤāĻŋ āĻ•āϰ⧇ āĻ•āĻžāϜ āĻ•āϰ⧇āĨ¤ āϝ⧇āĻŽāύ, āϚāϞāĻ•āϗ⧁āϞ⧋āϰ āĻŽāĻ§ā§āϝ⧇ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āϝ⧇āύ āϏāĻ¤ā§āϝāĻŋāχ āϏāϰāϞāϰ⧈āĻ–āĻŋāĻ• āĻšā§Ÿ, āĻĄā§‡āϟāĻž āĻĒā§Ÿā§‡āĻ¨ā§āϟāϗ⧁āϞ⧋ āϝ⧇āύ āϖ⧁āĻŦ āĻŦ⧇āĻļāĻŋ āĻ›ā§œāĻžāύ⧋-āĻ›āĻŋāϟāĻžāύ⧋ āύāĻž āĻĨāĻžāϕ⧇ (āφāωāϟāϞāĻžā§ŸāĻžāϰ āύāĻž āĻĨāĻžāϕ⧇), āĻāĻŦāĻ‚ āĻāϰāϰāϗ⧁āϞ⧋ āϝ⧇āύ āĻāϞ⧋āĻŽā§‡āϞ⧋āĻ­āĻžāĻŦ⧇ āĻ›ā§œāĻžāύ⧋ āĻĨāĻžāϕ⧇āĨ¤ āĻāχ āĻļāĻ°ā§āϤāϗ⧁āϞ⧋ āĻĒā§‚āϰāĻŖ āĻšāϞ⧇ āĻŽāĻĄā§‡āϞ⧇āϰ āĻĢāϞāĻžāĻĢāϞ āφāϰāĻ“ āύāĻŋāĻ°ā§āĻ­āϰāϝ⧋āĻ—ā§āϝ āĻšā§ŸāĨ¤ āĻ•āĻ–āύ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻŦ⧇āύ, āĻ•āĻ–āύ āĻ•āϰāĻŦ⧇āύ āύāĻž? (When to Use, When Not to Use?) āĻ•āĻ–āύ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻŦ⧇āύ?: āϝāĻ–āύ āφāĻĒāύāĻŋ āĻĻ⧁āϟāĻŋ āĻŦāĻž āϤāĻžāϰ āĻŦ⧇āĻļāĻŋ āϚāϞāϕ⧇āϰ āĻŽāĻ§ā§āϝ⧇ āĻāĻ•āϟāĻŋ āϏāϰāϞāϰ⧈āĻ–āĻŋāĻ• āϏāĻŽā§āĻĒāĻ°ā§āĻ• āφāϛ⧇ āĻŦāϞ⧇ āĻŽāύ⧇ āĻ•āϰ⧇āύ āĻāĻŦāĻ‚ āϏ⧇āχ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻž āĻŦ⧁āĻāϤ⧇ āϚāĻžāύāĨ¤ āϝāĻ–āύ āφāĻĒāύāĻŋ āĻāĻ•āϟāĻŋ āϚāϞāϕ⧇āϰ āĻŽāĻžāύ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰ⧇ āĻ…āĻ¨ā§āϝ āĻāĻ•āϟāĻŋ āϚāϞāϕ⧇āϰ āĻŽāĻžāύ āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāϤ⧇ āϚāĻžāύāĨ¤ āϝāĻ–āύ āφāĻĒāύāĻŋ āϜāĻžāύāϤ⧇ āϚāĻžāύ, āϕ⧋āύ āĻ•āĻžāϰāĻŖāϗ⧁āϞ⧋ (āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ•) āĻāĻ•āϟāĻŋ āύāĻŋāĻ°ā§āĻĻāĻŋāĻˇā§āϟ āĻĢāϞāĻžāĻĢāϞ⧇āϰ (āύāĻŋāĻ°ā§āĻ­āϰāĻļā§€āϞ āϚāϞāĻ•) āωāĻĒāϰ āϏāĻŦāĻšā§‡ā§Ÿā§‡ āĻŦ⧇āĻļāĻŋ āĻĒā§āϰāĻ­āĻžāĻŦ āĻĢ⧇āϞāϛ⧇āĨ¤ āϝāĻ–āύ āφāĻĒāύāĻŋ āϕ⧋āύ⧋ āϧāĻžāϰāĻžāĻŦāĻžāĻšāĻŋāĻ• āĻĢāϞāĻžāĻĢāϞ (continuous outcome) āϝ⧇āĻŽāύ, āϤāĻžāĻĒāĻŽāĻžāĻ¤ā§āϰāĻž, āĻŦāĻŋāĻ•ā§āϰāĻŋ, āύāĻŽā§āĻŦāϰ āχāĻ¤ā§āϝāĻžāĻĻāĻŋ āĻ…āύ⧁āĻŽāĻžāύ āĻ•āϰāϤ⧇ āϚāĻžāύāĨ¤ āĻ•āĻ–āύ āĻ•āϰāĻŦ⧇āύ āύāĻž? āϝāĻĻāĻŋ āϚāϞāĻ•āϗ⧁āϞ⧋āϰ āĻŽāĻ§ā§āϝ⧇ āϕ⧋āύ⧋ āϏāϰāϞāϰ⧈āĻ–āĻŋāĻ• āϏāĻŽā§āĻĒāĻ°ā§āĻ• āύāĻž āĻĨāĻžāϕ⧇ (āϝ⧇āĻŽāύ, āϏāĻŽā§āĻĒāĻ°ā§āĻ•āϟāĻŋ āĻŦāĻ•ā§āϰāϰ⧇āĻ–āĻžāϰ āĻŽāϤ⧋ āĻŦāĻž āĻāϞ⧋āĻŽā§‡āϞ⧋)āĨ¤ āĻāĻ•ā§āώ⧇āĻ¤ā§āϰ⧇ āĻ…āĻ¨ā§āϝ āϧāϰāύ⧇āϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻŽāĻĄā§‡āϞ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāϤ⧇ āĻšāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤ āϝāĻĻāĻŋ āφāĻĒāύāĻžāϰ āĻĄā§‡āϟāĻžā§Ÿ āĻ…āύ⧇āĻ• āĻŦ⧇āĻļāĻŋ āĻ…āĻ¸ā§āĻŦāĻžāĻ­āĻžāĻŦāĻŋāĻ• āĻŦāĻž āϭ⧁āϞ āĻĄā§‡āϟāĻž (outliers) āĻĨāĻžāϕ⧇, āϝāĻž āϰ⧇āĻ–āĻžāϟāĻŋāϕ⧇ āϭ⧁āϞāĻ­āĻžāĻŦ⧇ āĻĒā§āϰāĻ­āĻžāĻŦāĻŋāϤ āĻ•āϰāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤ āĻāχ 'āφāωāϟāϞāĻžā§ŸāĻžāϰ'āϗ⧁āϞ⧋ āĻĢāϞāĻžāĻĢāϞāϕ⧇ āϭ⧁āϞ āĻĒāĻĨ⧇ āϚāĻžāϞāĻŋāϤ āĻ•āϰāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤ āϝāĻĻāĻŋ āφāĻĒāύāĻžāϰ āĻ¸ā§āĻŦāĻžāϧ⧀āύ āϚāϞāĻ•āϗ⧁āϞ⧋ āĻāϕ⧇ āĻ…āĻĒāϰ⧇āϰ āϏāĻžāĻĨ⧇ āϖ⧁āĻŦ āĻŦ⧇āĻļāĻŋ āϏāĻŽā§āĻĒāĻ°ā§āĻ•āĻŋāϤ āĻšā§Ÿ (multicollinearity), āϤāĻžāĻšāϞ⧇ āĻŽāĻžāĻ˛ā§āϟāĻŋāĻĒāϞ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻŦā§āϝāĻŦāĻšāĻžāϰ āĻ•āϰāĻž āĻ•āĻ āĻŋāύ āĻšāϤ⧇ āĻĒāĻžāϰ⧇āĨ¤ āĻāϟāĻŋ āĻ…āύ⧇āĻ•āϟāĻž āĻāĻŽāύ āϝ⧇, āĻĻ⧁āϟāĻŋ āĻ•āĻžāϰāĻŖ āĻāĻ•āχ āϰāĻ•āĻŽ āĻĒā§āϰāĻ­āĻžāĻŦ āĻĢ⧇āϞāϛ⧇, āϤāĻ–āύ āĻŦā§‹āĻāĻž āĻ•āĻ āĻŋāύ āĻšā§Ÿā§‡ āϝāĻžā§Ÿ āϕ⧋āύāϟāĻŋ āφāϏāϞ āĻĒā§āϰāĻ­āĻžāĻŦāĻ•āĨ¤ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āĻšāϞ⧋ āĻĄā§‡āϟāĻž āĻŦāĻŋāĻļā§āϞ⧇āώāϪ⧇āϰ āĻāĻ• āĻĻāĻžāϰ⧁āĻŖ āĻšāĻžāϤāĻŋ⧟āĻžāϰ, āϝāĻž āφāĻĒāύāĻžāϕ⧇ āĻĄā§‡āϟāĻžāϰ āϭ⧇āϤāϰ⧇āϰ āϞ⧁āĻ•āĻžāύ⧋ āĻ—āĻ˛ā§āĻĒāϗ⧁āϞ⧋ āϖ⧁āρāĻœā§‡ āĻŦ⧇āϰ āĻ•āϰāϤ⧇ āϏāĻžāĻšāĻžāĻ¯ā§āϝ āĻ•āϰāĻŦ⧇āĨ¤ āĻāϟāĻŋ āĻļ⧁āϧ⧁ āϏāĻ‚āĻ–ā§āϝāĻž āύ⧟, āĻŦāϰāĻ‚ āϏāĻ‚āĻ–ā§āϝāĻžāϰ āĻĒ⧇āĻ›āύ⧇āϰ āĻ•āĻžāϰāĻŖ āĻ“ āĻĒā§āϰāĻ­āĻžāĻŦāϕ⧇ āĻŦ⧁āĻāϤ⧇ āĻļ⧇āĻ–āĻžā§ŸāĨ¤ āφāĻļāĻž āĻ•āϰāĻŋ, āĻāχ āĻŦāĻŋāĻ¸ā§āϤāĻžāϰāĻŋāϤ āφāϞ⧋āϚāύāĻž āφāĻĒāύāĻžāϰ āϞāĻŋāύāĻŋ⧟āĻžāϰ āϰāĻŋāĻ—ā§āϰ⧇āĻļāύ āϏāĻŽā§āĻĒāĻ°ā§āϕ⧇ āϧāĻžāϰāĻŖāĻž āφāϰāĻ“ āĻĒāϰāĻŋāĻˇā§āĻ•āĻžāϰ āĻ•āϰ⧇āϛ⧇āĨ¤ āφāĻĒāύāĻžāϰ āϝāĻĻāĻŋ āφāϰāĻ“ āĻ•āĻŋāϛ⧁ āϜāĻžāύāĻžāϰ āĻĨāĻžāϕ⧇, āϤāĻžāĻšāϞ⧇ āφāĻŽāĻžāϕ⧇ āϜāĻžāύāĻžāϤ⧇ āĻĒāĻžāϰ⧇āύ! Md. Rony Masud BBA, MBA (DU), MS (Japan)
    0 Comments 0 Shares 273 Views
  • Japan has developed robotic bees to help with crop pollination, addressing the global decline in bee populations. These tiny flying bots, equipped with cameras, sensors, and soft horsehair coated in a sticky gel, mimic the natural pollination process of real bees. Guided by AI, they can identify flowers, collect pollen, and transfer it efficiently between plants.

