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Post #835
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𝗣-𝗩𝗮𝗹𝘂𝗲𝘀 𝗳𝗼𝗿 𝗥𝗲𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻 𝗠𝗼𝗱𝗲𝗹 𝗘𝘅𝗽𝗹𝗮𝗶𝗻𝗲𝗱
𝗪𝗵𝗲𝗻 𝗯𝘂𝗶𝗹𝗱𝗶𝗻𝗴 𝗮 𝗿𝗲𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻 𝗺𝗼𝗱𝗲𝗹, 𝗻𝗼𝘁 𝗲𝘃𝗲𝗿𝘆 𝘃𝗮𝗿𝗶𝗮𝗯𝗹𝗲 𝗶𝘀 𝗰𝗿𝗲𝗮𝘁𝗲𝗱 𝗲𝗾𝘂𝗮𝗹.
Some variables will genuinely impact your predictions, while others are just background noise.
𝗧𝗵𝗲 𝗽-𝘃𝗮𝗹𝘂𝗲 𝗵𝗲𝗹𝗽𝘀 𝘆𝗼𝘂 𝗳𝗶𝗴𝘂𝗿𝗲 𝗼𝘂𝘁 𝘄𝗵𝗶𝗰𝗵 𝗶𝘀 𝘄𝗵𝗶𝗰𝗵.
𝗪𝗵𝗮𝘁 𝗲𝘅𝗮𝗰𝘁𝗹𝘆 𝗶𝘀 𝗮 𝗣-𝗩𝗮𝗹𝘂𝗲?
𝗔 𝗽-𝘃𝗮𝗹𝘂𝗲 𝗮𝗻𝘀𝘄𝗲𝗿𝘀 𝗼𝗻𝗲 𝗾𝘂𝗲𝘀𝘁𝗶𝗼𝗻:
➔ If this variable had no real effect, what’s the probability that we’d still observe results this extreme just by chance?
• 𝗟𝗼𝘄 𝗣-𝗩𝗮𝗹𝘂𝗲 (𝘂𝘀𝘂𝗮𝗹𝗹𝘆 < 0.05): Strong evidence that the variable is important.
• 𝗛𝗶𝗴𝗵 𝗣-𝗩𝗮𝗹𝘂𝗲 (> 0.05): The variable’s relationship with the output could easily be random.
𝗛𝗼𝘄 𝗣-𝗩𝗮𝗹𝘂𝗲𝘀 𝗚𝘂𝗶𝗱𝗲 𝗬𝗼𝘂𝗿 𝗥𝗲𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻 𝗠𝗼𝗱𝗲𝗹
𝗜𝗺𝗮𝗴𝗶𝗻𝗲 𝘆𝗼𝘂’𝗿𝗲 𝗮 𝘀𝗰𝘂𝗹𝗽𝘁𝗼𝗿.
You start with a messy block of stone (all your features).
P-values are your chisel.
𝗥𝗲𝗺𝗼𝘃𝗲 the features with high p-values (not useful).
𝗞𝗲𝗲𝗽 the features with low p-values (important).
This results in a leaner, smarter model that doesn’t just memorize noise but learns real patterns.
𝗪𝗵𝘆 𝗣-𝗩𝗮𝗹𝘂𝗲𝘀 𝗠𝗮𝘁𝘁𝗲𝗿
𝗪𝗶𝘁𝗵𝗼𝘂𝘁 𝗽-𝘃𝗮𝗹𝘂𝗲𝘀, 𝗺𝗼𝗱𝗲𝗹 𝗯𝘂𝗶𝗹𝗱𝗶𝗻𝗴 𝗯𝗲𝗰𝗼𝗺𝗲𝘀 𝗴𝘂𝗲𝘀𝘀𝘄𝗼𝗿𝗸.
✅ 𝗟𝗼𝘄 𝗣-𝗩𝗮𝗹𝘂𝗲 ➔ Likely genuine effect.
❌ 𝗛𝗶𝗴𝗵 𝗣-𝗩𝗮𝗹𝘂𝗲 ➔ Likely coincidence.
