The second entry in each row shows a scatter plot of the original data set upon which a graph of the best-fit model has been superimposed. If we only use this measure of goodness of fit, all four models would be judged to have strong negative relationships. The value of r ranges from -0.957 to -0.997 for the four models for which correlation coefficients have been computed. The closer this value is to 1 or to -1, the better the fit. The correlation coefficient provides one measure of goodness of fit. The left entry in each row in the table above shows TI-83 screens displaying the names of the particular models that have been generated, the equation of each model, and, when calculated by the TI-83, the correlation coefficients for the models. While such characteristics are vitally important in selecting and then justifying the use of a particular model of best fit, we will not take up a discussion of those characteristics here.Įach row of the table shows information about one model. In courses such as MAT 207 you may have studied properties and characteristics of these and other non-linear models. In addition to the two linear models we've discussed in class (least-squares linear regression line and median-median line), the table above provides information for three non-linear models, including an exponential model, a logarithmic model, and a power model. The information in the table below is from a TI-83 calculator using the data set above. We also have generated several non-linear models. Our focus has been on linear models, so we begin by generating a least-squares linear regression model as well as a median-median line of best fit. This ought to motivate us to determine one or more models for the relationship that appears to exist. The scatter plot above reveals a strong negative relationship. Wholesale Price for Used Ford LTD Automobiles We will use the data set below to help focus on each of these criteria.
After a brief review of linear relationships (finding slope and intercepts, determining equations, making real-world interpretations), we went on to consider a variety of ways to generate linear models, or lines of best fit, for two-variable relationships. In our study of two-variable data sets, we have identified important characteristics of relationships between data sets (direction, strength, shape) and we have generated numerical and visual representations of such relationships (centroid, median-median points, scatter plot). Roger Day ( the Goodness of Fit of a Proposed Model MAT 312: Probability and Statistics for Middle School Teachersĭr.
Illinois State University Mathematics Department MAT 312: Judging the Goodness of Fit of a Proposed Model
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