Regression Analysis with Residuals

Transcription

1 Create a scatterplot Use stat edit and the first 2 lists to enter your data. If L 1 or any other list is missing then use stat set up editor to recreate them. After the data is entered, remember to turn on the stat plot with appropriate list locations and use zoom stat for a good window. Make sure any equations in your y list are turned off.

2 Choosing a regression model from the scatterplot must include justification. MODEL TYPE Linear JUSTIFICATION Points are clustered and monotonic but do not appear to show concavity. Polynomial: Quadratic, Cubic, Quartic Sinusoidal Exponential Log Power Logistic Points are NOT monotonic and appear to have a finite number of turning points. (1, 2, or 3) Points are NOT monotonic and appear to have an infinite number of turning points with an oscillating pattern. Points are monotonic and appear to show concavity with a horizontal asymptote. Points are monotonic and appear to show concavity with a vertical asymptote. Power functions have many different shapes. They may have BOTH horizontal and vertical asymptotes or NO asymptotes. Choose power when it is monotonic, shows concavity and seems to have 2 asymptotes seems to have NO asymptotes Points are monotonic and appear to show a point of inflection with 2 different horizontal asymptotes.

3 Based on the scatterplot you should be able to choose a regression model. Be sure to store it in an empty y register and record both the correlation coefficient, r, and the coefficient of determination, R 2. If you do NOT generate the coefficients, then you must use the catalog to choose diagnostic on so they will be displayed with the regression.

4 Creating a residual plot Once you have completed your regression calculation, recorded the correlation coefficient and coefficient of determination, and checked graphically to see the fit, then we will consider residuals. The residuals are automatically stored in your calculator as soon as you generate a regression equation. Go to stat edit and place your cursor on the name of the list you wish to use to store the residuals and choose list (not stat) then scroll down to RESID hit enter and enter again to see the values stored in the list. Now turn off the regression model in your y list and turn off the original plot. Turn on a new plot in which the y list corresponds to the location of your residuals. Don't forget to use zoom stat again for a good window.

5 Analyzing the residual If the residual plot shows no pattern which can be modeled with one of our regression equations then we conclude the errors are just random fluctuations and we cannot improve our model If the residual plot shows a pattern which can be modeled with one of our regression equations then we conclude we will improve our model by summing it with a new regression which is created using the original list of x values and the residual list for the y values. Once we improve our regression model by summing the 2 models in the 2 different y registers, then we must create a new set of residuals but it is NOT stored in the calculator. To create the new residuals use stat edit and place the cursor at the top on the name of the list where you will store the new residuals. Then enter L 2 (which is the original y values) y 3 (L 1 ) (choose the subscript for y to be wherever you put the sum of the regression models and L 1 represents the original x values.) You must hit enter to see the values placed in the list. Now change the stat plot to make this new list of residuals your y list, turn off all y registers and any other stat plots and use zoom stat again to get a good window for this new residual plot.

6 Final regression model should be plotted with the original data probably stat plot 1 and hopefully it yields a good fit. All other y registers and stat plots should be off. We then use this regression model to interpolate or extrapolate our predictions for either the dependent or independent variables. Remember: if we know the independent variable then we simply evaluate our regression model at that value to make our prediction (Do this on the graph, in a table, or on the home screen in function notation) if we know the dependent value then we should enter that value in an empty y register and graph it with our regression model to calculate the intersection.

7 Sample scatterplots and residuals Choose and justify a model