𝗜𝗳 𝘆𝗼𝘂 𝗶𝗴𝗻𝗼𝗿𝗲 𝗶𝘁, 𝘆𝗼𝘂 𝗿𝗶𝘀𝗸:
• Overfitting your model with junk features
• Lowering your model’s accuracy and interpretability
• Making wrong business decisions based on faulty insights
𝗧𝗵𝗲 𝟬.𝟬𝟱 𝗧𝗵𝗿𝗲𝘀𝗵𝗼𝗹𝗱: 𝗡𝗼𝘁 𝗔 𝗠𝗮𝗴𝗶𝗰 𝗡𝘂𝗺𝗯𝗲𝗿
You’ll often hear: If p < 0.05, it’s significant!
𝗕𝘂𝘁 𝗯𝗲 𝗰𝗮𝗿𝗲𝗳𝘂𝗹.
This threshold is not universal.
• In critical fields (like medicine), you might need a much lower p-value (e.g., 0.01).
• In exploratory analysis, you might tolerate higher p-values.
Context always matters.
𝗥𝗲𝗮𝗹-𝗪𝗼𝗿𝗹𝗱 𝗔𝗱𝘃𝗶𝗰𝗲
When evaluating your regression model:
➔ 𝗗𝗼𝗻’𝘁 𝗷𝘂𝘀𝘁 𝗹𝗼𝗼𝗸 𝗮𝘁 𝗽-𝘃𝗮𝗹𝘂𝗲𝘀 𝗮𝗹𝗼𝗻𝗲.
𝗖𝗼𝗻𝘀𝗶𝗱𝗲𝗿:
• The feature’s practical importance (not just statistical)
• Multicollinearity (highly correlated variables can distort p-values)
• Overall model fit (R², Adjusted R²)
𝗜𝗻 𝗦𝗵𝗼𝗿𝘁:
𝗟𝗼𝘄 𝗣-𝗩𝗮𝗹𝘂𝗲 = 𝗧𝗵𝗲 𝗳𝗲𝗮𝘁𝘂𝗿𝗲 𝗺𝗮𝘁𝘁𝗲𝗿𝘀.
𝗛𝗶𝗴𝗵 𝗣-𝗩𝗮𝗹𝘂𝗲 = 𝗜𝘁’𝘀 𝗽𝗿𝗼𝗯𝗮𝗯𝗹𝘆 𝗷𝘂𝘀𝘁 𝗻𝗼𝗶𝘀𝗲.
𝗪𝗵𝗲𝗻 𝗯𝘂𝗶𝗹𝗱𝗶𝗻𝗴 𝗮 𝗿𝗲𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻 𝗺𝗼𝗱𝗲𝗹, 𝗻𝗼𝘁 𝗲𝘃𝗲𝗿𝘆 𝘃𝗮𝗿𝗶𝗮𝗯𝗹𝗲 𝗶𝘀 𝗰𝗿𝗲𝗮𝘁𝗲𝗱 𝗲𝗾𝘂𝗮𝗹.
Some variables will genuinely impact your predictions, while others are just background noise.
𝗧𝗵𝗲 𝗽-𝘃𝗮𝗹𝘂𝗲 𝗵𝗲𝗹𝗽𝘀 𝘆𝗼𝘂 𝗳𝗶𝗴𝘂𝗿𝗲 𝗼𝘂𝘁 𝘄𝗵𝗶𝗰𝗵 𝗶𝘀 𝘄𝗵𝗶𝗰𝗵.
𝗪𝗵𝗮𝘁 𝗲𝘅𝗮𝗰𝘁𝗹𝘆 𝗶𝘀 𝗮 𝗣-𝗩𝗮𝗹𝘂𝗲?
𝗔 𝗽-𝘃𝗮𝗹𝘂𝗲 𝗮𝗻𝘀𝘄𝗲𝗿𝘀 𝗼𝗻𝗲 𝗾𝘂𝗲𝘀𝘁𝗶𝗼𝗻:
➔ If this variable had no real effect, what’s the probability that we’d still observe results this extreme just by chance?
• 𝗟𝗼𝘄 𝗣-𝗩𝗮𝗹𝘂𝗲 (𝘂𝘀𝘂𝗮𝗹𝗹𝘆 < 0.05): Strong evidence that the variable is important.
• 𝗛𝗶𝗴𝗵 𝗣-𝗩𝗮𝗹𝘂𝗲 (> 0.05): The variable’s relationship with the output could easily be random.
