634179361 - Regression model Investigation of possible...

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Regression model: Investigation of possible relationship between 2 variables: Examples: Is there any relationship between smoking Cigarette and Cancer? Is there any relationship between Environmental factors and Cancer Is there any relationship between Genetic factors and Cancer Is there any relationship between X and Y Is there any relationship between Adverting Expenditure and Sales Is there any relationship between Price and Sales Is there any relationship between Quality and Sales Is there any relationship between Location and Sales Is there any relationship between X and Y Investigation of possible relationship between 2 variables: 1- Tabular Methods 2- Graphical Methods 3- Numerical Methods 1- Tabular Methods The use of the Cross Tabs allows us to make a comment on the possible relationship between X and Y. 2- Graphical Methods The use of the scatter Plot allows us to make a comment on the possible relationship between X and Y: X and Y appear to be: a- Not related b- Related in a non-linear fashion (Polynomial, Exponential, Log etc.) c- Related in a linear fashion : I- Is it a direct linear relationship? II- Is it an indirect linear relationship? 3- Numerical Methods Regression and correlation analysis will be used to make a comment on the possible relationship between X and Y. The main idea is to: a- Calculate and interpret the intercept (b 0 ) and the slope (b 1 ). b- Calculation and interpret the Coefficient of Determination (r 2 ). c- Calculate and interpret the Correlation Coefficient (r). d- Test the significance of relationship (from sample to Population). e- Conduct forecasting. 1
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Steps in Regression Analysis: 1- Step 1 - Model Building – Purpose is to establish a Cause and effect relationship between the Dependent (Y) and The Independent variables ( X1, X2,, ….. ) Y = f ( X 1 , X 2 , X 3 , X 4 ,……. ) Multivariate Model 2- Step 2 - Specification Step - Purpose is to simplify the model as a “Simple” “Linear” model. Number of Independent variables : 1- Simple model ( only ONE independent variable) Y = f ( X ) Simple Model 2- Multivariate model ( More than ONE independent variable) Y = f ( X 1 , X 2 , X 3 , X 4 ,……. ) Type of Functional relationship : I- Linear relationship Y = b 0 + b 1 X Intercept (b 0 ): At X = 0, the Y is EXPECTED (or estimated) to be b 0 Slope ( b 1 ): For every additional unit increase in X , Y is estimated to increase (decrease if negative) by b 1 II- Non-linear relationship i.e. Exponential, Cubic, Log etc Y = b 0 + b 1 X 2 Y = b 0 + b 1 X 1/3 * X 1/2 3- Step 3 - Data collection step 2
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I- Time series Data (Historical Data)- Collecting data across different Time Periods.
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