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Aravali College of Engineering and Management, Faridabad

Session on regression in machine learning

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Aravali College of Engineering and Management, Faridabad

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  1. Program Name : B.Tech CSESemester : 5thCourse Name: Machine LearningCourse Code:PEC-CS-D-501 (I)Facilitator Name: Aastha

  2. Introduction to RegressionAnalysis • Regression analysis is used to: • Predict the value of a dependent variable based on the value of at least one independentvariable • Explain the impact of changes in an independent variable on the dependentvariable • Dependentvariable: the variable we wish to predict orexplain • Independentvariable: the variable used toexplain • the dependentvariable

  3. Simple LinearRegression Model • Only one independent variable,X • Relationshipbetween X and Y is described by a linearfunction • Changesin Y are assumed to be caused bychangesin X

  4. Types ofRelationships Linearrelationships Curvilinearrelationships Y Y X X Y Y X X

  5. Types ofRelationships (continued) Strongrelationships Weakrelationships Y Y X X Y Y X X

  6. Types ofRelationships (continued) Norelationship Y X Y X

  7. Simple LinearRegression Model Random Error term Population Slope Coefficient Population Y intercept Independent Variable Dependent Variable Yi β0 β1Xi Linearcomponent • εi • RandomError component

  8. Simple LinearRegression Model (continued) Yi β0 β1Xi εi Y ObservedValue of Y forXi εi Slope =β1 PredictedValue RandomError of Y forXi for this Xvalue i Intercept =β0 X Xi

  9. Simple Linear Regression Equation (PredictionLine) The simple linear regression equation provides an estimate of the population regressionline Estimated (orpredicted) Y valuefor observationi Estimate of theregression Estimate of the regressionslope intercept Value of Xfor observationi Yˆi b0 b1Xi The individual randomerrorterms ei have a mean ofzero

  10. Sample Data for House Price Model

  11. Regression UsingExcel • Tools / Data Analysis / Regression

  12. Assumptions ofRegression • Use the acronymLINE: • Linearity • The underlying relationship between X and Y islinear • Independence ofErrors • Error values are statisticallyindependent • Normality ofError • Error values (ε) are normally distributed for any given value of X • Equal Variance(Homoscedasticity) • The probability distribution of the errors has constantvariance Department of Statistics, ITSSurabaya

  13. Pitfalls of RegressionAnalysis • Lacking an awareness of the assumptions underlying least-squaresregression • Not knowing how to evaluate theassumptions • Not knowing the alternatives to least-squares regression if a particular assumption isviolated • Using a regression model without knowledge of the subject matter • Extrapolating outside the relevantrange Department of Statistics, ITSSurabaya

  14. Aravali College of Engineering And Management Jasana, Tigoan Road, Neharpar, Faridabad, Delhi NCR Toll Free Number : 91- 8527538785 Website : www.acem.edu.in

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