𝗛𝗼𝘄 𝗣-𝗩𝗮𝗹𝘂𝗲𝘀 𝗚𝘂𝗶𝗱𝗲 𝗬𝗼𝘂𝗿 𝗥𝗲𝗴𝗿𝗲𝘀𝘀𝗶𝗼𝗻 𝗠𝗼𝗱𝗲𝗹
𝗜𝗺𝗮𝗴𝗶𝗻𝗲 𝘆𝗼𝘂’𝗿𝗲 𝗮 𝘀𝗰𝘂𝗹𝗽𝘁𝗼𝗿.
You start with a messy block of stone (all your features).
P-values are your chisel.
𝗥𝗲𝗺𝗼𝘃𝗲 the features with high p-values (not useful).
𝗞𝗲𝗲𝗽 the features with low p-values (important).
This results in a leaner, smarter model that doesn’t just memorize noise but learns real patterns.
𝗪𝗵𝘆 𝗣-𝗩𝗮𝗹𝘂𝗲𝘀 𝗠𝗮𝘁𝘁𝗲𝗿
𝗪𝗶𝘁𝗵𝗼𝘂𝘁 𝗽-𝘃𝗮𝗹𝘂𝗲𝘀, 𝗺𝗼𝗱𝗲𝗹 𝗯𝘂𝗶𝗹𝗱𝗶𝗻𝗴 𝗯𝗲𝗰𝗼𝗺𝗲𝘀 𝗴𝘂𝗲𝘀𝘀𝘄𝗼𝗿𝗸.
✅ 𝗟𝗼𝘄 𝗣-𝗩𝗮𝗹𝘂𝗲 ➔ Likely genuine effect.
❌ 𝗛𝗶𝗴𝗵 𝗣-𝗩𝗮𝗹𝘂𝗲 ➔ Likely coincidence.
𝗜𝗳 𝘆𝗼𝘂 𝗶𝗴𝗻𝗼𝗿𝗲 𝗶𝘁, 𝘆𝗼𝘂 𝗿𝗶𝘀𝗸:
• Overfitting your model with junk features
• Lowering your model’s accuracy and interpretability
• Making wrong business decisions based on faulty insights
𝗧𝗵𝗲 𝟬.𝟬𝟱 𝗧𝗵𝗿𝗲𝘀𝗵𝗼𝗹𝗱: 𝗡𝗼𝘁 𝗔 𝗠𝗮𝗴𝗶𝗰 𝗡𝘂𝗺𝗯𝗲𝗿
You’ll often hear: If p < 0.05, it’s significant!
𝗕𝘂𝘁 𝗯𝗲 𝗰𝗮𝗿𝗲𝗳𝘂𝗹.
This threshold is not universal.
• In critical fields (like medicine), you might need a much lower p-value (e.g., 0.01).
• In exploratory analysis, you might tolerate higher p-values.
Context always matters.
𝗥𝗲𝗮𝗹-𝗪𝗼𝗿𝗹𝗱 𝗔𝗱𝘃𝗶𝗰𝗲
When evaluating your regression model:
➔ 𝗗𝗼𝗻’𝘁 𝗷𝘂𝘀𝘁 𝗹𝗼𝗼𝗸 𝗮𝘁 𝗽-𝘃𝗮𝗹𝘂𝗲𝘀 𝗮𝗹𝗼𝗻𝗲.
𝗖𝗼𝗻𝘀𝗶𝗱𝗲𝗿:
• The feature’s practical importance (not just statistical)
• Multicollinearity (highly correlated variables can distort p-values)
• Overall model fit (R², Adjusted R²)
𝗜𝗻 𝗦𝗵𝗼𝗿𝘁:
𝗟𝗼𝘄 𝗣-𝗩𝗮𝗹𝘂𝗲 = 𝗧𝗵𝗲 𝗳𝗲𝗮𝘁𝘂𝗿𝗲 𝗺𝗮𝘁𝘁𝗲𝗿𝘀.
𝗛𝗶𝗴𝗵 𝗣-𝗩𝗮𝗹𝘂𝗲 = 𝗜𝘁’𝘀 𝗽𝗿𝗼𝗯𝗮𝗯𝗹𝘆 𝗷𝘂𝘀𝘁 𝗻𝗼𝗶𝘀𝗲.
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