Aravali college of engineering and management

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1. Department of Computer Science & Engineering (July – Dec 2020) 9/15/2020 1
8. Introduction to Regression Analysis Slide-8  Regression analysis is used to:  Predict the value of a dependent variable based on the value of at least one independent variable  Explain the impact of changes in an independent variable on the dependent variable Dependent variable: the variable we wish to predict or explain Independent variable: the variable used to explain the dependent variable
9. Simple Linear Regression Model Slide-9  Only one independent variable, X  Relationship between X and Y is described by a linear function  Changes in Y are assumed to be caused by changes in X
10. Types of Relationships Slide-10 Y Y X Y Y X Linear relationships Curvilinear relationships X X
11. Types of Relationships Slide-11 Y Y X Y Y X Strong relationships Weak relationships (continued) X X
12. Types of Relationships Slide-12 Y X Y X No relationship (continued)
13. Y i  β 0  β 1 X i Linear component Simple Linear Regression Model Slide-13 Population Y intercept Population Slope Coefficient Random Error term Dependent Variable Independent Variable  ε i Random Error component
14. Random Error i for this X value X Y Observed Value of Y for Xi Predicted Value of Y for Xi Y i  β 0  β 1 X i  ε i X i Slope = β 1 Simple Linear Regression Model (continued) Slide-14 Intercept = β 0 ε i
15. Yˆ i  b 0  b 1 X i The simple linear regression equation provides an estimate of the population regression line Simple Linear Regression Equation (Prediction Line) Slide-15 Estimate of the regression intercept Estimate of the regression slope Estimated (or predicted) Y value for observation i Value of X for observation i The individual random error terms ei have a mean of zero
16. Sample Data for House Price Model Slide-16 House Price in $1000s (Y) Square Feet (X) 245 1400 312 1600 279 1700 308 1875 199 1100 219 1550 405 2350 324 2450 319 1425 255 1700
17. Regression Using Excel Slide-17  Tools / Data Analysis / Regression
18. Assumptions of Regression Department of Statistics, ITS Surabaya Slide-18 Use the acronym LINE:  Linearity  The underlying relationship between X and Y is linear  Independence of Errors  Error values are statistically independent  Normality of Error  Error values (ε) are normally distributed for any given value of X  Equal Variance (Homoscedasticity)  The probability distribution of the errors has constant variance
19. Pitfalls of Regression Analysis Department of Statistics, ITS Surabaya Slide-19  Lacking an awareness of the assumptions underlying least-squares regression  Not knowing how to evaluate the assumptions  Not knowing the alternatives to least-squares regression if a particular assumption is violated  Using a regression model without knowledge of the subject matter  Extrapolating outside the relevant range
20. 9/15/2020 20 Aravali College of Engineering And Management Jasana, Tigoan Road, Neharpar, Faridabad, Delhi NCR Toll Free Number : 91- 8527538785 Website : www.acem.edu.in