    The robotic bees are being tested in greenhouses and open fields, ensuring crops like fruits and vegetables receive proper pollination even when natural bee numbers are low. Their lightweight design allows them to hover and navigate complex floral patterns without damaging delicate plants.

    This innovation could safeguard global food production, especially in regions facing severe pollinator shortages. By blending robotics with nature’s design, Japan is offering a futuristic yet practical solution to one of agriculture’s biggest challenges.

    #AgriTech #BeeBots #FutureFarming
    Japan has developed robotic bees to help with crop pollination, addressing the global decline in bee populations. These tiny flying bots, equipped with cameras, sensors, and soft horsehair coated in a sticky gel, mimic the natural pollination process of real bees. Guided by AI, they can identify flowers, collect pollen, and transfer it efficiently between plants. The robotic bees are being tested in greenhouses and open fields, ensuring crops like fruits and vegetables receive proper pollination even when natural bee numbers are low. Their lightweight design allows them to hover and navigate complex floral patterns without damaging delicate plants. This innovation could safeguard global food production, especially in regions facing severe pollinator shortages. By blending robotics with nature’s design, Japan is offering a futuristic yet practical solution to one of agriculture’s biggest challenges. #AgriTech #BeeBots #FutureFarming
    0 Comments 0 Shares 319 Views
  • A quake so powerful, it shook the entire Pacific.

    It all began on July 30, at ~11:24 a.m. PETT (23:24 UTC Jul 29) when a powerful 8.8 magnitude earthquake struck off Russia’s Kamchatka Peninsula, unleashing tsunami waves that raced across the Pacific at jet-like speeds. From Japan to Hawaii, Chile to California, coastlines went on high alert.

    The quake originated about 118 kilometers southeast of Petropavlovsk-Kamchatsky, at a depth of approximately 19 kilometers. It was initially reported as magnitude 8.0 but later upgraded to 8.8—placing it among the six strongest earthquakes ever recorded.

    This wasn’t just a regional event. It set off a tsunami that raced across the Pacific Ocean, prompting tsunami warnings for over 40 countries across four continents. That level of global alert hasn't been seen since the 2004 Indian Ocean tsunami—but even then, the warnings weren’t as Pacific-wide.

    This quake occurred in the Kuril-Kamchatka Trench, where the Pacific Plate dives beneath the Okhotsk Plate. It’s part of the Pacific Ring of Fire, Earth’s most seismically active zone. Because the earthquake was shallow and along a subduction zone, it violently displaced the seafloor—pushing a massive wall of water outward in all directions.

    This was the first time in decades that tsunami alerts were issued across Asia, Oceania, North America, and South America simultaneously. In total, over 100 million people were placed under some form of tsunami advisory or warning.

    The earthquake triggered dozens of aftershocks, including one measuring 6.9, further heightening concerns of secondary quakes or tsunamis. Fortunately, due to improved global early warning systems developed after previous disasters, mass casualties were largely avoided.
    🌍 A quake so powerful, it shook the entire Pacific. It all began on July 30, at ~11:24 a.m. PETT (23:24 UTC Jul 29) when a powerful 8.8 magnitude earthquake struck off Russia’s Kamchatka Peninsula, unleashing tsunami waves that raced across the Pacific at jet-like speeds. From Japan to Hawaii, Chile to California, coastlines went on high alert. The quake originated about 118 kilometers southeast of Petropavlovsk-Kamchatsky, at a depth of approximately 19 kilometers. It was initially reported as magnitude 8.0 but later upgraded to 8.8—placing it among the six strongest earthquakes ever recorded. This wasn’t just a regional event. It set off a tsunami that raced across the Pacific Ocean, prompting tsunami warnings for over 40 countries across four continents. That level of global alert hasn't been seen since the 2004 Indian Ocean tsunami—but even then, the warnings weren’t as Pacific-wide. This quake occurred in the Kuril-Kamchatka Trench, where the Pacific Plate dives beneath the Okhotsk Plate. It’s part of the Pacific Ring of Fire, Earth’s most seismically active zone. Because the earthquake was shallow and along a subduction zone, it violently displaced the seafloor—pushing a massive wall of water outward in all directions. This was the first time in decades that tsunami alerts were issued across Asia, Oceania, North America, and South America simultaneously. In total, over 100 million people were placed under some form of tsunami advisory or warning. The earthquake triggered dozens of aftershocks, including one measuring 6.9, further heightening concerns of secondary quakes or tsunamis. Fortunately, due to improved global early warning systems developed after previous disasters, mass casualties were largely avoided.
    0 Comments 0 Shares 200 Views
More Results
BlackBird Ai
https://bbai.shop