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SOFTWARE TECHNIQUES CUSTOMCAMA SOLUTIONS

What is Regression. Determination of a mathematical equation that describes the nature of the relationship between one or more predictor variables.Y = A B CY = A Bx Cy Dz. What is a Predictor Variable?. Things you knowThings you can measureThings you can quantifyThings you can qualif

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SOFTWARE TECHNIQUES CUSTOMCAMA SOLUTIONS

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    1. SOFTWARE TECHNIQUES CUSTOMCAMA SOLUTIONS Regression Basics Larry Zirbel – Software Techniques, inc. Tim Wilmath – Hillsborough County, FL www.customcama.com

    2. What is Regression Determination of a mathematical equation that describes the nature of the relationship between one or more predictor variables. Y = A + B + C Y = A + Bx + Cy + Dz

    3. What is a Predictor Variable? Things you know Things you can measure Things you can quantify Things you can qualify A data element that Influences value (helps predict value)

    4. Predictor Variables If you know square footage of a building, can you predict? Maximum occupancy Number of bathrooms it will have Market Value What else would you need to know to predict these things?

    5. Selecting Predictor Variables What do you think effects value? What do you know effects value? Test your thinking Scatter plots Simple regression Correlation

    6. The Regression Model A model is a collection of variables along with the equation that defines the relationship between those values. The art is in the variables What influences value What is the nature of the relationship Transform the variables Get a better relationship The Math determines the relationships and gives you the equation

    7. Running Regression Perform the mathematical steps to determine the equation. The variables in the equation are the values for the predictor variables. Like all equations, you put in values for the variables and it will give a result.

    8. Basic Assumptions There is a relationship between the variables and the results There is a relationship between the independent variable (result) and the dependent variables. Sales price is the result, neighborhood is a variable. You possess the values of variables and the results for at least some cases (sample data) You have the sales price (market value) and the values of variables such as square footage, age, neighborhood. The resulting equation will predict a result based on the set of variables.

    9. Coefficients in the equation The equation is a set of coefficients that you multiply by the value of the variables. The coefficient of the variable “Square Feet” is the price per square foot or the base rate in a cost approach

    10. The many types of Regression Simple Linear Regression (SLR) Multivariate Linear Regression (MLR) Multiple Regression Analysis (MRA) Multivariate Regression Analysis (MRA) Curvilinear Regression Analysis (CRA)

    11. The Goal is the SAME Find the BEST equation that most accurately predicts the value. Knowing your industry is better than knowing math. How do we know it is the best? The math gives specific indicators Check the difference between actual and predicted values Garbage in – Garbage out

    12. How good are the relationships? R-Squared Multiple correlation coefficient squared (MSR) Provides a measurement to show how much of the relationship between variables is explained. Desire a high value such as .98 Will always be between 0 and 1 S-Squared The mean square of errors (MSE) Desire a low value

    13. How good are the relationships? Variance-Covariance Matrix Used to create the Correlation Matrix Correlation Matrix Shows the relationship between each variable Confidence Intervals Shows the range of expected values for a variable based on the sample data

    14. Linear

    15. The Math Behind the Scenes The math is really quite simple Matrix or Linear Algebra Gauss – Jordan Elimination The matrix times its transformation inverted, times its transformation times the results = the coefficients. The math is tedious Matrix algebra involves lots of simple transformations Best done with a computer Can be done by hand for small sample sets

    16. Stepwise Regression Forward Stepwise Start with no variables Add Variable if it yields a better equation Backward Stepwise Start with all variables Remove Variable if it yields a better equation Can be done manually or automatically

    17. Linear or Non-Linear Do variables relate in a linear fashion? Can non-linear variables be transformed into a linear relationship?

    18. Additive or Multiplicative or Hybrid The math is just math in all cases Fancier math does not give better results Its all about the relationship to variables Variables contribute to value independently Variables have strong relationships with each other and with the result.

    19. Form of the Equations

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