Since mathematical models (regression models) are often used to predict the relationship between paired data elements, it is important to understand how to choose a model that will be a "good fit" for the particular data set. There are several things to keep in mind when attempting to develop a model that will be a "good fit": 
Linear based regression models:
Other regressions:


2. Calculate
a correlation coefficient, r (for some models). The correlation coefficient measures the strength and the direction of a linear relationship between two variables. A value of  r  near one may indicate a "good fit". 

3. Calculate
a coefficient of determination, r^{2 }(R^{2}). The coefficient of determination represents the percent of the data that is the closest to the line of best fit. For example, if r = 0.922, then r ^{2} = 0.850, which means that 85% of the total variation in y can be explained by the linear relationship between x and y (as described by the regression equation). The other 15% of the total variation in y remains unexplained. Do not place too much importance on
small differences between r^{2} values, such as r^{2 }= 0.987 and
r^{2} = 0.984. Also, keep in mind that r,
r^{2} and R^{2} values cannot
be directly compared when calculating certain regression models. 

4. Examine the residuals. Examine the scatter plot of the residuals, which depicts the measure of the signed distances between the actual data values and the outputs predicted by the model. A good linear model has residuals that are near zero and are randomly distributed. 

5. Think about your answer. Is your choice realistic? Don't use a model that will lead to predicted values that are totally unrealistic.



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