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Finding a Regression Equation
Finding the regression equation: First be sure you have entered your data into the calculator (see Entering and Plotting Data Sets). No matter what type of regression equation you want (linear, exponential, quadratic) you will start the same way. Push the black STAT button. Use the arrow keys to move to the CALC heading. In the list of options that follows, select the one you want: #4 will give the linear regression equation #5 will give the quadratic regression equation #0 will give the exponential regression equation. Your screen will now display "LinReg", "QuadReg" or "ExpReg" depending on your selection. If you have put your data into a table with columns called L1 and L2, all you have to do is push ENTER. If you used other names for your columns you must type (name of first column, name of second column) before you push ENTER. The calculator will display the results. Notice that it first gives the general form of the the equation (y=a*x+b or y=a*x^2+b*x+c or y=a*b^x) and then it gives the specific values of a, b, and c that should be plugged in to get your regression equation. Graphing the regression equation: There are two ways to do this: If you don't want to mess with any new stuff: You can simply write down the equation generated by the steps above, then push the Y= button and type the equation. Be sure your WINDOW settings are what you want and push GRAPH. If you want to avoid typing the equation: Push the Y= button. Clear any equations that are already there. Push the black VARS button (just below the arrow keys). Select option #5: Statistics. Use the arrow keys to move to "EQ" (for equations) and select option #1: RegEQ (for regression equation). This will automatically put the regression equation into your "Y1=". Make sure your WINDOW settings are alright and then push GRAPH. Whichever method you choose, notice that if you have a scatterplot of this data already drawn, your regression equation will be graphed on the same axes. This is a nice way to see how close the regression equation is to the actual data points, and whether there are any outliers (points way off the graph) amongst the data points. Determining how good the fit is: You can ask the calculator to find the correlation coefficient for the regression equation. The correlation coefficient is just a number that tells us whether the regression equation fits the data very well, fairly well, or not well at all. If the correlation coefficient is very close to 1 or -1, you have a very good fit. The further from 1 or -1, the worse the fit. To see the correlation coefficient, go into your calculator's catalog by pushing 2nd CATALOG. Note that CATALOG is above the button for the number 0. You will get a list of everything the calculator does! Use the arrow keys to scroll down to "Diagnostic On". When your pointer points to it, push ENTER. Your calculator screen will now say "Diagnostic On". Push ENTER. Your screen will say "Done". Now run your regression again (following the steps above). This after the values of a,b and c you should be given values for r2 and r. The correlation coefficient is the number listed as "r". NOTE: From now on, you will be given the correlation coefficient every time you find a regression equation. If you do not want to see it you need to go back into the catalog, following the above directions, but this time choose "Diagnostic Off".
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