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5- Error Functions | Machine Learning Course
- 1. Hassan Badawy Ai Simplification Series 5- Errors Functions
- 2. Hassan Badawy Y X 100 200 300 400 500 k 50 100 50 150 200 50 300 250 𝑚2 100 150 200 150 250 200 Solution Model2 Linear Regression Area Price (k) 100 200 150 400 200 450 250 550 300 450 x y ො𝑦 ො𝑦 e2 e1 e3 e4 e5 𝐞 = ෝ𝒚 - y 𝑒1+𝑒2+𝑒3+𝑒4+𝑒5 5 y = m x + b y = w0 + w1 x ---> (1) Error Parametric solution ො𝑦 y
- 3. Hassan Badawy Linear RegressionSolution Model2 Error Functions Standard Error 𝒆𝒊 = ො𝑦𝒊 − 𝒚𝒊 𝐸 = 𝑒1 + 𝑒2 + 𝑒3 𝑬 = σ𝒊 𝒆𝒊 = σ𝒊=𝟏 𝒏 (ො𝑦𝒊 − 𝒚𝒊) Y 300 𝑚2 250 X 100 200 300 400 500 k 50 100 150 200 +50 -100 +75 𝐸 = +50 − 100 + 75 = 25
- 4. Hassan Badawy Linear RegressionSolution Model2 Error Functions Mean Absolut Error MAE MA𝐸 = 𝑒1 + 𝑒2 + 𝑒3 3 𝑴𝑨𝑬 = 𝟏 𝒏 σ𝒊=𝟏 𝒏 𝒆𝒊 = 𝟏 𝒏 σ𝒊=𝟏 𝒏 ෝ𝒚 − 𝒚 MA𝐸 = +50 + −100 + +75 3 MA𝐸 = 50+100+75 3 = 75 Y 300 𝑚2 250 X 100 200 300 400 500 k 50 100 150 200 +50 -100 +75
- 5. Hassan Badawy 𝑀𝑆𝐸 = (𝑒1)2+(𝑒2)2+(𝑒3)2 3 𝑴𝑺𝑬 = 𝟏 𝟐𝒏 σ𝒊=𝟏 𝒏 𝒆𝒊 𝟐 = 𝟏 𝒏 σ𝒊=𝟏 𝒏 (ො𝑦𝒊 − 𝒚𝒊) 𝟐 Linear RegressionSolution Model2 Error Functions Mean Square Error MSE Y 300 𝑚2 250 X 100 200 300 400 500 k 50 100 150 200 +50 -100 +75 𝑀𝑆𝐸 = (+50)2+(−100)2+(+75)2 3 𝑀𝑆𝐸 = 2500+10000+5625 3 = 6041.67 W𝑀𝑆𝐸 = 𝑀𝑆𝐸 𝑤 = 𝑀𝑆𝐸 2 = 320.83
- 6. Hassan Badawy Linear RegressionSolution Model2 Error Functions Root Mean Square Error RMSE 𝑅𝑀𝑆𝐸 = (𝑒1)2+(𝑒2)2+(𝑒3)2 3 R𝑴𝑺𝑬 = 𝟏 𝒏 σ𝒊=𝟏 𝒏 𝒆𝒊 𝟐 = 𝟏 𝒏 σ𝒊=𝟏 𝒏 (ො𝑦𝒊 − 𝒚𝒊) 𝟐 Y 300 𝑚2 250 X 100 200 300 400 500 k 50 100 150 200 +50 -100 +75 𝑅𝑀𝑆𝐸 = 𝑀𝑆𝐸 = 6041.67 = 77.73
- 7. Hassan Badawy SE MAE MSE WMSE RMSE 25 75 6041 3020 78 𝒊 𝒆𝒊 𝟏 𝒏 𝒊=𝟏 𝒏 𝒆𝒊 𝟏 𝟐𝒏 𝒊=𝟏 𝒏 𝒆𝒊 𝟐 𝟏 𝒏 𝒊=𝟏 𝒏 𝒆𝒊 𝟐 𝟏 𝒏 𝒊=𝟏 𝒏 𝒆𝒊 𝟐 Linear RegressionSolution Model2 Error Functions