Ch3 Project - Minitab Instructions Least-Sguares Regression...

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Unformatted text preview: Minitab Instructions Least-Sguares Regression NOTE: These instructions are for the Macintosh version of the Student Edition of Minitab, v.8. Windows procedures are similar. Launch Minitab. Enter data into a blank worksheet, or load a (data) worksheet from a stored file. To consruct a scatterplot: Choose Graph > Scatter Plot . . . In the Scatterplot window, double click on the variables to go into the vertical axis box and horizontal box, respectively. Ignore the other fields in the window. Make sure that you have the variables you want on the correct axes. This is critical. When it’s right, click OK. To calculate the correlation: Select Stat > Basic Statistics > Correlation. In the window of columns or variable names, double click on the two variables of interest. Click on OK. To determine the equation of the least-squares regression line (LSRLI: Choose Stat > Regression > Regression. Select the Response and Predictors variables. Click the Residuals, Standard. resids., and Fits checkboxes. Click OK. This will have Minitab compute the fitted (predicted) and residual values and save them in the worksheet. You may want to return to the Data window and check that there are three new columns of data. . The Sessions window will fill with lots of information, including: the equation for the LSRL, information about data points with large residuals, influential observations, other deviations that you should notice, and R2. Minitab also prints out an Analysis of Variance (ANOVA) table—ignore this part for now. To graph the scatterplot AND the least-sguares line: Choose Graph > Multiple Scatter Plot... Double click FITSI for the first Vertical Axis, and double click the x-axis variable for the Horizontal Axis. Make sure that you enter the FITS (the predicted values) in the top row. , 0 For the plot of the data points (scatterplot), double click the original response variable for the second Vertical Axis. Double click the original explanatory variable for the second Horizontal Axis. 0 To have Minitab draw a line through the predicted values, click on the Lines button. Then double click FITSI for the first Vertical Axis, and double click the x- axis variable for the Horizontal Axis. Click OK. ' 0 Minitab constructs a line through the fitted values (points designated by A). Data points are represented by E. Special Problem 3A Minitab Instructions .y. .658 __ . 5.76 7.71 Special Problem 3A Exploring Least-Sguares Regression The purpose of this investigation is to analyze three different data sets, compute the correlation coefficients, and in each case plot the scatterplot and the least-squares regression line. You should use Minitab for Macintosh or Windows for this assignment. The table below presents three sets of two-variable data prepared by the statistician Frank Anscombe to illustrate the dangers of calculating without first plotting the data. All three sets have the same correlation and the same least-squares regression line to several decimal places. Data Set A x 10 8 13 9 11 14 6 4 12 7 5 y 8.04 6.95 7.58 8.81 8.83 9.96 7.24 4.26 10.84 4.82 5.68 Data Set B x 10 8 13 9 11 14 6 4 12 7 5 3/ 9.14 8.14 8.74 8.77 9.26 8.10 6.13 3.10 9.13 7.26 4.74 Data Set C x 8 8 8 8 8 8 8 8 8 8 19 8.84 8.47 7.04 5.25 5.56 7.91 6.89 12.50 1. Make a scatterplot for the first data set and calculate the correlatiOn. Study this ----scatterplot;and-think-aboutanapprOpriate-m-odelfor the data: Regardless- of your“ " ’ decision, calculate the regression equation and plot a second graph that shows the scatterplot with the leastesquares regression line superimposed. 2. Repeat step 1 for each 'of the three data sets. Verify that the regression equations and c0rrelations for all three data sets agree to two decimal place accuracy. 3. For each data set, identify any obvious regression outliers and/ or influential observations. 4. In which of the three cases would you be willing to use the fitted regression line to predict y given that x = 14? Explain your answer in each case. 5. Write a report that summarizes your investigation. Refer to the Special Problem Guidelines for information on preparing your report. It is preferable to insert computed results and graphs into your reports at appropriate places. It is acceptable, but less desirable, to include Minitab plots and printouts at the end of your narrative, like appendices. Try to keep graphs and your commentaries about these graphs together on the same page, if possible, so the reader won’t have to flip back and forth when reading your report. 6. Minitab instructions for this Special Problem are provided separately. You may work on this assignment individually, _Qr you may work with one partner (not more than one) in the class. If you work with a partner, then both must contribute equally, and both names must appear on the report cover sheet. Deadline. This Special Problem 3A is due on Chapter 3 Special Problem 3A ...
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Ch3 Project - Minitab Instructions Least-Sguares Regression...

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