Line than some other point, then the scatter diagram has at least one If one point of a scatter diagram is farther from the regression Is usually at least one outlier and usually only one outlier on a scatterĭiagram. All values of the correlation coefficient areīelow provides a way to categorize the values of correlation coefficients. If the correlation coefficient is positive,Ĭorrelation coefficient is negative, the line slopes downward. Tells how closely the scatter diagram points are to being on a line. Variation is determined by the regression line, and 53% of the variation is Variation is determined by the regression line, and 18% of the variation isĭetermined by some other factor or factors. Than 100%, then the difference between 100% and the coefficient ofĭetermination tells what percent of the variation is determined by something Tells what percent of the variation in data values is explained by the One thing to try if this happens is switching x and y values. The data, that means you made a mistake in computing the regression line. Then if the regression line is nowhere near Switched somewhere in the process of finding the regression line. When this happens, it means the x and y variables have been Plugging these into the equation gives:īeen extended to show the line, but since the line is nowhere near the data, In the above example, 99 is the minimum x-value and 105 is the Use, but you could use any numbers that are close to these x-values. The minimum and maximum x-values are good to Since you have theĮquation of the regression line, all you need are some x-values to To plot the regression line on the scatterĭiagram, you need to find two points on the regression line. See Coefficients of Determination and Correlationīelow to find out how to interpret the coefficients of determination and That about 88.1% of the variation in the data is determined by the regressionĠ.939, indicates a strong positive correlation. The coefficient of determination, 0.881, says The equation of the regression line is y = 3.166 x-55.797. If your data is in L4 and L5, for example, you would press " 2ND", " 4", " ," (comma), " 2ND", " 5" and then " ENTER" to compute the regression line for In some other lists besides L1 and L2, you could choose those lists by pressing " ENTER" just one time after selecting " LinReg(ax+b)", typing in the correct lists,Īnd pressing" ENTER" again. This demonstration, we will use the data from Table 1 again: Need to be working with two variables with each value of the first variable Is reset to the manufacturer’s default settings, or (2) you start using aįind regression lines and coefficients of determination and correlation, you You should only need to do this procedure again if (1) your calculator On your calculator screen, you should see: Make sure you choose " DiagnosticOn" and NOT " DiagnosticOff". Use the down-arrow key to put the triangleĬursor next to " DiagnosticOn". The procedures in the calculator in alphabetical order. The TI 83/84 Calculator to Find Equations of Regression Lines and CoefficientsĬoefficients of determination and correlation, you must first make a change in Similar to those shown in the figure below. Once you make that decision, your axes should be fairly You would pick the first row or column as your x-values and the second row or column as your y-values. Once the axes are set up, you just act like each pair of x- and y-values is an ordered pair, and you plot these ordered pairs onĬonsider Table 1 on page 178 of Sullivan, which is reproduced below. Number line on your horizontal axis so that the values extend from the minimum x-value to the maximum x-value but not much farther.Īnd set up a uniform number line on the vertical axis so that the values extendįrom the minimum y-value to the maximum y-value Outliers and Influential Observations inĭiagram is a fairly straightforward process. Coefficients of Determination and CorrelationĮ. Equations of Regression Lines and Coefficients of Determination andĭ.
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