regression

# regression - 1 Regression Analysis Some Points to Remember...

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Regression Analysis: Some Points to Remember In applying regression as a forecasting tool, one must be cautious on several grounds: 1. There may be a double jeopardy involved if the values of the independent variable must be forecasted in order to perform a regression analysis. For example if it is determined that gross domestic products has a strong relationship with consumer confidence index, then given values of both variables over several years, GDP can be used as independent variable (X) to forecast CCI, dependent variable (Y). So, if we have values for both variables starting with 1990 through 2001, our regression model could predict CCI for the year 2002. However, to do so, we would need the 2002 GDP! So, this regression forecasting of CCI requires us to first forecast and predict a value for 2002 GDP so we can use that value in forecasting CCI. 2. For a set of X and Y values, the regression model (regression equation) calculated is valid for that particular range of value of X to make a prediction for Y. For example, if the range of values of X that is used to develop the model is from 300 to 500, then in using the model to make our predictions, it would not be wise to step too much outside of that range when predicting Y. Please study the graph and inserts on page 2 of this document for further detail. 3. Regression, correlation, and forecasting go hand in hand. In applying regression analysis, one must always be aware of the correlation coefficient and the coefficient of determination for the analysis. Please see page 3 of this document for details. 4. In using multiple regression analysis, theoretically speaking, for each independent variable, one must have approximately 30 data values. This rule, of course, is often violated in practice. 5. Also read section on Lagged Regression at the end of this document. 1

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Regression Analysis: Ranging Estimated Y values Y X Xp 2 1. This linear black line is the regression line that forecasts Y for any given value of X. For example, at X=Xp, go up to the regression line and trace your way to Y-axis. The value read on the Y-axis is the estimated value of Y when the independent variable equals Xp. 3. The two non-linear blue lines represent confidence intervals placed on the regression estimates made by the regression equation. You can see that they create a band, which is narrow in the middle and wide at the ends. The middle part sectioned off by the vertical red dashed lines represents the range of X values that were used in calculating the regression equation. 2. These pink normal curves represent the distribution of values for the estimated Y. Actually, there is an infinite number of normal curves that could be placed on the regression line. Here, I have shown only three! Take the middle curve.
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regression - 1 Regression Analysis Some Points to Remember...

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