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<ul><li> 1. Presented by, Saravanan L (13UTA30) Karthikeya B (13UTA17) Ashwin sankar (13UTA06) Bharath VS (13UTA08) Sathiyaseelun A RM (13UTA45)</li></ul>
<p> 2. Objectives: 1.Meaning 2.Definition 3.Simple linear regression 4. Nature of regression lines 5. Equation 6. Properties 7. Where it used? 3. Study of finding a functional relationship between the variables. Simple regression study of functional relationship between two variables. Multiple regression Study of functional relationship between more then two numbers. 4. Simple LinearMultiple Regression NonLinearSimple Multiple 5. Simple Regression: A regression model is a mathematical equation that describes the relationship between two or more variables. A simple regression model includes two variables; one is Independent and one Dependent. The dependent variable is the one being explained, and independent variable is the one used to explain the variation in the dependent variable. 6. Linear regression: A (simple) regression model that gives straight-line relationship between two variables called linear regression model Non Linear regression A (Simple) regression model that gives curve-line relationship between two variables called non-linear regression model. a aa a 7. Simple Linear RegressionDependent variable (y)SIMPLE LINEAR REGRESSIONy = b0 + b1X b0 (y intercept)B1 = slope = y/ xIndependent variable (x)The output of a regression is a function that predicts the dependent variable based upon values of the independent variables. Simple regression fits a straight line to the data. 8. Simple Linear RegressionSIMPLE LINEAR REGRESSIONDependent variableObservation: y Prediction: ^ yZero Independent variable (x)The function will make a prediction for each observed data point. The observation is denoted by y and the prediction is denoted by y.^ 9. NATURE OF REGRESSION LINES 1.Perfect Correlation (r=+1 or r=-1)2.No Correlation ( r=0 ) 10. 3.Strong & Weak Correlation4.Point of intersection & nature of slope 11. Equation for Y on X : Y = a+b.X ,a,b are constantsbyx = Regression co-efficient of Y on Xbyx = r.Y/X 12. Equation of X on Y X = a0 + b0.Y ,a0 & b0 are constantsbxy = Regression Co-efficient of X on Ybxy = r.x/y 13. The correlation co-efficient is the geometric mean of the regression co-efficient. r = byx.bxy . Both the regression co-efficient are either positive or negative. Correlation coefficient has the same sign as that of regression co-efficient If one regression co-efficient is greater then 1, the other must be less then 1. Shift of origin does not affect the regression co-efficients, but shift in scale affects. Arithmetic mean of regression co-efficients is greater than or equal to correlation coefficient. 14. Regression analysis allows you to model, examine, and explore spatial relationships, and can help explain the factors behind observed spatial patterns. Regression analysis is also used for prediction. Eg. to predict rainfall where there are no rain gauges It provides a global model of the variable or process you are trying to understand or predict.</p>