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Regression intuition

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Rahul Tiwari
Rahul Tiwari

Regression is one of the technique comes under supervised learning. Regression will be used to predict the continuous variable like Salary, House Price etc. In this slide we will discuss about the intuition of Linear Regression and Assumptions of linear regression.

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Introductionto Regression Copyright © Cognitior www.cognitior.com
Copyright © Cognitior www.cognitior.com Regression–AnIntuition Experience Salary 𝑦 = 𝛽0 + 𝛽1 𝑋1 + 𝜀 Difference
Copyright © Cognitior www.cognitior.com Regression–AnIntuition Experience Salary 𝑦 𝑦 Experience Salary
Copyright © Cognitior www.cognitior.com Regression–AnIntuition 𝑬𝒙𝒑𝒆𝒓𝒊𝒆𝒏𝒄𝒆 2 3 4 𝑺𝒂𝒍𝒂𝒓𝒚 (𝒚) 10000 13000 14500 𝑨𝒗𝒈 𝑺𝒂𝒍𝒂𝒓𝒚 12500 12500 12500 𝑺 − 𝑺𝑨𝒗𝒈 -2500 500 2000 (𝑺 − 𝑺𝑨𝒗𝒈) 𝟐 SST – Sum Squared Total 6250000 250000 4000000 𝒚 = 𝟐𝟐𝟓𝟎 ∗ 𝑬𝒙𝒑𝒆𝒓𝒊𝒆𝒏𝒄𝒆 + 𝟓𝟕𝟓𝟎 10250 12500 14750 𝒚 − 𝒚 -250 500 250 (𝒚 − 𝒚) 𝟐 SSE - Sum Squared errors 62500 250000 62500 𝑅2 = 1 − 𝑆𝑆𝐸 𝑆𝑆𝑇 1,05,00,000 3,75,000 𝑅2 = 1 − 375000 10500000 = 96.42
Copyright © Cognitior www.cognitior.com Assumptions–Linear Experience Salary Experience Salary
Copyright © Cognitior www.cognitior.com Assumptions–NoHeteroscedasticity Experience Salary Experience Salary
Copyright © Cognitior www.cognitior.com NoHeteroscedasticity-Solution • Remove the outliers • Transform the data • Square root transformation • Cube root transformation • Log transformation
Copyright © Cognitior www.cognitior.com Assumptions–NoAutocorrelation Experience Salary Experience Salary
Copyright © Cognitior www.cognitior.com Assumptions–NoMulticollinearity Age Salary Experience Salary Experience Age
Copyright © Cognitior www.cognitior.com NoMulticollinearity-Solution • Remove one of the correlated variable • Variance inflation factor • Any variable with VIF more than 5
ThankYou!!! AnyQuestions? support@cognitior.com Copyright © Cognitior www.cognitior.com

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Regression intuition

  • 2. Copyright © Cognitior www.cognitior.com Regression–AnIntuition Experience Salary 𝑦 = 𝛽0 + 𝛽1 𝑋1 + 𝜀 Difference
  • 3. Copyright © Cognitior www.cognitior.com Regression–AnIntuition Experience Salary 𝑦 𝑦 Experience Salary
  • 4. Copyright © Cognitior www.cognitior.com Regression–AnIntuition 𝑬𝒙𝒑𝒆𝒓𝒊𝒆𝒏𝒄𝒆 2 3 4 𝑺𝒂𝒍𝒂𝒓𝒚 (𝒚) 10000 13000 14500 𝑨𝒗𝒈 𝑺𝒂𝒍𝒂𝒓𝒚 12500 12500 12500 𝑺 − 𝑺𝑨𝒗𝒈 -2500 500 2000 (𝑺 − 𝑺𝑨𝒗𝒈) 𝟐 SST – Sum Squared Total 6250000 250000 4000000 𝒚 = 𝟐𝟐𝟓𝟎 ∗ 𝑬𝒙𝒑𝒆𝒓𝒊𝒆𝒏𝒄𝒆 + 𝟓𝟕𝟓𝟎 10250 12500 14750 𝒚 − 𝒚 -250 500 250 (𝒚 − 𝒚) 𝟐 SSE - Sum Squared errors 62500 250000 62500 𝑅2 = 1 − 𝑆𝑆𝐸 𝑆𝑆𝑇 1,05,00,000 3,75,000 𝑅2 = 1 − 375000 10500000 = 96.42
  • 5. Copyright © Cognitior www.cognitior.com Assumptions–Linear Experience Salary Experience Salary
  • 6. Copyright © Cognitior www.cognitior.com Assumptions–NoHeteroscedasticity Experience Salary Experience Salary
  • 7. Copyright © Cognitior www.cognitior.com NoHeteroscedasticity-Solution • Remove the outliers • Transform the data • Square root transformation • Cube root transformation • Log transformation
  • 8. Copyright © Cognitior www.cognitior.com Assumptions–NoAutocorrelation Experience Salary Experience Salary
  • 9. Copyright © Cognitior www.cognitior.com Assumptions–NoMulticollinearity Age Salary Experience Salary Experience Age
  • 10. Copyright © Cognitior www.cognitior.com NoMulticollinearity-Solution • Remove one of the correlated variable • Variance inflation factor • Any variable with VIF more than 5