Regression & correlation

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  • 1. Working with Multiple Variables Response of One variable to Change in The Other Move together 1. Same Direction 2. Different Direction Don’t Move Together How much change in one variable in response to a unit change in the other. Correlation or Association Regression
  • 2. Studying Multi Variables Two Ways Deterministic Way Probabilistic Way Relation or Effect is Exact Relation or Effect is Non- exact (Error Term) Book Value BV = P– AD = P - nD BV = Book Value P = Price AD = Accumulated Depreciation D = Depreciation n = years Marks Obtained M = C + mH M = Marks Obtained in Exam H = Time Given to Study (Hrs) m = increase in marks in response to increase study by 1 hr
  • 3. RegressionWhatisit? Modeling of the functional relationship between a response variable and a set of explanatory variables The regression model tells what happens to the response variable for specified changes in the explanatory variables. Example What will be the cash flows based on specified values of interest rates, raw material costs, salary increases, and …. A regression line, also called a line of best fit, is the line for which the sum of the squares of the residuals is a minimum.
  • 4. Y = b 0+𝑏 1X + e Intercept or Constant Slope Deterministic Component Explained by Model Error Component Not Explained by Model
  • 5. Assumption 1 The mean of each error component is zero Assumption 2 Each error component follows an approximate normal distribution Assumption 3 Homoscedasticity Variance of error component is the same for each value of X Assumption 4 The errors are independent of each other Assumptions
  • 6. Regression Analysis S1: Scatter Diagram S2: Check the Assumptions S3: Draw the Line S4: Inference of Coefficient
  • 7. Y X x y 65 175 67 133 71 185 71 163 66 126 75 198 67 153 70 163 71 159 69 151 69 155 65 70 75 80 120 130 140 150 160 170 180 190 200 Scatter Diagram
  • 8. How the Assumptions Appear Zero Mean of Errors Normally Distributed Errors Independent Errors Constant Variance of Errors
  • 9. Not Linear Linear  x residuals x Y x Y x residuals Residual Analysis for Linearity
  • 10. Non-constant variance  Constant variance x x Y x x Y residuals residuals Residual Analysis for Homoscedasticity
  • 11. Not Independent Independent X X residuals residuals X residuals  Residual Analysis for Independence
  • 12. How to Check Regression Assumptions
  • 13. Estimating the Coefficient of Regression Line What we Finally Want How We Get it Get all Summations Get these Quantities
  • 14. A correlation is a relationship between two variables.Correlation
  • 15. Correlation & Data Type Scale Ordinal Nominal Pearson Correlation Spearman Correlation Phi Coefficient Cramer’s Coefficient Contingency Coefficient
  • 16. Pearson Correlation Data Both the variables be scale (Interval or Ratio)
  • 17. Sums Which are Required X2 Y2 XYX Y Total
  • 18. Values of Correlation & Interpretation Range -1 0 +1.5-.5 Perfectly Positive or Negative Relations No Linear Relation Strong Positive or Negative Correlation Weak Positive or Negative Correlation
  • 19. Value Relation 0.00 None 0.01 to 0.09 Negligible 0.10 to0.29 Weak 0.30 to 0.59 Moderate 0.60 to 0.74 Strong 0.75 to 0.99 Very Strong 1 Perfect Values of Correlation & Interpretation