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Regression Analysis

Lecture 9. Regression Analysis. Regression analysis establishes relationship between a dependent variable and independent variables Relationship between “Cause” and “Effect” t Relationship between variables. Usefulness of regression analysis.

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Regression Analysis

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  1. Lecture 9 Regression Analysis

  2. Regression analysis establishes relationship between a dependent variable and independent variables Relationship between “Cause” and “Effect”t Relationship between variables

  3. Usefulness of regression analysis • Regression analysis is a vary widely used tool for research. • It shows type and magnitude of relationship between two variables.

  4. Example of Usefulness of Regression Analysis : • Shows for example whether there is any relationship between an increase in household income (Y) land an increase in consumption (C ). • Whether there is positive or negative relationship between Y and C. Whether if : Y C or reverse • How much of an increase in income (Y) is spent on consumption ( C ).

  5. Example of Usefulness of Regression Analysis • Regression is also used for prediction and forecasting, • Regression analysis allows to measure confidence or significance level of the findings.

  6. Example of Usefulness of Regression Analysis • Increase in traffic jam (hours of non-movement) depends on Increase in number of cars in Dhaka City. (+ dependency) • A decrease in number of School drop-out depends on an increase I income of parents.(-ve dependency) • An increase in household income leads to an increase in household consumption.

  7. Other Logical Examples of Positive and Negative Dependency

  8. Forms of regression models • A regression model relates dependent variable Y to be a function/relation of independent variable X. • Symbolically, Y = f (Xi) • Where i = 1,2,3,4,…

  9. Consumption Expenditure(,000Tk) Diagrammatic Representation of Regression Model Each dot represent sample data for Income and Expenditure for each sample household 100 90 130 Income of the Household (,000 Tk) 0 120

  10. Consumption Expenditure ( C ) C = a + by Regression analysis draw a mean /average line with equation C = a + b Y so that difference between sample data and estimated data is minimized. 0 Income of the Household (Y) Does dotted line minimize deviations?

  11. Deviations between sample value and the mean value Mean value line

  12. Diagrammatic Representation of Regression Equation • In mean or average line, square of the deviation ( C i) for each of the sample from mean ( C )is minimized. Why ? • Because simple sum of difference from mean is always zero.

  13. Example

  14. Formula for Regression coefficient b when sum of square is minimized , b =(Ci – C) (Yi –Y) (Yi – Y) 2i = 1,2, ….n

  15. General Formula • If Y is dependent variable and X is independent variable e.g. Y = f (x) then • Regression coefficient = Sum of (Xi –X) (Yi – Y) Sum of (Xi –X)**2

  16. Example : Given the following data C = f (Y), predict Consumption level for a household with annual income of 500 thousand Taka

  17. Example : Given the following data, predict Consumption level for a household with annual income of 500 thousand Taka. (Fig in,000Tk)

  18. Example (Ci – C) (Yi –Y) = 2000 +500 +0 + 500 + 2000 = 5000 (Yi – Y) 2 = 10000+2500 + 0 + 2500+ 10000 = 25000 Therefore b = (Ci – C) (Yi –Y) / (Yi – Y) 2 = 0.2

  19. Calculated Regression Equation Example C = a + b Y Or C = a + 0.2 Y or C = a + 0.2 Y Or a = C -0.2 Y Or a = 100-0.2 x 200 = 100 – 40 = 60 Therefore C = 60 + 0.2 Y

  20. Calculated Regression Equation Example C = 60 +0.2 Y What kind of relationship between Y and C ? How much consumption increases for Tk 1000 increase in income ?

  21. C = 60 +0.2 Y What is consumption, when income is zero? What is predicted consumption, when income is Tk 500,000?

  22. Correlation : A measure of simple relationship • Correlation shows only associanship or relationship between two variables. • Whereas Regression analysis shows dependency relationship • Correlation between two variables ( for example Income and Expenditure) is measured by a formula shown as ;

  23. Formula of Correlation coefficientr is (Ci – C) (Yi –Y) (Yi – Y) 2 (Ci – C)2

  24. Formula of Correlation coefficientrin terms of regression coefficient r (Yi – Y)**2 r = b (Ci – C )**2

  25. The End

  26. Class Assignment Given the following data, calculate correlation coefficient between Income and Expenditure. Also predict how much Consumption will increase for a 1000 Tk increase in household income?

  27. The End

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