Regression analysis
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This document discusses regression analysis techniques. It defines regression as the tendency for estimated values to be close to actual values. Regression analysis investigates the relationship between variables, with the independent variable influencing the dependent variable. There are three main types of regression: linear regression which uses a linear equation to model the relationship between one independent and one dependent variable; logistic regression which predicts the probability of a binary outcome using multiple independent variables; and nonlinear regression which models any non-linear relationship between variables. The document provides examples of using linear and logistic regression and discusses their key assumptions and calculations.
Regression analysis
- 2. QUICK LOOK Price (in Rs) Product Sales 20 250 23 230 25 220 27 190 30 150 32 140
- 3. REGRESSION The property of the tendency of the actual value to lie close to the estimated value.
- 4. REGRESSION ANALYSIS It is a predictive modeling technique which investigates & estimates the relationship between the variables. In the Regression Analysis, The independent variable is known also as Regressor/Predictor/Explanatory variable. The dependent variable is known also as Regressed/Predicted/Explained variable
- 5. WHY WE USE REGRESSION ANALYSIS? The main theme is to estimate the relationship between two or more variables. The benefits of using regression analysis: It indicates the Significant Relationships between dependent and independent variable. It indicates the Strength of Impact of multiple independent variables on a dependent variable.
- 6. HOW MANY TYPES OF REGRESSION TECHNIQUES DO WE HAVE ?
- 7. HOW MANY TYPES OF REGRESSION TECHNIQUES DO WE HAVE ? There are various types of techniques for prediction but these techniques are classified into three categories: Number of Independent Variable Shape of the Regression Line Type of Dependent Variable REGRESSION
- 8. LINEAR REGRESSION The simplest mathematical relationship between two variables such as one being independent and other dependent The least square linear regression is a method for predicting the value of a dependent variable Y, based on the value of an independent variable X using the linear equation.
- 9. LINEAR EQUATION The Linear equation of two variables: y = a x + b Where, y – dependent variable x – independent variable a – slope of the line b – intercept (y-intercept)
- 10. SCATTER DIAGRAM
- 11. CALCULATION The regression equation obtained with the assumption that x –independent variable & y-dependent variable, then regression equation given by: Where, byx – regression co-efficient
- 12. EXAMPLE ? Reference to Excel Spreadsheet
- 14. LOGISTIC REGRESSION It is a regression method used to find the probability of an event which is a binary outcome. In other words, It is a regression analysis to conduct when the dependent variable is dichotomous(binary).
- 15. EXAMPLE How does the probability of placement (Selected / Not-selected) change for every additional percentage score in examination? Do change in body fat intake & age have an influence on the probability of having a heart attack (Yes / No)?
- 16. MAJOR ASSUMPTIONS & UNDERSTANDINGS The dependent variable should be dichotomous in nature (Ex: Pass/Fail, Present/Absent) There should be no high correlations (multi- colinearity) among the predictors(independent variables). It requires large sample size because maximum likelihood estimates are less powerful at low sample sizes. The regression doesn’t require linear relationship between dependent and independent variables.
- 17. RANGE, ODDS & LOGIT FUNCTION Here the value of Y-dependent variable ranges from 0 to 1 and it can be represented by following equation
- 18. PLACEMENT DATA Percentage Score Placement (0-Not Selected 1-Selected) 42 0 48 1 54 1 65 1 40 0 52 0 60 1 58 1 40 0
- 19. SCATTER PLOT BEST FIT ?
- 21. PROBABILITY
- 22. WHAT ARE THE ODDS?
- 23. ODDS RATIO
- 24. BRING BERNOULLI
- 28. After consideration of training datasets, we can get the values bo & b1 –co-efficient of regression & assuming the probability value is 0.76 for the placement score of 55, then the outcome can be approximated as 1 i.e selected.
- 29. LINEAR V/S LOGISTIC Linear Regression Logistic Regression Variable Type Continuous Dependent Variable Categorical Dependent Variable Estimation Method Least-Square Estimation Maximum Likelihood Estimation Equation y = ax + b y = b0 + b1x1 + b2x2 +…. Best fit line Straight Line Curve Output Predicted Integer Value Predicted Binary Value ( 0 or 1 )
- 30. THANK YOU