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Data Analysis Regression Analysis

Data Analysis Regression Analysis. Regression. Regression. Dependent variable (y). Independent variable (x). The attempt to explain the variation in a dependent variable using the variation in independent variables. Regression is thus an explanation of causation.

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Data Analysis Regression Analysis

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  1. Data AnalysisRegression Analysis

  2. Regression Regression Dependent variable (y) Independent variable (x) The attempt to explain the variation in a dependent variable using the variation in independent variables. Regression is thus an explanation of causation. If the independent variable(s) sufficiently explain the variation in the dependent variable, the model can be used for prediction. University Of Malakand | Department of Computer Science | UoMIPS| Dr. Engr. Sami ur Rahman | 2

  3. Simple Linear Regression y’ = b0 + b1X ± є є Dependent variable (y) b1= slope = ∆y/ ∆x b0(y intercept) Independent 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. University Of Malakand | Department of Computer Science | UoMIPS| Dr. Engr. Sami ur Rahman | 3

  4. Simple Linear Regression Observation: y ^ Prediction: y Dependent variable 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 University Of Malakand | Department of Computer Science | UoMIPS| Dr. Engr. Sami ur Rahman | 4

  5. Simple Linear Regression For each observation, the variation can be described as: y = y + ε Actual = Explained + Error ^ University Of Malakand | Department of Computer Science | UoMIPS| Dr. Engr. Sami ur Rahman | 5

  6. Sum of Squares of Error (SSE) Dependent variable Independent variable (x) A least squares regression selects the line with the lowest total sum of squared prediction errors. This value is called the Sum of Squares of Error, or SSE. University Of Malakand | Department of Computer Science | UoMIPS| Dr. Engr. Sami ur Rahman | 6

  7. Sum of Squares Regression (SSR) Population mean: y Dependent variable Independent variable (x) The Sum of Squares Regression (SSR) is the sum of the squared differences between the prediction for each observation and the population mean. University Of Malakand | Department of Computer Science | UoMIPS| Dr. Engr. Sami ur Rahman | 7

  8. Regression Formulas Total Sum of Squares (SST) The Total Sum of Squares (SST) is equal to SSR + SSE. University Of Malakand | Department of Computer Science | UoMIPS| Dr. Engr. Sami ur Rahman | 8

  9. The proportion of total variation (SST) that is explained by the regression (SSR) is known as the Coefficient of Determination, and is often referred to as R . R = = The value of R can range between 0 and 1, and the higher its value the more accurate the regression model is. It is often referred to as a percentage. 2 SSR SSR SST SSR + SSE 2 The Coefficient of Determination University Of Malakand | Department of Computer Science | UoMIPS| Dr. Engr. Sami ur Rahman | 9

  10. Click Click Regression Analysis in SPSS Example: Employee data Fields: Education level and salary University Of Malakand | Department of Computer Science | UoMIPS| Dr. Engr. Sami ur Rahman | 10

  11. University Of Malakand | Department of Computer Science | UoMIPS| Dr. Engr. Sami ur Rahman | 11 Thanks for your attention

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